Bolstad (version 0.2-41)

binobp: 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, pi = seq(0, 1, by = 0.001), ...)

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

pi

A range of values for the prior to be calculated over.

…

additional arguments that are passed to Bolstad.control

Value

An object of class 'Bolstad' is returned. This is a list with the following components:

prior

the prior density of \(\pi\), i.e. the \(beta(a,b)\) density

likelihood

the likelihood of \(x\) given \(\pi\) and \(n\), i.e. the \(binomial(n,\pi)\) density

posterior

the posterior density of \(\pi\) given \(x\) and \(n\) - i.e. the \(beta(a+x,b+n-x)\) 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

cdf

a cumulative distribution function for the posterior

quantileFun

a quantile function for the posterior

See Also

binodp binogcp

Examples

# NOT RUN {
## 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)
decomp(results)


# }