binomixp {Bolstad}R Documentation

Binomial sampling with a beta mixture prior

Description

Evaluates and plots the posterior density for pi, the probability of a success in a Bernoulli trial, with binomial sampling when the prior density for pi is a mixture of two beta distributions, beta(a_0,b_0) and beta(a_1,b_1).

Usage

binomixp(x, n, alpha0=c(1,1), alpha1=c(1,1), p=0.5, ret = FALSE)

Arguments

x the number of observed successes in the binomial experiment.
n the number of trials in the binomial experiment.
alpha0 a vector of length two containing the parameters, a0 and b0, for the first component beta prior - must be greater than zero. By default the elements of alpha0 are set to 1.
alpha1 a vector of length two containing the parameters, a1 and b1, for the second component beta prior - must be greater than zero. By default the elements of alpha1 are set to 1.
p The prior mixing proportion for the two component beta priors. That is the prior is p*beta(a0,b0)+(1-p)*beta(a1,b1). p is set to 0.5 by default
ret this argument is deprecated.

Value

A list will be returned with the following components:

pi the values of pi for which the posterior density was evaluated
posterior the posterior density of pi given n and x
likelihood the likelihood function for pi given x and n, i.e. the binomial(n,pi) density
prior the prior density of pi density

See Also

binodp binogcp normmixp

Examples

## simplest call with 6 successes observed in 8 trials and a 50:50 mix
## of two beta(1,1) uniform priors
binomixp(6,8)

## 6 successes observed in 8 trials and a 20:80 mix of a non-uniform
## beta(0.5,6) prior and a uniform beta(1,1) prior
binomixp(6,8,alpha0=c(0.5,6),alpha1=c(1,1),p=0.2)

## 4 successes observed in 12 trials with a 90:10 non uniform beta(3,3) prior
## and a non uniform beta(4,12).
## Plot the stored prior, likelihood and posterior
results = binomixp(4,12,c(3,3),c(4,12),0.9)

par(mfrow=c(3,1))
y.lims = c(0,1.1*max(results$posterior,results$prior))

plot(results$pi,results$prior,ylim=y.lims,type="l"
	,xlab=expression(pi),ylab="Density",main="Prior")
polygon(results$pi,results$prior,col="red")

plot(results$pi,results$likelihood,type="l"
	,xlab=expression(pi),ylab="Density",main="Likelihood")
polygon(results$pi,results$likelihood,col="green")

plot(results$pi,results$posterior,ylim=y.lims,type="l"
	,xlab=expression(pi),ylab="Density",main="Posterior")
polygon(results$pi,results$posterior,col="blue")




[Package Bolstad version 0.2-17 Index]