binomixp {Bolstad} | R Documentation |
Binomial sampling with a beta mixture prior
Description
Evaluates and plots the posterior density for pi, the
probability of a success in a Bernoulli trial, with binomial
sampling when the prior density for pi is a mixture of two
beta distributions, beta(a_0,b_0) and beta(a_1,b_1).
Usage
binomixp(x, n, alpha0=c(1,1), alpha1=c(1,1), p=0.5, ret = FALSE)
Arguments
x |
the number of observed successes in the binomial experiment. |
n |
the number of trials in the binomial experiment. |
alpha0 |
a vector of length two containing the parameters,
a0 and b0, for the first component beta prior - must be
greater than zero. By default the elements of alpha0 are set
to 1. |
alpha1 |
a vector of length two containing the parameters,
a1 and b1, for the second component beta prior - must be
greater than zero. By default the elements of alpha1 are set
to 1. |
p |
The prior mixing proportion for the two component beta
priors. That is the prior is
p*beta(a0,b0)+(1-p)*beta(a1,b1). p is set to 0.5 by default |
ret |
this argument is deprecated. |
Value
A list will be returned with the following components:
pi |
the values of pi for which the posterior density was evaluated |
posterior |
the posterior density of pi given n and x |
likelihood |
the likelihood function for pi
given x and n, i.e. the binomial(n,pi) density |
prior |
the prior density of pi density |
See Also
binodp
binogcp
normmixp
Examples
## simplest call with 6 successes observed in 8 trials and a 50:50 mix
## of two beta(1,1) uniform priors
binomixp(6,8)
## 6 successes observed in 8 trials and a 20:80 mix of a non-uniform
## beta(0.5,6) prior and a uniform beta(1,1) prior
binomixp(6,8,alpha0=c(0.5,6),alpha1=c(1,1),p=0.2)
## 4 successes observed in 12 trials with a 90:10 non uniform beta(3,3) prior
## and a non uniform beta(4,12).
## Plot the stored prior, likelihood and posterior
results = binomixp(4,12,c(3,3),c(4,12),0.9)
par(mfrow=c(3,1))
y.lims = c(0,1.1*max(results$posterior,results$prior))
plot(results$pi,results$prior,ylim=y.lims,type="l"
,xlab=expression(pi),ylab="Density",main="Prior")
polygon(results$pi,results$prior,col="red")
plot(results$pi,results$likelihood,type="l"
,xlab=expression(pi),ylab="Density",main="Likelihood")
polygon(results$pi,results$likelihood,col="green")
plot(results$pi,results$posterior,ylim=y.lims,type="l"
,xlab=expression(pi),ylab="Density",main="Posterior")
polygon(results$pi,results$posterior,col="blue")
[Package
Bolstad version 0.2-17
Index]