binombeta: Binomial sampling distribution with a beta distribution of...

In yijin71/statg012: statg012: Statistical Inference at UCL

Description

Define the posterior distribution function for π ( θ | r ), with a beta prior distribution π ( θ; α, β ) and a binomial sampling distribution p ( r | θ ).

Usage

binombeta(alpha = 1, beta = 1, n, r, theta = seq(0, 1, 0.001))

Arguments

alpha	the parameter for the beta distribution ( ≥ 0 ).
beta	the parameter for the beta distribution ( ≥ 0 ).
n	the number of trials in binomial distribution.
r	the number of successes in n trials.
theta	the range of the probability of success.

Value

An object of class "g12post" is returned.

prior	the prior distribution, i.e. the beta(α,β) distribution.
likelihood	the likelihood function of r given θ, i.e. the binomial(n,r) distribution.
posterior	the posterior distribution of θ given r, i.e. the beta(α+r, β+n-r) distribution.
theta	the range of the probability of success.
pri.alpha	the alpha parameter for the beta distribution of prior.
pri.beta	the beta parameter for the beta distribution of prior.
pos.alpha	the alpha parameter for the beta distribution of posterior.
pos.beta	the beta parameter for the beta distribution of posterior.
model	the prior and likelihood type to produce the posterior.

Source

For code binombeta, based on

Curren,J.(2017) R topics documentated:bingcp-Package
'Bolstad'. Pp15.

For the theory, based on

The STATG012 slides2 Example3.6 on Moodle at UCL.

STATG012 slides2

References

Bolstad, W.M. 2007. Introduction to Bayesian Statistics. (2nd ed.). Hoboken, New Jersey: John Wiley & Sons, Inc.

See Also

summary.g12post for summararies of prior and posterior distribution.

plot.g12post for plots of prior and posterior distribution.

Examples

## simplest one with 3 successes in 10 trials and a constant
## (uniform beta(1,1)) prior, then the posterior distribution
## has exactly the same shape as the likelihood function.
a <- binombeta(n = 6, r = 2)
summary(a)

## example 3.6 : 3 successes in 10 trials and a beta(4,6) prior.
ex <- binombeta(4, 6, 10, 3)
plot(ex, lty = 1:2, col = c(4,2))

yijin71/statg012 documentation built on May 23, 2019, 4:04 p.m.