binodp: Binomial sampling with a discrete prior

In Bolstad: Functions for Elementary Bayesian Inference

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, ...)

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
...	additional arguments that are passed to Bolstad.control

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(pi)))
box()
legend("topleft", bty = "n", cex = 0.7, 
       legend = c("Prior", "Posterior"), fill = c("red", "blue"))

Bolstad documentation built on Jan. 8, 2021, 2:03 a.m.