binodp {Bolstad}R Documentation

Binomial sampling with a discrete prior

Description

Evaluates and plots the posterior density for pi, the probability of a success in a Bernoulli trial, with binomial sampling and a discrete prior on pi

Usage

binodp(x,n, pi = NULL, pi.prior = NULL, n.pi = 10, ret = FALSE)

Arguments

x the number of observed successes in the binomial experiment.
n the number of trials in the binomial experiment.
pi a vector of possibilities for the probability of success in a single trial. if pi is NULL then a discrete uniform prior for pi will be used.
pi.prior the associated prior probability mass.
n.pi the number of possible pi values in the prior
ret this argument is deprecated.

Value

A list will be returned with the following components:
pi the vector of possible pi values used in the prior
pi.prior the associated probability mass for the values in pi
likelihood the scaled likelihood function for pi given x and n
posterior the posterior probability of pi given x and n
f.cond the conditional distribution of x given pi and n
f.joint the joint distribution of x and pi given n
f.marg the marginal distribution of x

See Also

binobp binogcp

Examples

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

## same as previous example but with more possibilities for pi
binodp(6,8,n.pi=100)

## 6 successes, 8 trials and a non-uniform discrete prior
pi = seq(0,1,by=0.01)
pi.prior = runif(101)
pi.prior = sort(pi.prior/sum(pi.prior))
binodp(6,8,pi,pi.prior)

## 5 successes, 6 trials, non-uniform prior
pi = c(0.3,0.4,0.5)
pi.prior = c(0.2,0.3,0.5)
results = binodp(5,6,pi,pi.prior)

## plot the results from the previous example using a side-by-side barplot
results.matrix = rbind(results$pi.prior,results$posterior)
colnames(results.matrix) = pi
barplot(results.matrix,col=c("red","blue"),beside=TRUE
	,xlab=expression(pi),ylab=expression(Probability(pin)))
box()
legend(1,0.65,legend=c("Prior","Posterior"),fill=c("red","blue"))

[Package Bolstad version 0.2-17 Index]