binobp {Bolstad}R Documentation

Binomial sampling with a beta prior

Description

Evaluates and plots the posterior density for pi, 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 this argument is deprecated.

Value

A list will be returned with the following components:
posterior the posterior density of pi given x and n - i.e. the beta(a+x,b+n-x) density
likelihood the likelihood of x given pi and n, i.e. the binomial(n,pi) density
prior the prior density of pi, i.e. the beta(a,b) density
pi the values of pi 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)

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,ylim=c(0,0.25),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]