y is a numeric vector representing an evenly spaced regular time series. Missing values such as NA and NaN are allowed.

• If y is irregular or unordered in time (e.g., daily data spanning multiple years with leap years: 365 points in some years, 366 in others), use beast.irreg instead.

• If y is a matrix or 3D array consisting of multiple regular or irregular time series (e.g., stacked images), use beast123 instead.

• If y is an object of class "ts", "xts", or "zoo", its time attributes (i.e., start, end, frequency) are used to infer start, deltat, period, and season. User-specified values for these arguments are then ignored to honor the time attributes of y. For example, if y is a ts object with frequency = 1, season = "none" is always assumed; if frequency > 1 (i.e., some periodic component is present in y) but season = "none" is supplied, it is silently replaced by season="harmonic".

If y is provided as a list of multiple time series, the multivariate version of the BEAST algorithm is invoked to decompose multiple series and detect common changepoints jointly. This feature is experimental and under active development. See ohio for a working example.

start is numeric (default 1.0) or Date; the time of the first data point of y. It can be specified as:

• a scalar (e.g., 2021.0644);

• a numeric vector c(year, month, day) (e.g., c(2021, 1, 24));

• an R Date object (e.g., as.Date("2021-01-24")).

deltat is numeric (default 1.0) or character string; the time interval between consecutive data points. Its unit must be consistent with start.

• If start is numeric, the unit is arbitrary and is not interpreted by BEAST (e.g., 2021.3 can be be of any unit, a time, a distance, etc.).

• If start is a c(year, month, day) vector or a Date, deltat is interpreted in units of years. For example, for a monthly series with start = c(2021, 1, 24), start is internally converted to a fractional year 2021 + (24 - 0.5)/365 = 2021.0644 and deltat = 1/12 can be used to specify a 1-month interval (1/12 yr).

• Alternatively, deltat can be a character string encoding both the value and the unit, such as "7 days", "7d", "1/2 months", "1 mn", "1 year", or "1y".

Character (default "harmonic"). Specifies whether y has a periodic component and how it is modeled:

• "none": y is treated as trend-only; no periodic components are modeled. Seasonal parameters (e.g., sorder.minmax, scp.minmax, sseg.min) are ignored.

• "harmonic": y has a periodic/seasonal component. The term season is used broadly for any periodic variation in y. The period of the seasonal component is not a BEAST model parameter; it is treated as known and must be supplied via period. For "harmonic", the seasonal component is modeled as a harmonic curve (a combination of sines and cosines).

• "dummy": As for "harmonic", except that the periodic/seasonal component is modeled as a non-parametric curve. The harmonic order argument sorder.minmax is then irrelevant and ignored.

• "svd" (experimental): As for "harmonic", but with the seasonal component expressed as a linear combination of basis functions derived from a singular value decomposition (SVD). These basis functions can be more parsimonious than pure harmonic bases and may improve detection of subtle seasonal changepoints.

Numeric or character string. The period of the seasonal/periodic component in y. It is needed only when a periodic component is present (e.g., season = "harmonic", "svd", or "dummy") and is ignored for trend-only data (season = "none"). The period must be in the same time unit as deltat, and it should satisfy period = deltat * freq, where freq is the number of data points per period.

• In earlier versions, a separate freq argument was used; it is now obsolete and replaced by period. For backward compatibility, freq is still accepted via ..., but period takes precedence if both are provided.

• If period is missing, BEAST attempts to guess a plausible period via autocorrelation. This guess can be unreliable, so users are strongly encouraged to specify period explicitly whenever a periodic component is present.

• If period <= 0, season = "none" is assumed and a trend-only model is fitted.

• When start or deltat is specified using dates, period may also be provided as a string, such as "1 year", "12 months", "365d", or "366 days".

A numeric vector of length 2 (integers >= 0); the minimum and maximum numbers of seasonal changepoints (scp) allowed in segmenting the seasonal component. Used only when y has a seasonal component (i.e., season = "harmonic", "svd", or "dummy") and ignored for trend-only data. scp.minmax[2] couldn't be smaller than scp.minmax[1].

• If scp.minmax[1] == scp.minmax[2], BEAST assumes a fixed number of seasonal changepoints and does not infer the posterior distribution over the number of changepoints, though it still estimates the probabilities and locations of most likely changepoints over time.

• If scp.minmax[1] == scp.minmax[2] == 0, both the min and max numbers of scp are set to 0. That is, no seasonal changepoints are allowed; a single global seasonal model is used, but the harmonic order may still be inferred if sorder.minmax[1] != sorder.minmax[2].

A numeric vector of length 2 (integers >= 1); the minimum and maximum harmonic orders considered for the seasonal component. Used only when season = "harmonic" or "svd" and ignored for trend-only data or when season = "dummy".

• If sorder.minmax[1] == sorder.minmax[2], BEAST assumes a fixed harmonic order and does not infer the posterior distribution over harmonic orders.

A numeric vector of length 2 (integers >= 0); the minimum and maximum numbers of trend changepoints (tcp) allowed in segmenting the trend component.

• If tcp.minmax[1] == tcp.minmax[2], BEAST assumes a fixed number of trend changepoints and does not infer the posterior distribution over the number of changepoints, though it still estimates changepoint probabilities and locations.

• If tcp.minmax[1] == tcp.minmax[2] == 0, both the min and max numbers are set to 0. That is, no trend changepoints are allowed, and a single global polynomial trend is fitted. The polynomial order may still be inferred if torder.minmax[1] != torder.minmax[2].

A numeric vector of length 2 (integers >= 0); the minimum and maximum polynomial orders considered for the trend component. If missing, tcp.minmax defaults to c(0,1). Order 0 corresponds to a constant (flat) trend; order 1 corresponds to a linear trend.

• If torder.minmax[1] == torder.minmax[2], BEAST assumes a fixed polynomial order and does not infer the posterior distribution over polynomial orders.

An integer (> 0); the minimum segment length, in number of time steps, allowed between neighboring seasonal changepoints. When fitting a piecewise seasonal model, two seasonal changepoints cannot be closer than sseg.min time intervals. sseg.min is unitless (counts of time steps); the corresponding time window in the underlying units is sseg.min * deltat. If NULL, a default is chosen internally (typically based on the the period).

Integer (>= 0); the number of leftmost observations excluded from seasonal changepoint detection. No seasonal changepoints are allowed in the initial window of length sseg.leftmargin. This is specified in time steps; the corresponding time window is sseg.leftmargin * deltat. If NULL, it defaults to sseg.min.

Integer (>= 0); the number of rightmost observations excluded from seasonal changepoint detection. No seasonal changepoints are allowed in the final window of length sseg.rightmargin. This is specified in time steps; the corresponding time window is sseg.rightmargin * deltat. If NULL, it defaults to sseg.min.

Integer (> 0); the minimum segment length, in number of time steps, allowed between neighboring trend changepoints. When fitting a piecewise polynomial trend, two trend changepoints cannot be closer than tseg.min time intervals. tseg.min is unitless (counts of time steps); the corresponding time window is tseg.min * deltat. If NULL, a default is chosen internally (often in reference to the presence or absence of a cyclic component).

Integer (>= 0); the number of leftmost observations excluded from trend changepoint detection. No trend changepoints are allowed in the initial window of length tseg.leftmargin. This is specified in time steps; the corresponding time window is tseg.leftmargin * deltat. If NULL, it defaults to tseg.min.

Integer (>= 0); the number of rightmost observations excluded from trend changepoint detection. No trend changepoints are allowed in the final window of length tseg.rightmargin. This is specified in time steps; the corresponding time window is tseg.rightmargin * deltat. If NULL, it defaults to tseg.min.

Numeric (default 0.0); a hyperprior parameter–newly added in Version 1.02–controlling the complexity of the seasonal curve (i.e., the number of seasonal changepoints). A prior of the form p(k) \propto \exp[\lambda (k+1)] is placed on the number of seasonal changepoints k, where \lambda is seasonComplexityFactor. Setting \lambda = 0 yields a non-informative prior p(k) \propto 1.0 where all model dimensions are equally likely a priori. Users may tune seasonComplexityFactor in the range [-20, 20] or an even wider range: negative values (e.g., \lambda = -15.9) favor fewer changepoints (simpler seasonal curves), whereas positive values (e.g., \lambda = 5.76) favor more changepoints (more complex curves).

Numeric (default 0.0); analogous to s.complexfct, but for the trend component and the number of trend changepoints.

Character (default "bayes"). Specifies how model posterior probabilities are formulated or approximated:

• "bayes": Full Bayesian formulation as described in Zhao et al. (2019).

• "bic": Approximate posterior probabilities using the Bayesian Information Criterion (BIC), \mathrm{BIC} = n \log(\mathrm{SSE}) + k \log(n), where k is the number of parameters and n the number of observations.

• "aic": Approximate posterior probabilities using Akaike's Information Criterion (AIC), \mathrm{AIC} = n \log(\mathrm{SSE}) + 2k.

• "aicc": Approximate posterior probabilities using the corrected AIC (AICc), \mathrm{AICc} = \mathrm{AIC} + \frac{2k^2 + 2k}{n - k - 1}.

• "hic": Approximate posterior probabilities using the Hannan-Quinn Information Criterion (HIC), \mathrm{HIC} = n \log(\mathrm{SSE}) + 2k \log(\log(n)).

• "bic0.25": BIC-type approximation adopted from Kim et al. (2016) doi:10.1016/j.jspi.2015.09.008 with reduced complexity penalty, \mathrm{BIC}_{0.25} = n \log(\mathrm{SSE}) + 0.25 k \log(n).

• "bic0.5": As above but with penalty factor 0.5.

• "bic1.5": As above but with penalty factor 1.5.

• "bic2": As above but with penalty factor 2.0.

Logical; if TRUE, a global trend is first fitted and removed from the series before running BEAST, and then added back to the BEAST result at the end.

Logical; if TRUE, a global seasonal model is first fitted and removed before running BEAST, and then added back to the BEAST result. Ignored if season = "none" (trend-only data).

Integer (>= 0); seed for the random number generator used in the MCMC. If mcmc.seed = 0, an arbitrary seed is used and results may vary across runs. Using the same non-zero seed makes results reproducible on the same machine, though differences across platforms/CPUs may still arise due to differences in random number libraries or CPU instruction sets.

Integer (> 0); the number of parallel MCMC chains.

Integer (> 0); thinning factor. If mcmc.thin = k, every k-th iteration is retained and the others are discarded.

Integer (> 0); number of initial iterations discarded as burn-in for each chain.

Integer (>= 0); number of samples collected per MCMC chain. The total number of iterations is (mcmc.burnin + mcmc.samples * mcmc.thin) * mcmc.chains.

Numeric (> 0); hyperparameter for the precision priors on model coefficients. The default is 1.5. It is used directly only when precPriorType = "constant" (see below); in other cases it serves as an initial value.

Character; one of "constant", "uniform", "componentwise" (default), or "orderwise". These control how precision parameters for the model coefficients are treated:

1. "constant": A single precision parameter is fixed at precValue. The fit may be sensitive to the chosen value.

2. "uniform": A single precision parameter is treated as a random variable with initial value precValue; its posterior is inferred via MCMC. The results are less sensitive to the initial choice of precValue.

3. "componentwise": Separate precision parameters are used for different components (e.g., season vs. trend), each initialized by precValue and inferred via MCMC.

4. "orderwise": Separate precision parameters are used for different components and for different orders within each component, all initialized by precValue and inferred via MCMC.

Logical; if TRUE, fit a model with an outlier component representing potential spikes or dips at isolated data points:

• Y = trend + outlier + error if season = "none",

• Y = trend + season + outlier + error otherwise.

Numeric vector of length 2 (integers >= 0); the minimum and maximum numbers of outlier-type changepoints (ocp) allowed in the series. Outliers refer to spikes or dips at isolated times that cannot be captured by the trend or seasonal components.

Logical; if TRUE, the full list of internal BEAST parameters (metadata, prior, mcmc, extra) is printed before MCMC begins. These internal objects correspond one-to-one with the arguments of beast. For example, prior$trendMinSepDist corresponds to tseg.min. See beast123 or inspect the source of beast for details.

Logical; if TRUE, a progress bar is printed.

Logical; if TRUE, warning messages are printed.

Logical; if TRUE, suppress most console output (overrides print.param and print.progress).

Logical; if TRUE, credible intervals for the trend and seasonal components (e.g., out$trend$CI, out$season$CI) are computed and returned. Computing credible intervals is relatively time-consuming (due to sorting and summarizing many MCMC samples). If only symmetric uncertainty summaries are needed, the posterior standard deviations out$trend$SD and out$season$SD may suffice and dump.ci can be set to FALSE.

Logical; if TRUE, individual MCMC samples are dumped to the output.

Logical; if TRUE, BEAST runs with a GUI window showing an animation of the MCMC sampling in model space (numbers and locations of trend/seasonal changepoints). This feature is experimental and currently available only on 64-bit Windows systems (not 32-bit Windows, macOS, or Linux).

Additional arguments reserved for future extensions and backward compatibility. Certain low-level settings are only available via beast123() (through metadata, prior, mcmc, and extra), not via beast().

Numeric vector of length N; the time associated with each observation. By default, this is simply 1:N if start, deltat, and any time attributes are missing.

A vector, matrix, or 3D array; a copy of the input y if the underlying extra$dumpInputData = TRUE. If extra$dumpInputData = FALSE, this is NULL. For irregular inputs (as in beast.irreg), this field stores the aggregated regular series at time intervals spaced by deltat (or metadata$deltaTime in the beast123 interface).

Numeric; the average marginal likelihood of the sampled models. Larger values indicate better fit for a given time series (e.g., -1 is better than -10; 10 is better than -1 or -10).

Numeric; coefficient of determination (R-squared) of the fitted model.

Numeric; root mean squared error of the fitted model.

Numeric; estimated variance of the residual error.

trend is a list of outputs related to the estimated trend component:

• ncp: Mean number of trend changepoints. Since individual sampled models can have different numbers of changepoints, several alternative summaries (ncp_mode, ncp_median, ncp_pct90) are also provided. For example, if mcmc$samples = 10 and the numbers of changepoints across models are c(0, 2, 4, 1, 1, 2, 7, 6, 6, 1), then the mean ncp is 3.1, the median 2.5, the mode 1, and the 90th percentile (ncp_pct90) 6.5.

• ncp_mode: Mode of the number of trend changepoints.

• ncp_median: Median of the number of trend changepoints.

• ncp_pct90: 90th percentile of the number of trend changepoints.

• ncpPr: Numeric vector of length tcp.minmax[2] + 1; probability distribution over the number of trend changepoints in 0:tcp.minmax[2]. For example, ncpPr[1] is the probability of having no trend changepoint; ncpPr[i] is the probability of having i - 1 changepoints.

• cpOccPr: Numeric vector of length N; changepoint occurrence probability at each time index for the trend component. Plotting cpOccPr yields a continuous "probability-of-being-a-changepoint" curve. A higher peak at a single time step does not necessarily imply a higher overall probability of a changepoint in a neighborhood compared to a broader peak with lower maximum but higher summed probability. For example, a window of cpOccPr values c(0, 0, 0.5, 0, 0) (peak 0.5, sum 0.5) likely indicates a smaller chance of a changepoint than another window c(0.1, 0.2, 0.21, 0.2, 0.1) (peak 0.21, sum 0.71).

• order: Numeric vector of length N; average polynomial order of the trend over sampled models at each time step. As a posterior average, it need not be an integer.

• cp: Numeric vector of length up to tcp.minmax[2]; estimated trend changepoint locations. These are obtained by smoothing cpOccPr with a window of size tseg.min and selecting up to tcp.minmax[2] peaks from the smoothed curve. Some entries may be NaN if fewer changepoints are identified. Not all reported changepoints should be treated as "true"; some may be false positives. Check the associated posterior probabilities (cpPr) for confidence.

• cpPr: Numeric vector of length tcp.minmax[2]; posterior probability associated with each changepoint in cp. Trailing entries are NaN if fewer changepoints are identified.

• cpCI: Numeric matrix of dimension tcp.minmax[2] x 2; credible intervals for changepoint locations in cp.

• cpAbruptChange: Numeric vector of length tcp.minmax[2]; magnitude of jumps in the trend at the detected changepoints.

• Y: Numeric vector of length N; estimated trend component (Bayesian model average over sampled trends).

• SD: Numeric vector of length N; posterior standard deviation of the trend.

• CI: Numeric matrix of dimension N x 2; credible interval for the trend, with lower and upper envelopes.

• slp: Numeric vector of length N; time-varying slope of the trend component.

• slpSD: Numeric vector of length N; posterior standard deviation of the slope.

• slpSgnPosPr: Numeric vector of length N; posterior probability that the slope is positive at each time point (i.e., increasing trend). For example, slpSgnPosPr = 0.80 at a given time indicates that 80% of sampled trends have a positive slope there.

• slpSgnZeroPr: Numeric vector of length N; posterior probability that the slope is effectively zero at each time point. The probability of negative slope can be obtained as 1 - slpSgnZeroPr - slpSgnPosPr.

• pos_ncp, neg_ncp, pos_ncpPr, neg_ncpPr, pos_cpOccPr, neg_cpOccPr, pos_cp, neg_cp, pos_cpPr, neg_cpPr, pos_cpAbruptChange, neg_cpAbruptChange, pos_cpCI, neg_cpCI: As above, but restricted to trend changepoints with positive jumps (pos_*) or negative jumps (neg_*) in the trend. For example, pos_ncp is the mean number of trend changepoints where the trend level jumps up.

• inc_ncp, dec_ncp, inc_ncpPr, dec_ncpPr, inc_cpOccPr, dec_cpOccPr, inc_cp, dec_cp, inc_cpPr, dec_cpPr, inc_cpAbruptChange, dec_cpAbruptChange, inc_cpCI, dec_cpCI: As above, but restricted to changepoints where the trend slope increases (inc_*) or decreases (dec_*). For example, if the trend slope changes from 0.4 to 2.5, that changepoint contributes to inc_ncp.

season is a list analogous to trend, but for the seasonal/periodic component (when present):

• ncp: Mean number of seasonal changepoints.

• ncp_mode, ncp_median, ncp_pct90: As for trend, but for seasonal changepoints.

• ncpPr: Numeric vector of length scp.minmax[2] + 1; probability distribution over the number of seasonal changepoints in 0:scp.minmax[2]. For example, ncpPr[1] is the probability of having no seasonal changepoint.

• cpOccPr: Numeric vector of length N; seasonal changepoint occurrence probability over time. The same caveat applies as for trend$cpOccPr: the height of a single peak does not fully determine the overall probability of a changepoint in its neighborhood.

• order: Numeric vector of length N; average harmonic order needed to approximate the seasonal component. As a posterior average over piecewise harmonic/SVD-based curves, this need not be an integer.

• cp, cpPr, cpCI, cpAbruptChange: Analogous to the trend fields, but for the seasonal component, with length determined by scp.minmax[2].

• Y: Numeric vector of length N; estimated seasonal component (Bayesian model average).

• SD: Numeric vector of length N; posterior standard deviation of the seasonal component.

• CI: Numeric matrix of dimension N x 2; credible interval for the seasonal component.

• amp: Numeric vector of length N; time-varying amplitude of the seasonal component.

• ampSD: Numeric vector of length N; posterior standard deviation of the amplitude.

• pos_ncp, neg_ncp, pos_ncpPr, neg_ncpPr, pos_cpOccPr, neg_cpOccPr, pos_cp, neg_cp, pos_cpPr, neg_cpPr, pos_cpAbruptChange, neg_cpAbruptChange, pos_cpCI, neg_cpCI: Seasonal analogues of the trend outputs with the same names, restricted to seasonal changepoints with positive (pos_*) or negative (neg_*) jumps in the seasonal curve. For example, pos_ncp refers to the average number of seasonal changepoints at which the seasonal component jumps up.

outlier is a list analogous to trend or season, but for the outlier component ( present only if setting hasOutlier=TRUE)

y is a numeric vector for an irregular or unordered time series. Missing values such as NA and NaN are allowed.

• If y is evenly spaced in time (regular), use beast instead.

• If y is a matrix or 3D array (e.g., a stack of images) consisting of multiple regular or irregular time series, use beast123 instead.

If y is a list of multiple time series, the multivariate version of the BEAST algorithm is invoked to jointly decompose the series and detect common changepoints. This feature is currently experimental and under development. See ohio for a working example.

time is a vector (or list) specifying the times of each observation in y. Its length must match the time dimension of y. It can be numeric, Date, character, or a list of date components. Supported formats include:

1. Numeric vector
   For example c(1984.23, 1984.27, 1984.36, ...). The unit of time is irrelevant to BEAST as long as it is used consistently with deltat and period.

2. R Date vector
   For example as.Date(c("1984-03-27", "1984-04-10", "1984-05-12", ...)).

3. Character vector of date strings
   For example:

   • c("1984-03-27", "1984-04-10", "1984-05-12")

   • c("1984/03/27", "1984,04,10", "1984 05 12") (delimiters may differ as long as the year-month-day order is consistent)

   • c("LT4-1984-03-27", "LT4-1984-04-10", "LT4-1984+05,12")

   • c("LT4-1984087ndvi", "LT4-1984101ndvi", "LT4-1984133ndvi")

   • c("1984,,abc 3/ 27", "1984,,ddxfdd 4/ 10", "ggd1984,, 5/ ttt 12")

   BEAST uses several heuristics to parse date strings without an explicit format specifier and may fail for ambiguous patterns (e.g., in "LC8-2020-09-20-1984" it is unclear whether 2020 or 1984 is the year). For robust parsing, consider using a list with an explicit format (see the next).

4. List with date strings and format
   A list of the form time = list(datestr = ..., strfmt = "..."), where time$datestr is a character vector of date strings and time$strfmt is a format specifier describing how to extract year, month, day, or day-of-year. Three classes of formats are supported:

   • (a) Fixed positions for year/month/day.
     For example, to extract 2001/12/02 etc. from time$datestr = c("P23R34-2001.1202333xd", "O93X94-2002.1108133fd", "TP3R34-2009.0122333td") use time$strfmt = "P23R34-yyyy.mmdd333xd", where yyyy, mm, and dd mark the positions of year, month, and day; all other characters are wildcards.

   • (b) Fixed positions for year and day-of-year (doy).
     For example, to extract years and days-of-year from strings like "P23R342001888045" use time$strfmt = "123123yyyy888doy", where yyyy and doy mark year and day-of-year; all other positions are wildcards. doy must be three digits.

   • (c) Patterns based on separators between Y/M/D.
     For example, to extract 2002/12/02 from "2002,12/02", " 2002 , 12/2", "2002,12 /02 " use time$strfmt = "Y,M/D"; whitespace is ignored. To extract 2002/12/02 from "2--12, 2012", use time$strfmt = "D--M,Y".

5. List of date components
   A list specifying dates component-wise, using either

   • time$year, time$month, and time$day, or

   • time$year and time$doy

   where each element is a vector of the same length as the time dimension of y. For the doy representation, values must lie between 1 and 365/366.

Numeric or character; the time interval used to aggregate the irregular time series into a regular one.

The BEAST model is formulated for regular (evenly spaced) data; therefore beast.irreg first re-bins the irregular time series into regular intervals of length deltat. If deltat is missing, a heuristic guess is used. The unit of deltat must be consistent with time:

• If time is numeric, the unit of deltat is arbitrary but must be consistent with time.

• If time is a Date vector or date strings, the default unit of deltat is fractional years.

To specify the unit explicitly, supply a character string, for example "7 days", "7d", "1/2 months", "1 mn", "1.0 year", or "1y".

Character (default "harmonic"); indicates whether y has a periodic component, and how it should be modeled. Allowed values are:

• "none": y is trend-only; no periodic component is modeled. Seasonal arguments (e.g., sorder.minmax, scp.minmax, sseg.min) are ignored.

• "harmonic": y has a periodic/seasonal component. Here, ‘season’ is used broadly to mean any periodic variation. The period is a known constant supplied via period and is not estimated as a model parameter. The seasonal component is modeled as a harmonic curve (sum of sines and cosines).

• "dummy": As in "harmonic", but the periodic component is modeled via non-parametric dummy bases. The harmonic-order argument sorder.minmax is irrelevant and ignored.

• "svd": (experimental) As in "harmonic", but the seasonal component is modeled as a linear combination of basis functions derived via singular value decomposition (SVD). These SVD-based bases can be more parsimonious than the standard harmonic bases and can improve sensitivity to subtle changepoints.

Numeric or character. The period of the seasonal/periodic component in y. Required only when a periodic component is present (i.e., season is "harmonic", "svd", or "dummy"), and ignored if season = "none".

The period must have units consistent with deltat, and satisfies period = deltat * freq, where freq is the number of samples per period. The historical freq argument (number of data points per period) is still supported via ..., but is deprecated; if both period and freq are supplied, period takes precedence.

period (or equivalently freq) is not itself a BEAST model parameter and must usually be specified by the user. If period is missing, BEAST attempts to guess it via autocorrelation before fitting the model.

If period <= 0, season = "none" is assumed and a trend-only model is fitted. To specify units explicitly for date-based time axes, use a string such as "1.0 year", "12 months", "365d", or "366 days".

Integer vector of length 2 (>= 0); minimum and maximum numbers of seasonal changepoints (SCPs) allowed in the seasonal component. Used only when a seasonal component is present (i.e., season != "none") and ignored otherwise.

If scp.minmax[1] == scp.minmax[2], BEAST assumes a fixed number of seasonal changepoints and does not infer the posterior on the number of changepoints, but still estimates when those changepoints occur.

If both values are 0, no seasonal changepoints are allowed; a global harmonic (or SVD/dummy) model is used, but the most likely harmonic order is still inferred if sorder.minmax[1] != sorder.minmax[2].

Integer vector of length 2 (>= 1); minimum and maximum harmonic orders considered for the seasonal component. Used only if season = "harmonic" or "svd" and ignored for trend-only data or when season = "dummy".

If sorder.minmax[1] == sorder.minmax[2], BEAST assumes a fixed harmonic order and does not infer the posterior distribution of harmonic orders.

Integer vector of length 2 (>= 0); minimum and maximum numbers of trend changepoints (TCPs) allowed in the trend component.

If tcp.minmax[1] == tcp.minmax[2], BEAST assumes a fixed number of trend changepoints and does not infer the posterior on the number of trend changepoints, but still estimates their occurrence probabilities over time.

If both values are 0, no trend changepoints are allowed; a global polynomial trend is used, but the most likely polynomial order is still inferred if torder.minmax[1] != torder.minmax[2].

Integer vector of length 2 (>= 0); minimum and maximum polynomial orders considered for the trend component. Order 0 corresponds to a constant (flat) trend; order 1 is a line.

If torder.minmax[1] == torder.minmax[2], BEAST assumes a fixed polynomial order and does not infer the posterior distribution of trend orders.

Integer (> 0); minimum length (in data points) of a segment between two neighboring seasonal changepoints. When fitting a piecewise seasonal model, no two seasonal changepoints are allowed to occur within sseg.min time steps.

sseg.min is unitless (number of time intervals); in the original time unit the window length is sseg.min * deltat. If NULL, a default based on the implied frequency is used.

Integer (>= 0); number of leftmost data points excluded from seasonal changepoint detection. No seasonal changepoints are allowed in the initial window of length sseg.leftmargin.

sseg.leftmargin is unitless (number of samples). In the original time unit, the excluded window length is sseg.leftmargin * deltat. If NULL, defaults to sseg.min.

Integer (>= 0); number of rightmost data points excluded from seasonal changepoint detection. No seasonal changepoints are allowed in the ending window of length sseg.rightmargin.

sseg.rightmargin is unitless, and the corresponding time window is sseg.rightmargin * deltat. If NULL, defaults to sseg.min.

Integer (> 0); minimum length (in data points) of a segment between two neighboring trend changepoints. When fitting a piecewise polynomial trend, no two trend changepoints are allowed within a window of length tseg.min.

tseg.min is unitless; in the original time unit the window is tseg.min * deltat. If NULL, a default based on the implied frequency is used when a cyclic component is present.

Integer (>= 0); number of leftmost data points excluded from trend changepoint detection. No trend changepoints are allowed in the starting window of length tseg.leftmargin.

tseg.leftmargin is unitless; the excluded time window is tseg.leftmargin * deltat. If NULL, defaults to tseg.min.

Integer (>= 0); number of rightmost data points excluded from trend changepoint detection. No trend changepoints are allowed in the ending window of length tseg.rightmargin.

tseg.rightmargin is unitless; the excluded time window is tseg.rightmargin * deltat. If NULL, defaults to tseg.min.

Numeric (default 0.0). A hyperprior parameter–newly added in Version 1.02– controlling the complexity of the seasonal curve (i.e., the number of seasonal changepoints). A prior of the form p(k) \propto \exp[\lambda (k+1)] is placed on the number of seasonal changepoints k, where \lambda is seasonComplexityFactor. Setting \lambda = 0 yields a non-informative prior p(k) \propto 1.0 where all model dimensions are equally likely a priori. Users may tune seasonComplexityFactor in the range [-20, 20] or an even wider range: negative values (e.g., \lambda = -15.9) favor fewer changepoints (simpler seasonal curves), whereas positive values (e.g., \lambda = 5.76) favor more changepoints (more complex curves).

Numeric scalar (default 0.0); analogous to s.complexfct but for the trend component and the number of trend changepoints.

Character (default "bayes"); specifies how model posterior probabilities are formulated or approximated:

• "bayes": full Bayesian formulation as in Zhao et al. (2019).

• "bic": BIC approximation, bic = n * ln(SSE) + k * ln(n), where k and n are the numbers of parameters and data points.

• "aic": AIC approximation, aic = n * ln(SSE) + 2k.

• "aicc": corrected AIC, aicc = aic + (2k^2 + 2k) / (n - k - 1).

• "hic": Hannan–Quinn information criterion, hic = n * ln(SSE) + 2k * ln(ln(n)).

• "bic0.25": BIC-type approximation adopted from Kim et al. (2016) <doi:10.1016/j.jspi.2015.09.008>, bic0.25 = n * ln(SSE) + 0.25 k * ln(n), with a weaker penalty on model complexity.

• "bic0.50": same as above but with penalty factor 0.50.

• "bic1.5": same as above but with penalty factor 1.5.

• "bic2": same as above but with penalty factor 2.0.

Logical; if TRUE, a global trend is first fitted and removed from the series before running BEAST, and then added back to the final result. This can help when the global trend dominates other components.

Logical; if TRUE, a global seasonal model is first fitted and removed from the series before running BEAST, then added back to the final result. Ignored when season = "none".

Integer (>= 0); seed for the random number generator used in the MCMC sampler. If mcmc.seed = 0, an arbitrary seed is chosen and results vary across runs. Using a fixed non-zero seed improves reproducibility on the same machine; results may still differ across architectures because the underlying random number generator can depend on CPU instruction sets.

Integer (> 0); number of parallel MCMC chains.

Integer (> 0); thinning factor for the chains (e.g., if mcmc.thin = 5, every 5th iteration is retained).

Integer (> 0); number of burn-in samples discarded at the beginning of each chain.

Integer (>= 0); number of post-burn-in samples collected per MCMC chain. The total number of iterations is (mcmc.burnin + mcmc.samples * mcmc.thin) * mcmc.chains.

Numeric (> 0); hyperparameter for the precision prior. It is directly used only when precPriorType = "constant"; otherwise it serves as an initial value that is updated within MCMC (see below).

Character; one of "constant", "uniform", "componentwise" (default), or "orderwise". These options control how precision parameters for model coefficients are treated:

1. "constant": a single precision parameter is fixed to precValue. The result may be sensitive to precValue.

2. "uniform": a single precision parameter is treated as a random variable; its initial value is precValue, but its posterior is inferred via MCMC, making results less sensitive to the initial choice.

3. "componentwise": separate precision parameters are used for different components (e.g., one for season, another for trend), initialized by precValue and updated via MCMC.

4. "orderwise": separate precision parameters are used not only for components but also for individual orders within each component, again initialized by precValue and inferred via MCMC.

Logical; if TRUE, fits a model with an additional outlier component capturing spikes or dips at isolated data points:

• Y = trend + outlier + error when season = "none",

• Y = trend + season + outlier + error otherwise.

Outliers are modeled as changepoints that cannot be captured by trend or seasonal terms.

Integer vector of length 2 (>= 0); minimum and maximum numbers of outlier-type changepoints (OCPs) allowed in the series. OCPs correspond to isolated spikes/dips that are not captured by trend or seasonality.

Logical; if TRUE, the full list of internal BEAST parameters (organized as metadata, prior, mcmc, and extra) is printed before MCMC. The internal naming differs slightly from the beast.irreg interface, but there is a one-to-one mapping (e.g., prior$trendMinSepDist <- tseg.min). See beast123 or View(beast) for details.

Logical; if TRUE, prints a progress bar during model fitting.

Logical; if TRUE, prints warning messages.

Logical; if TRUE, suppresses all console output (overrides other printing options).

Logical; if TRUE, computes explicit credible intervals (i.e., out$season$CI, out$trend$CI) for the estimated seasonal and trend components. This requires sorting and can be time-consuming. If only symmetric intervals are needed, use the standard deviations (out$trend$SD, out$season$SD) and set dump.ci = FALSE.

Logical; if TRUE, dumps individual MCMC samples for further custom analysis.

Logical; if TRUE, launches a GUI window that animates MCMC sampling in the model space (numbers and timings of seasonal and trend changepoints). This experimental GUI is currently available only on 64-bit Windows, not on 32-bit Windows, macOS, or Linux.

Additional implementation-level arguments passed to the underlying beast123() engine. For full control over advanced settings, use beast123 directly.

Numeric vector of length N; the regularized time axis after aggregating the original irregular series. If no explicit time is available, it defaults to 1:N.

A vector, matrix, or 3D array containing a copy of the regularized input data if extra$dumpInputData = TRUE. Otherwise NULL. If the original input was irregular, this field stores the aggregated regular series at the time interval specified by metadata$deltaTime.

Numeric; the (average) model marginal likelihood. Larger values correspond to better fits for a given time series (e.g., -1 is better than -10; 10 is better than -1).

Numeric; coefficient of determination (R^2) for the fitted model.

Numeric; root mean squared error of the fitted model.

Numeric; estimated variance of the model residuals.

List containing summaries for the estimated trend component:

• ncp: Mean number of trend changepoints across sampled models. Because individual models have varying numbers of changepoints, additional summaries are provided: ncp_mode, ncp_median, ncp_pct90. For example, if mcmc$samples = 10 yields changepoint counts c(0, 2, 4, 1, 1, 2, 7, 6, 6, 1), then the mean is 3.1, median 2.5, mode 1, and 90th percentile 6.5.

• ncp_mode: Mode of the posterior distribution of the number of trend changepoints.

• ncp_median: Median of the posterior distribution of the number of trend changepoints.

• ncp_pct90: 90th percentile of the posterior distribution of the number of trend changepoints.

• ncpPr: Vector of length tcp.max + 1 where tcp.max = tcp.minmax[2]; gives the probability of having 0, 1, ..., tcp.max trend changepoints. For example, ncpPr[1] is the probability of having no trend changepoint; ncpPr[i] is the probability of having i - 1 changepoints.

• cpOccPr: Numeric vector of length N; the marginal probability at each time index of being a trend changepoint. Plotting cpOccPr yields a continuous curve of "probability of being a changepoint". Note: a higher peak in this curve reflects a higher probability at that specific time index, but not necessarily a higher probability of a changepoint in a neighborhood around that time. For instance, a window c(0, 0, 0.5, 0, 0) (peak 0.5, sum 0.5) can be less likely to contain a changepoint than c(0.1, 0.2, 0.21, 0.2, 0.1) (peak 0.21, sum 0.71).

• order: Numeric vector of length N; average polynomial order of the trend at each time index, averaged over sampled piecewise polynomial trends. It is not necessarily an integer.

• cp: Numeric vector of length tcp.max; the most probable locations of trend changepoints. These are derived by smoothing cpOccPr with a window of length tseg.min and picking up to prior$MaxKnotNum (subject to tcp.max) of the highest peaks in the smoothed curve. Entries may be NaN if insufficient changepoints are identified. Many entries may be false positives; they should not be treated as confirmed changepoints without further scrutiny.

• cpPr: Numeric vector of length tcp.max; the probabilities associated with the detected changepoints in cp. Remaining entries are NaN if ncp < tcp.max.

• cpCI: Numeric matrix of dimension tcp.max x 2; credible intervals for the detected changepoints in cp.

• cpAbruptChange: Numeric vector of length tcp.max; the jumps in the fitted trend at the detected changepoints.

• Y: Numeric vector of length N; posterior mean estimate of the trend component (Bayesian model average over sampled models).

• SD: Numeric vector of length N; posterior standard deviation of the trend estimate.

• CI: Numeric matrix of dimension N x 2; credible intervals (lower and upper envelopes) for the trend component.

• slp: Numeric vector of length N; time-varying slope of the fitted trend.

• slpSD: Numeric vector of length N; posterior standard deviation of the trend slope.

• slpSgnPosPr: Numeric vector of length N; probability that the trend slope is positive (i.e., increasing). For example, slpSgnPosPr[t] = 0.8 means that at time index t, 80% of sampled trend curves have positive slope.

• slpSgnZeroPr: Numeric vector of length N; probability that the trend slope is approximately zero (flat). The probability of a negative slope is given by 1 - slpSgnZeroPr - slpSgnPosPr.

• pos_ncp, neg_ncp, pos_ncpPr, neg_ncpPr, pos_cpOccPr, neg_cpOccPr, pos_cp, neg_cp, pos_cpPr, neg_cpPr, pos_cpAbruptChange, neg_cpAbruptChange, pos_cpCI, neg_cpCI:
  As above, but distinguishing changepoints where the trend jumps up (positive jump) versus jumps down (negative jump). For example, pos_ncp is the average number of changepoints with positive jumps.

• inc_ncp, dec_ncp, inc_ncpPr, dec_ncpPr, inc_cpOccPr, dec_cpOccPr, inc_cp, dec_cp, inc_cpPr, dec_cpPr, inc_cpAbruptChange, dec_cpAbruptChange, inc_cpCI, dec_cpCI:
  Analogous to the above, but distinguishing changepoints where the trend slope increases vs. decreases. For instance, if the slope changes from 0.4 to 2.5 at a changepoint, that changepoint contributes to inc_ncp.

List containing summaries for the estimated seasonal/periodic component (if present):

• ncp: Mean number of seasonal changepoints.

• ncpPr: Vector of length scp.max + 1, where scp.max = scp.minmax[2]; the probability of having 0, 1, ..., scp.max seasonal changepoints.

• cpOccPr: Numeric vector of length N; marginal probability that each time index is a seasonal changepoint. The same interpretation caveats as for the trend component apply.

• order: Numeric vector of length N; average harmonic order required to approximate the seasonal component. This is an average over sampled piecewise harmonic curves and is not necessarily an integer.

• cp: Numeric vector of length scp.max; the most probable seasonal changepoint locations, derived from the smoothed cpOccPr curve using a window size of sseg.min. If ncp < scp.max, the remaining entries are filled with NaN.

• cpPr: Numeric vector of length scp.max; probabilities associated with cp. Remaining entries are NaN if ncp < scp.max.

• cpCI: Numeric matrix of dimension scp.max x 2; credible intervals for the detected seasonal changepoints.

• cpAbruptChange: Numeric vector of length scp.max; jumps in the fitted seasonal component at the detected changepoints.

• Y: Numeric vector of length N; posterior mean estimate of the seasonal component.

• SD: Numeric vector of length N; posterior standard deviation of the seasonal estimate.

• CI: Numeric matrix of dimension N x 2; credible intervals (lower and upper envelopes) for the seasonal component.

• amp: Numeric vector of length N; time-varying amplitude of the seasonal component.

• ampSD: Numeric vector of length N; posterior standard deviation of the amplitude.

• pos_ncp, neg_ncp, pos_ncpPr, neg_ncpPr, pos_cpOccPr, neg_cpOccPr, pos_cp, neg_cp, pos_cpPr, neg_cpPr, pos_cpAbruptChange, neg_cpAbruptChange, pos_cpCI, neg_cpCI:
  Analogous to the trend component, but for seasonal changepoints that correspond to positive vs. negative jumps in the seasonal signal.

outlier is a list analogous to trend or season, but for the outlier component ( present only if setting hasOutlier=TRUE)

Y is a numeric 1D vector, 2D matrix, or 3D array. Missing values are allowed and can be indicated by NA, NaN, or a customized value specified via the 2nd argument metadata (e.g., metadata$missingValue=-9999).

• If Y is a vector of size N x 1 or 1 x N, it is treated as a single time series of length N.

• If Y is a 2D matrix or 3D array of dimension N1 x N2 or N1 x N2 x N3 (e.g., stacked images of geospatial data), it contains multiple time series of equal length. The dimension corresponding to time must be specified in metadata$whichDimIsTime. For example, metadata$whichDimIsTime = 1 for a 190 x 35 matrix indicates 35 time series of length 190; metadata$whichDimIsTime = 2 for a 100 x 200 x 300 array indicates 100 * 300 = 30000 time series of length 200 each.

Y can be either regular (evenly spaced in time) or irregular/unordered in time.

• Regular data: Individual times are determined from the time of the first data point (startTime) and the time interval between consecutive points (deltaTime), specified via metadata$startTime and metadata$deltaTime. If not provided, both default to 1.0.

• Irregular or unordered data: The times must be explicitly supplied via metadata$time. The BEAST model is currently formulated for regular data only, so beast123 internally aggregates/re-bins irregular data into a regular series. For this aggregation, metadata$deltaTime should also be provided to specify the desired bin size (time interval) of the regularized time series.

Y may contain both a periodic component and a trend, or only a trend. Use the argument season to specify the case:

• season = "none": Y is treated as trend-only; no periodic components are assumed.

• season = "harmonic": Y has a periodic/seasonal component. The term "season" is used broadly here to refer to any periodic variation. The period is not a model parameter estimated by BEAST; instead it must be supplied by the user via metadata$period, the unit of which should be consistent with that of metadata$deltaTime (see metadata$period below). If season = "harmonic", The seasonal component is modeled as a harmonic curve (a combination of sines and cosines).

• season = "dummy": As for "harmonic", except that the periodic/seasonal component is modeled as a non-parametric curve.

• season = "svd" (experimental): As for "harmonic", except that the periodic/seasonal component is modeled as a linear combination of basis functions derived from a singular value decomposition (SVD). The SVD-based basis functions can be more parsimonious than harmonic bases in parameterizing seasonal variations and may facilitate the detection of more subtle seasonal changepoints.

metadata is optional. If present, it can be:

• a scalar specifying the period of Y;

• a vector of numbers, character strings, or Dates specifying the times of Y; or

• more commonly, a list object specifying various parameters describing the first argument Y.

If missing, default values are used. However, when Y is a 2D matrix or 3D array, metadata should be supplied explicitly to avoid misinterpreting which dimension corresponds to time. metadata is not part of the Bayesian BEAST model itself; it provides additional information needed to correctly interpret Y.

When metadata is a list, the following fields are supported (not all are needed in every case; the relevant subset depends on the input type and regularity of the series):

• metadata$whichDimIsTime: Integer (<= 3). Specifies which dimension of Y corresponds to time for 2D or 3D inputs. Ignored if Y is a vector.

• metadata$isRegularOrdered: Logical. Obsolete and no longer used in this version. Regularity is now inferred from metadata$time; if metadata$time is missing, Y is assumed to be regular.

• metadata$time: A vector of the same length as the time dimension of Y, or a more complex object providing time information. It can be a vector of numbers, Dates, or date strings; it can also be a list of vectors of year, months, and days. Possible formats include:

  1. A vector of numeric values (e.g., c(1984.23, 1984.27, 1984.36, ...)). The time unit is arbitrary but must be consistent with the units used in metadata$startTime, metadata$deltaTime, and metadata$period.

  2. A vector of Dates (e.g., as.Date(c("1984-03-27","1984-04-10","1984-05-12", ...))).

  3. A vector of character strings. Examples are:

     • c("1984-03-27","1984-04-10","1984-05-12")

     • c("1984/03/27","1984,04,10","1984 05 12") (delimiters can differ as long as the Y-M-D order is consistent)

     • c("LT4-1984-03-27","LT4-1984-04-10","LT4-1984+05,12")

     • c("LT4-1984087ndvi","LT4-1984101ndvi","LT4-1984133ndvi")

     • c("1984,,abc 3/ 27","1984,,ddxfdd 4/ 10","ggd1984,, 5/ ttt 12")

     BEAST uses several heuristics to parse date strings without an explicit format specifier, but may fail when strings are ambiguous (e.g., "LC8-2020-09-20-1984", where both 2020 and 1984 look like possible years). To ensure correct parsing, use a list with an explicit date format specifier (see next item).

  4. A list object time = list(datestr = ..., strfmt = "...") consisting of:

     • time$datestr: a character vector of date strings, and

     • time$strfmt: a format string that specifies how to parse datestr.

     Three types of formats are supported:

     • (a) Fixed pattern of year, month, and day positions. For example, to extract 2001/12/02, 2002/11/08, etc. from time$datestr = c("P23R34-2001.1202333xd","O93X94-2002.1108133fd","TP3R34-2009.0122333td"), use time$strfmt = "P23R34-yyyy.mmdd333xd", where yyyy, mm, and dd denote the year, month, and day. All other positions are treated as wildcards and nd can be filled with any other letters different from yyyy, mm and dd..

     • (b) Fixed pattern of year and day-of-year (DOY) positions. For example, to extract year and DOY from "P23R342001888045", use time$strfmt = "123123yyyy888doy", where yyyy and doy are specifiers and other characters are wildcards. doy must be three digits.

     • (c) Fixed pattern of separators between year, month, and day. For example, to get 2002/12/02 from "2002,12/02", " 2002 , 12/2", or "2002,12 /02", use time$strfmt = "Y,M/D", where whitespace is ignored. To get 2002/12/02 from "2--12, 2012", use time$strfmt = "D--M,Y".

  5. A list object of separate vectors for dates. Use time$year, time$month, and time$day to specify dates, or alternatively time$year and time$doy (day of year, 1-365/366). Each vector must have the same length as the time dimension of Y.

• metadata$startTime: Numeric (defaults to 1.0 if missing). The time of the first data point. It can be given as a scalar (e.g., 2021.23) or as a vector of length 3 in the form of c(year, month, day) (e.g., c(2021, 1, 24)). metadata$startTime is needed for regular data; for irregular data it is optional and, if missing, may be derived from metadata$time.

• metadata$deltaTime: Numeric or character string. The time interval between consecutive data points. For regular data it is optional (default 1.0); for irregular data it should be specified, as it determines the bin size when aggregating irregular times to regular intervals. If metadata$time is numeric, the unit of deltaTime is arbitrary but must be consistent with the numeric scale of metadata$time. If metadata$time is given as Dates or date strings, deltaTime is interpreted as a fraction of a year by default. Alternatively, use a string instead of a number to specify the interval with a unit, such as deltaTime="7 days", "7d", "1/2 months", "1mn", "1 year", or "1y".

• metadata$period: Numeric or character string. The period of the periodic/seasonal component in Y. This is needed only when a seasonal component is present (i.e., season = "harmonic" or season = "dummy") and is ignored for trend-only data (season = "none"). The period must be in the same time unit as deltaTime and should satisfy period = deltaTime * freq, where freq is the number of data points per period. (The older argument freq is now obsolete and replaced by period.) The period is not a BEAST model parameter and must be provided by the user. But if period is missing, BEAST first attempts to infer a plausible period via autocorrelation before fitting. If period <= 0, no seasonal component is assumed (equivalent to season = "none"). As with deltaTime, character strings such as period="1 year", "12 months", "365d", or "366 days" can be used.

• metadata$missingValue: Numeric; a customized value indicating bad or missing values in addition to NA or NaN.

• metadata$maxMissingRateAllowed: Numeric in [0, 1]; the maximum proportion of missing values allowed. Time series with a missing rate higher than this threshold are skipped and not fitted by BEAST.

• metadata$hasOutlier: Logical; if TRUE, fit a model with an outlier component representing potential spikes or dips at isolated data points: Y = trend + outlier + error if season = "none", and Y = trend + season + outlier + error otherwise.

• metadata$deseasonalize: Logical; if TRUE, remove a global seasonal component before fitting BEAST (see examples).

• metadata$detrend: Logical; if TRUE, remove a global trend before fitting BEAST.

prior (optional) is a list of hyperparameters defining the priors in the Bayesian BEAST model. Because these are part of the model specification, the BEAST results may be sensitive to their values. If prior is missing, default values are used and printed to the console at the start of the run. The following fields are supported:

• prior$seasonMinOrder: Integer (>= 1).

• prior$seasonMaxOrder: Integer (>= 1). The minimum and maximum harmonic orders considered for the seasonal component. These are used only when the series has a seasonal component (i.e., season = "harmonic" or "svd") and ignored for trend-only data or when season='none' or 'dummy'. If seasonMinOrder == seasonMaxOrder, the harmonic order is fixed and BEAST does not infer the posterior distribution of harmonic orders.

• prior$seasonMinKnotNum: Integer (>= 0).

• prior$seasonMaxKnotNum: Integer (>= 0). The minimum and maximum numbers of seasonal changepoints allowed in segementing the seasonal component. Used only when the data have a a seasonal component (e.g.,season = "harmonic", "svd" or "dummy" and ignored for trend-only data. If seasonMinKnotNum == seasonMaxKnotNum, the number of seasonal changepoints is fixed but their possible locations and occurrence probabilities over time are still estimated. If seasonMinKnotNum == seasonMaxKnotNum == 0, no seasonal changepoints are allowed and a single global harmonic model is used with no changepoints.

• prior$seasonMinSepDist: Integer (> 0). The minimum separation, in number of time steps, between neighboring seasonal changepoints. That is, when fitting a piecewise seasonal model, no two changepoints may be closer than seasonMinSepDist time intervals. The corresponding time window in original time units is seasonMinSepDist * metadata$deltaTime.

• prior$seasonLeftMargin: Integer (>= 0). The number of leftmost observations excluded from seasonal changepoint detection. No seasonal changepoints are allowed in the initial window of length seasonLeftMargin. It is specified in units of time steps and thus corresponds to a time window of seasonLeftMargin * metadata$deltaTime. If missing, it defaults to seasonMinSepDist.

• prior$seasonRightMargin: Integer (>= 0). The number of rightmost observations excluded from seasonal changepoint detection. Similarly, no seasonal changepoints are allowed in the final window of length seasonRightMargin. Specified in time steps and corresponds to seasonRightMargin * metadata$deltaTime in the time unit. If missing, it defaults to seasonMinSepDist.

• prior$seasonComplexityFactor: Numeric (default 0.0). A hyperprior parameter–newly added in Version 1.02– controlling the complexity of the seasonal curve (i.e., the number of seasonal changepoints). A prior of the form p(k) \propto \exp[\lambda (k+1)] is placed on the number of seasonal changepoints k, where \lambda is seasonComplexityFactor. Setting \lambda = 0 yields a non-informative prior p(k) \propto 1.0 where all model dimensions are equally likely a priori. Users may tune seasonComplexityFactor in the range [-20, 20] or an even wider range: negative values (e.g., \lambda = -15.9) favor fewer changepoints (simpler seasonal curves), whereas positive values (e.g., \lambda = 5.76) favor more changepoints (more complex curves).

• prior$trendMinOrder: Integer (>= 0).

• prior$trendMaxOrder: Integer (>= 0). The minimum and maximum polynomial orders considered to fit the trend component. Order 0 corresponds to a constant (flat) trend; order 1 to a linear trend. If trendMinOrder == trendMaxOrder, the polynomial order is fixed and BEAST does not infer the posterior distrubtion of polynomial orders.

• prior$trendMinKnotNum: Integer (>= 0).

• prior$trendMaxKnotNum: Integer (>= 0). The minimum and maximum numbers of trend changepoints allowed. If trendMinKnotNum == trendMaxKnotNum, the number of trend changepoints is fixed but ther locations and occurrence probabilities over time are still estimated. If trendMinKnotNum == trendMaxKnotNum == 0, no trend changepoints are allowed and a single global polynomial trend is fitted.

• prior$trendMinSepDist: Integer (> 0). The minimum separation, in number of time steps, between neighboring trend changepoints. That is, when fitting a piecewise tremd model, no two changepoints may be closer than trendMinSepDist time intervals. The corresponding time window in original time units is trendMinSepDist * metadata$deltaTime.

• prior$trendLeftMargin: Integer (>= 0). The number of leftmost observations excluded from trend changepoint detection. No trend changepoints are allowed in the initial window of length trendLeftMargin. Specified in time steps; the corresponding time window is trendLeftMargin * metadata$deltaTime. If missing, defaults to trendMinSepDist.

• prior$trendRightMargin: Integer (>= 0). The number of rightmost observations excluded from trend changepoint detection. No trend changepoints are allowed in the final window of length trendRightMargin. Specified in time steps; the corresponding time window is trendRightMargin * metadata$deltaTime. If missing, defaults to trendMinSepDist.

• prior$trendComplexityFactor: Numeric (default 0.0). Analogous to seasonComplexityFactor, but for the trend component. A prior of the form p(k) \propto \exp[\lambda (k+1)] is placed on the number of trend changepoints k, where \lambda is trendComplexityFactor. Setting \lambda = 0 yields a non-informative prior p(k) \propto 1.0 where all model dimensions are equally likely a priori. Users may tune seasonComplexityFactor in the range [-20, 20] or an even wider range: negative values (e.g., \lambda = -15.9) favor fewer changepoints (simpler trend curves), whereas positive values (e.g., \lambda = 5.76) favor more changepoints (more complex curves).

• prior$precValue: Numeric (> 0); default 10. Useful only if prior$precPriorType = "constant".

• prior$precPriorType: Character string, one of "constant", "uniform" (default), "componentwise", or "orderwise". These options control how precision parameters (for model coefficients) are treated:

  1. "constant": A single precision parameter is fixed at prior$precValue. The results may be sensitive to the choice of prior$precValue.

  2. "uniform": A single precision parameter is treated as a random variable, with initial value prior$precValue. Its posterior is inferred via MCMC, making the results less sensitive to the initial choice of prior$precValue.

  3. "componentwise": Separate precision parameters are used for different components (e.g., season vs. trend), starting from prior$precValue. Each precision parameter is inferred via MCMC.

  4. "orderwise": Separate precision parameters are used for different components and different orders within components, starting from prior$precValue. All the precision parameters are inferred via MCMC.

• prior$outlierMinKnotNum: Integer (>= 0).

• prior$outlierMaxKnotNum: Integer (>= 0). These are used only if metadata$hasOutlier = TRUE to specify the minimum and maximum numbers of outlier-type changepoints (spikes or dips) allowed in the series.

mcmc (optional) is a list object of parameters configuring the reversible-jump MCMC procedure. These settings are not part of the Bayesian model itself but control the sampling process and chain length. In general, longer chains yield more stable estimates. Supported fields are:

• mcmc$seed: Integer (>= 0); the seed for the random number generator. If mcmc$seed = 0, an arbitrary seed is used and results can vary slightly across runs. Using the same non-zero seed makes results reproducible on the same machine, but differences across platforms/CPUs may still occur from the same seed due to differences in random number libraries or CPU instruction sets.

• mcmc$chainNumber: Integer (> 0); the number of parallel MCMC chains.

• mcmc$samples: Integer (> 0); the number of samples collected per MCMC chain.

• mcmc$thinningFactor: Integer (> 0); thinning factor. If thinningFactor = k, every k-th sample is retained and the others discarded.

• mcmc$burnin: Integer (> 0); the number of initial samples discarded as burn-in per chain.

• mcmc$maxMoveStepSize: Integer (> 0). In the RJMCMC sampler, a "move" proposal shifts changepoint locations. maxMoveStepSize specifies the maximum step size (in time steps) allowed in such moves.

• mcmc$seasonResamplingOrderProb: Numeric in (0, 1); probability of proposing a resampling of the seasonal harmonic order.

• mcmc$trendResamplingOrderProb: Numeric in (0, 1); probability of proposing a resampling of the trend polynomial order.

• mcmc$credIntervalAlphaLevel: Numeric in (0, 1) (default 0.95); the confidence level used to compute credible intervals (e.g., 0.95 for 95% credible intervals).

extra (optional) is a list of flags and options controlling output content, console messages, and parallel computation. Supported fields include:

• extra$dumpInputData: Logical (default FALSE). If TRUE, copies of the input time series are included in the output. If the input Y is irregular the dumped copy is the aggregated regular series.

• extra$whichOutputDimIsTime: Integer (<= 3). For 2D or 3D inputs (multiple time series, e.g., stacked images), this specifies which output dimension corresponds to time. Defaults to 3 for 3D inputs. Ignored if Y is a single time series.

• extra$ncpStatMethod: Character string (deprecated). Formerly used to specify the statistic used to determine the number of changepoints (ncp) when computing the most likely changepoint locations (e.g., out$trend$cp and out$season$cp). Possible values were "mode", "mean", and "median" (default "mode"). Individual MCMC-sampled models have a varying number of changepoints. For example, if mcmc$samples=10 and assuming that the numbers of changepoints for the 10 sampled models are [0, 2, 4, 1, 1, 2, 7, 6, 6, 1], the mean ncp is 3.1 (rounded to 3), the median is 2.5 (2), and the mode is 1. ncpStatMethod is now deprecated: BEAST outputs all possible changepoints together with several summaries of ncp, including ncp, ncp_median, ncp_mode, and ncp_pct90. The choice of ncp for plotting is now controlled by the ncpStat argument in plot.beast.

• extra$computeCredible: Logical (default TRUE). If TRUE, credible intervals are computed and returned.

• extra$fastCIComputation: Logical (default TRUE). If TRUE, a faster approximate method is used to compute credible intervals. CI computation can be one of the most time-consuming steps, so fastCIComputation = TRUE is recommended unless more precise CI estimates are desired.

• extra$computeSeasonOrder: Logical (default TRUE). If TRUE, a posterior estimate of the seasonal harmonic order is returned. Only meaningful when season = "harmonic" or "svd" and prior$seasonMinOrder != prior$seasonMaxOrder.

• extra$computeTrendOrder: Logical (default TRUE). If TRUE, a posterior estimate of the trend polynomial order is returned. Only meaningful when prior$trendMinOrder != prior$trendMaxOrder.

• extra$computeSeasonChngpt: Logical (default TRUE). If TRUE, compute the most likely times/positions at which changepoints occur in the seasonal component. This is relevant only when a seasonal component is present (i.e., season = "harmonic", "svd", or "dummy") and prior$seasonMaxKnotNum > 0.

• extra$computeTrendChngpt: Logical (default TRUE). If TRUE, compute the most likely changepoint locations in the trend component. This is relevant only when prior$trendMaxKnotNum > 0.

• extra$computeSeasonAmp: Logical (default FALSE). If TRUE, output the time-varying amplitude of the seasonal component.

• extra$computeTrendSlope: Logical (default FALSE). If TRUE, output the time-varying slope of the trend component.

• extra$tallyPosNegSeasonJump: Logical (default FALSE). If TRUE, classify seasonal changepoints by the sign of the jump (positive vs. negative) and output separate summaries for each group.

• extra$tallyPosNegTrendJump: Logical (default FALSE). If TRUE, classify trend changepoints by whether the trend level jumps up or down at the changepoint and output separate summaries.

• extra$tallyIncDecTrendJump: Logical (default FALSE). If TRUE, classify trend changepoints by changes in slope (increasing vs. decreasing) and output separate summaries for those changepoints with increased slopes and those with decreased slopes.

• extra$printProgress: Logical (default FALSE). If TRUE, a progress bar is displayed showing the progress of the run. For multiple time series (e.g., stacked images), the progress bar also reports an estimate of remaining time.

• extra$consoleWidth: Integer (default 0). The width (in characters) of each status line printed when extra$printProgress = TRUE. If 0, the width of the current console is used.

• extra$printParameter: Logical (default TRUE). If TRUE, the values used in metadata, prior, mcmc, and extra are printed at the start of the run.

• extra$printWarning: Logical (default TRUE). If TRUE, warning messages are printed.

• extra$quiet: Logical. If TRUE, suppress most console output.

• extra$dumpMCMCSamples: Logical. If TRUE, dump individual MCMC samples.

• extra$numThreadsPerCPU: Integer (default 2); the number of threads scheduled per CPU core.

• extra$numParThreads: Integer (default 0). Total number of parallel threads used when fitting many time series. If 0, the actual number of threads is set to extra$numThreadsPerCPU * (number of CPU cores). That is, each CPU core will generate a number 'numThreadsPerCPU' of thread. On 64-bit Windows, BEAST is group-aware and distributes threads across NUMA nodes. Currently, up to 256 CPU cores are supported.

Character (default "harmonic"). Specifies whether Y has a periodic component and how it is modeled:

• "none": Y is trend-only; no periodic components are modeled. Seasonal prior parameters (e.g., seasonMaxKnotNum and seasonMinSepDist) are ignored.

• "harmonic": Y has a periodic/seasonal component modeled as a harmonic series (e.g., combination of sines and cosines). The term season is used broadly to refer to any periodic variation. The period is not estimated but must be specified by the user (via metadata$period); see metadata$period.

• "dummy": As "harmonic", except that the seasonal component is modeled as a non-parametric curve. The harmonic-order prior settings (e.g., prior$seasonMinOrder and prior$seasonMaxOrder) are irrelevant and ignored if season="dummy".

• "svd": (Experimental) As "harmonic", except that the seasonal component is expressed as a linear combination of basis functions derived from a Single-value decomposition. These basis functions can be more parsimonious than pure harmonic bases, and may improve detection of subtle seasonal changepoints.

Character (default "bayes"). Specifies how the model posterior probability is formulated or approximated:

• "bayes": Full Bayesian formulation as described in Zhao et al. (2019).

• "bic": Approximate posterior probabilities using the Bayesian Information Criterion (BIC), \mathrm{BIC} = n \log(\mathrm{SSE}) + k \log(n), where k is the number of parameters and n the number of observations.

• "aic": Approximate posterior probabilities using Akaike's Information Criterion (AIC), \mathrm{AIC} = n \log(\mathrm{SSE}) + 2k.

• "aicc": Approximate posterior probabilities using the corrected AIC (AICc), \mathrm{AICc} = \mathrm{AIC} + \frac{2k^2 + 2k}{n - k - 1}.

• "hic": Approximate posterior probabilities using the Hannan-Quinn Information Criterion (HIC), \mathrm{HIC} = n \log(\mathrm{SSE}) + 2k \log(\log(n)).

• "bic0.25": BIC-type approximation adopted from Kim et al. (2016) doi:10.1016/j.jspi.2015.09.008 with reduced complexity penalty, \mathrm{BIC}_{0.25} = n \log(\mathrm{SSE}) + 0.25 k \log(n).

• "bic0.5": As above but with penalty factor 0.5.

• "bic1.5": As above but with penalty factor 1.5.

• "bic2": As above but with penalty factor 2.0.

Additional parameters reserved for future extensions; currently unused.

A numeric vector of length N: the time associated with each sampled observation. By default, this is simply 1:N if metadata$time, metadata$startTime, or metadata$deltaTime are missing.

A vector, matrix, or 3D array; a copy of the input Y if extra$dumpInputData = TRUE. If extra$dumpInputData = FALSE, this is NULL. For irregular inputs in Y , this field stores the aggregated regular series at time intervals spaced by metadata$deltaTime.

Numeric; the average marginal likelihood of the sampled models. Larger values indicate better fit for a given time series.

Numeric; coefficient of determination (R-squared) of the fitted model.

Numeric; root mean squared error of the fitted model.

Numeric; estimated variance of the residual error.

trend is a list of outputs related to the estimated trend component:

• ncp: Numeric scalar; mean number of trend changepoints. Because individual models sampled by BEAST can have varying numbers of changepoints, several alternative summaries (ncp_mode, ncp_median, ncp_pct90) are also provided. For example, if mcmc$samples = 10 and the numbers of changepoints across models are c(0, 2, 4, 1, 1, 2, 7, 6, 6, 1), then the mean number of changepoints (ncp) is 3.1, the median 2.5, the mode 1, and the 90th percentile (ncp_pct90) 6.5.

• ncp_mode: Mode of the number of trend changepoints. See the above for explanations.

• ncp_median: Median of the number of trend changepoints. See the above for explanations.

• ncp_pct90: 90th percentile of the number of trend changepoints. See the above for explanations.

• ncpPr: Numeric vector of length prior$trendMaxKnotNum + 1. Probability distribution over the number of trend changepoints in the range 0:prior$trendMaxKnotNum. For example, ncpPr[1] is the probability of having no trend changepoint; ncpPr[i] is the probability of having i - 1 changepoints.

• cpOccPr: Numeric vector of length N. The changepoint occurrence probability at each time index for the trend component. Plotting cpOccPr yields a continuous probability-of-being-a-changepoint curve. A peak with a high value at a single time step does not necessarily imply a higher overall probability of a changepoint in a neighborhood, compared to a broader peak with a lower maximum but higher total probability. Specifically, a higher peak indicates a higher chance of being a changepoint only at that particular SINGLE point in time and but not necessarily mean a higher chance of observing a changepoint AROUND that time. For example, a window of cpOccPr values c(0,0,0.5,0,0) (i.e., the peak prob is 0.5 and the summed probability over the window is 0.5) is less likely to be a changepoint compared to another window c(0.1,0.2,0.21,0.2,0.1) where the peak of 0.21 is lower but the summed probablity of 0.71 is larger.

• order: Numeric vector of length N. The average polynomial order of the trend across sampled models at each time step. Because this is a posterior average, it need not be an integer.

• cp: Numeric vector (up to length prior$trendMaxKnotNum). Estimated trend changepoint locations. These are obtained by smoothing cpOccPr with a window of size prior$trendMinSepDist and then selecting up to prior$trendMaxKnotNum peaks in the smoothed curve. Some entries may be NaN if the number of detected changepoints is fewer than trendMaxKnotNum. Not all listed changepoints should be treated as "true" changepoints; some may be false positives. Check the associated posterior probabiliites (given in the next field trend$cpPr for the confidence levels.

• cpPr: Numeric vector of length prior$trendMaxKnotNum; the posterior probabilities associated with each changepoint in cp. Trailing entries are NaN if fewer than prior$trendMaxKnotNum changepoints are identified.

• cpCI: Numeric matrix of dimension prior$trendMaxKnotNum x 2; credible intervals for the changepoint locations in cp.

• cpAbruptChange: Numeric vector of length prior$trendMaxKnotNum; the estimated magnitude of the jump in the trend at each detected changepoint in cp.

• Y: Numeric vector of length N; the estimated trend component (Bayesian model average over all sampled trends).

• SD: Numeric vector of length N; posterior standard deviation of the estimated trend.

• CI: Numeric matrix of dimension N x 2; credible interval for the trend, with lower and upper envelopes.

• slp: Numeric vector of length N; time-varying slope of the trend component.

• slpSD: Numeric vector of length N; posterior standard deviation of the slope.

• slpSgnPosPr: Numeric vector of length N; posterior probability that the slope of the trend is positive at each time point. For example, slpSgnPosPr = 0.80 at a given time means that 80% of sampled trend models have a positive slope there.

• slpSgnZeroPr: Numeric vector of length N; posterior probability that the slope of the trend is effectively zero (flat) at each time point. The probability of a negative slope can be derived as 1 - slpSgnZeroPr - slpSgnPosPr.

• pos_ncp, neg_ncp, pos_ncpPr, neg_ncpPr, pos_cpOccPr, neg_cpOccPr, pos_cp, neg_cp, pos_cpPr, neg_cpPr, pos_cpAbruptChange, neg_cpAbruptChange, pos_cpCI, neg_cpCI: As above, but restricted to trend changepoints with positive jumps (pos_*) or negative jumps (neg_*) in the trend. For example, pos_ncp is the mean number of changepoints at which the trend level jumps up.

• inc_ncp, dec_ncp, inc_ncpPr, dec_ncpPr, inc_cpOccPr, dec_cpOccPr, inc_cp, dec_cp, inc_cpPr, dec_cpPr, inc_cpAbruptChange, dec_cpAbruptChange, inc_cpCI, dec_cpCI: As above, but restricted to changepoints where the trend slope increases (inc_*) or decreases (dec_*). For example, if the trend slope changes from 0.4 to 2.5 at a changepoint, that changepoint is counted toward inc_ncp.

season is a list analogous to trend, but for the seasonal/periodic component (when present):

• ncp: Mean number of seasonal changepoints. Because individual models sampled by BEAST can have varying numbers of changepoints, several alternative summaries (ncp_mode, ncp_median, ncp_pct90) are also provided. For example, if mcmc$samples = 10 and the numbers of changepoints across models are c(0, 2, 4, 1, 1, 2, 7, 6, 6, 1), then the mean number of changepoints (ncp) is 3.1, the median 2.5, the mode 1, and the 90th percentile (ncp_pct90) 6.5.

• ncp_mode: Mode of the number of seasonal changepoints. See the above for explanations.

• ncp_median: Median of the number of seasonal changepoints. See the above for explanations.

• ncp_pct90: 90th percentile of the number of seasonal changepoints. See the above for explanations.

• ncpPr: Numeric vector of length prior$seasonMaxKnotNum + 1; probability distribution over the number of seasonal changepoints in 0:prior$seasonMaxKnotNum. For example, ncpPr[1] is the probability of having no seasonal changepoint; ncpPr[i] is the probability of having i - 1 changepoints.

• cpOccPr: Numeric vector of length N; seasonal changepoint occurrence probability over time. Plotting cpOccPr yields a continuous probability-of-being-a-changepoint curve. A peak with a high value at a single time step does not necessarily imply a higher overall probability of a changepoint in a neighborhood, compared to a broader peak with a lower maximum but higher total probability. Specifically, a higher peak indicates a higher chance of being a changepoint only at that particular SINGLE point in time and does not necessarily mean a higher chance of observing a changepoint AROUND that time. For example, a window of cpOccPr values c(0,0,0.5,0,0) (i.e., the peak prob is 0.5 and the summed probability over the window is 0.5) is less likely to be a changepoint compared to another window c(0.1,0.2,0.21,0.2,0.1) where the peak of 0.21 is lower but the summed probablity of 0.71 is larger.

• order: Numeric vector of length N; average harmonic order needed to approximate the seasonal component. Because this is a posterior average, it need not be an integer

• cp: Numeric vector (up to length prior$seasonMaxKnotNum); estimated seasonal changepoint locations. These are obtained by smoothing cpOccPr with a window of size prior$seasonMinSepDist and then selecting up to prior$seasonMaxKnotNum peaks in the smoothed curve. Some entries may be NaN if the number of detected changepoints is fewer than seasonMaxKnotNum. Not all listed changepoints should be treated as "true" changepoints; some may be false positives. Check the associated posterior probabiliites (given in the next field season$cpPr for the confidence levels.

• cpPr: Numeric vector of length prior$seasonMaxKnotNum; the posterior probabilities associated with each changepoint in cp. Trailing entries are NaN if fewer than prior$seasonMaxKnotNum changepoints are identified.

• cpCI: Numeric matrix of dimension prior$seasonMaxKnotNum x 2; credible intervals for seasonal changepoint locations.

• cpAbruptChange: Numeric vector of length prior$seasonMaxKnotNum; magnitude of jumps in the seasonal curve at each changepoint.

• Y: Numeric vector of length N; estimated seasonal component (Bayesian model average).

• SD: Numeric vector of length N; posterior standard deviation of the seasonal component.

• CI: Numeric matrix of dimension N x 2; credible interval for the seasonal component.

• amp: Numeric vector of length N; time-varying amplitude of the seasonality.

• ampSD: Numeric vector of length N; posterior standard deviation of the amplitude.

• pos_ncp, neg_ncp, pos_ncpPr, neg_ncpPr, pos_cpOccPr, neg_cpOccPr, pos_cp, neg_cp, pos_cpPr, neg_cpPr, pos_cpAbruptChange, neg_cpAbruptChange, pos_cpCI, neg_cpCI: Seasonal analogues of the trend outputs with the same names, but restricted to seasonal changepoints with positive (pos_*) or negative (neg_*) jumps in the seasonal component. For example, pos_ncp refers to the average number of seasonal changepoints that jump up (i.e., positively) in the seasonal curve.

outlier is a list analogous to trend or season, but for the outlier component ( present only if setting hasOutlier=TRUE)

numeric within [-180,180]

numeric within [-90, 90]

a positive number ( <=500 meters ); the radius of a buffer around the given latitude and longitude for aggregation. If radius=0, the single pixel at the lat and lon will be retrieved

character; if radius>0, used to specify the spatial aggregation method for pixels in the buffer. Possible values are 'mean','min','max', or 'median'.

integer; the seconds elapsed to wait for connection timeout. See the note for an explanation.

integer; number of rows of the mine grid along the vertical direction.

integer; number of columns of the mine grid along the horizontal direction.

numeric; a fraction between 0 and 1 to specify the probability of mine occurrence in the mine grid.

a "beast" object returned by beast,beast.irreg, or beast123. It may contain one or many time series.

an integer (default to 1 ) or a vector of two integers to specify the index of the time series to plot if x contains results for multiple time series. index is always 1 if x has 1 time series. If x is returned by beast123 with a 2D input,index should be a single integer. If x is from beast123 applied to 3D arrays of time series (e.g., stacked satellite images), index can be a linear index or two subscripts to specify the row and column of the pixel/grid.

a vector of strings indicating the elements or variables of x to plot. Possible vars strings include 'y' (season plus trend), 's' (season component), 't' (trend component), 'o' (outliers), 'scp', 'tcp', 'ocp' (occurrence probability of seasonal/trend/outlier changepoint), 'sorder' (seasonal harmonic order), 'torder' (trend polynomial order), 'samp' (amplitude of seasonality), 'tslp' (slope of trend), 'slpsgn' (probabilities of the slope being positive, zero, and negative) and 'error' (remainder).

a numeric vector of the same length as that of vars to specify the relative heights of subplots of individual variables in vars.

a string vector of the same length as that of vars to specify the colors of individual subplots associated with vars.

a string; the main title.

a string: the x axis title.

a string vector of the same length as that of vars to specify the y axis names of individual subplots associated with vars

cex for the main title

cex for the axis title

a bool scalar. If TRUE, an interactive GUI is used for examining individual elements of x.

character. A string to specify which statistic is used for the Number of ChangePoint (ncp). Five values are possible: 'mean', 'mode', 'median','pct90', and 'max'; the default is 'median'. Individual models sampled by BEAST has a varying dimension (e.g., number of changepoints or knots). For example, if mcmc$samples=10, the numbers of changepoints for the 10 sampled models are assumed to be c(0, 2, 4, 1, 1, 2, 7, 6, 6, 1). The mean ncp will be 3.1 (rounded to 3), the median is 2.5 (2), the mode is 1, and the maximum is 7. The 'max' option plots all the changepoints recorded in out$trend$cp, out$season$cp, or out$outlier$cp; many of these changepoints are bound to be false positives, so do not treat all of them as actual changepoints.

additional parameters to be implemented.

a "beast" object returned by beast, beast.irreg, or beast123. It may contain one or many time series.

an integer (default to 1 ) or a vector of two integers to specify the index of the time series to print if x contains results for multiple time series. If x has 1 time series, index should be always 1. If x is returned by beast123 applied to a 2D input,index should be a single index. If x is from beast123 applied to 3D arrays of time series (e.g., stacked satellite images), index can be a linear index or two subscripts to specify the row and column of the desired pixel/grid.

additional parameters to be implemented.

integer; number of rows of the mine grid along the vertical direction.

integer; number of columns of the mine grid along the horizontal direction.

numeric; a time interval between 0.05 and 2 seconds, specifying how fast the tetriminos moves down. The smaller, the faster.

a "beast" object returned by beast, beast.irreg, or beast123. It may contain one or many time series.

an integer (default to 1 ) or a vector of two integers to specify the index of the time series to extract if x contains results for multiple time series. If x has 1 time series, index should be always 1. If x is returned by beast123 applied to a 2D input,index should be a single index. If x is from beast123 applied to 3D arrays of time series (e.g., stacked satellite images), index can be a linear index or two subscripts to specify the row and column of the desired pixel/grid.