R: Binomial sampling with a beta prior

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, 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

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)
decomp(results)