binobp {Bolstad}R Documentation

Binomial sampling with a beta prior

Description

Evaluates and plots the posterior density for theta, the probability of a success in a Bernoulli trial, with binomial sampling and a continous Beta(a,b) prior.

Usage

binobp(x, n, a = 1, b = 1, ret = FALSE)

Arguments

x the number of observed successes in the binomial experiment.
n the number of trials in the binomial experiment.
a parameter for the beta prior - must be greater than zero
b parameter for the beta prior - must be greater than zero
ret if true then the prior and posterior are returned as a list.

Value

If ret is true, then a list will be returned with the following components:

posterior the posterior density of theta given x and n = the Beta(a+x,b+n-x) density
likelihood the likelihood of x given theta and n = the Binomial(n,theta) density
prior the prior density of theta = the Beta(a,b) density
theta the values of theta for which the posterior density was evaluated
mean the posterior mean
var the posterior variance
sd the posterior std. deviation
quantiles a set of quantiles from the posterior

See Also

binodp binogcp

Examples

## simplest call with 6 successes observed in 8 trials and a Beta(1,1) uniform 
## prior
binobp(6,8)

## 6 successes observed in 8 trials and a non-uniform Beta(0.5,6) prior
binobp(6,8,0.5,6)

## 4 successes observed in 12 trials with a non uniform Beta(3,3) prior
## plot the stored prior, likelihood and posterior
results<-binobp(4,12,3,3,ret=TRUE)

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

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

plot(results$theta,results$likelihood,ylim=c(0,0.25),type="l"
        ,xlab=expression(theta),ylab="Density",main="Likelihood")
polygon(results$theta,results$likelihood,col="green")

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



[Package Bolstad version 0.1-9 Index]