Bolstad (version 0.1-8)

binobp: 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")