binomLikelihoodSmooth {BiSeq} | R Documentation

## Calculates local likelihood estimations for binomial random variables

### Description

For a given set of binomial random variables with 1-dimensional coordinates, this function calculates the local likelihood estimation of the success probability p at a given point. For this purpose, a weighted likelihood estimation with weights obtained by a triangular kernel with given bandwidth is used. This can be used to predict values at points where no variable has been observed and/or to smooth observations using neighboured observations.

### Usage

    binomLikelihoodSmooth(pred.pos, pos, m, n, h)

### Arguments

`pred.pos` | A vector of positions where p should be estimated.
`pos` | A vector of positions where binomial variables have been observed.
`m` | A vector of length `pos` with the number of successfull experiments.
`n` | A vector of length `pos` with the number of experiments.
`h` | The bandwidth of the kernel.

### Details

For a given position x, the weighted likelihood for parameter p

L(p; m, n, w) = ∏_{i=1}^k B(m_i|n_i,p)^{w_i}

is maximized. B denotes the binomial probability function. The weights w_i are calculated using a triangular kernel with bandwidth h:

w_i = K(x_i) = (1 - (|x - x_i|)/h) \mathbf{1}_{((|x - x_i|)/h) ≤ 1}

### Value

A vector of length `pred.pos` giving the local likelihood estimation of the success probability p at the given positions.

### Author(s)

Hans-Ulrich Klein

### See Also

`predictMeth`

### Examples

    n = rpois(100, lambda=10)
    E = c(rep(0.4, 30), rep(0.8, 40), rep(0.1, 30))
    m = rbinom(100, n, E)
    pos = 1:100
    p_10 = binomLikelihoodSmooth(pos, pos, m, n, h=10)
    p_20 = binomLikelihoodSmooth(pos, pos, m, n, h=20)

    ## Not run: plot(x=pos, y=m/n)
    points(x=pos, y=p_10, col="green")
    lines(x=pos, y=p_10, col="green")
    points(x=pos, y=p_20, col="red")
    lines(x=pos, y=p_20, col="red")
    ## End(Not run)

[Package BiSeq version 1.22.0 Index]