normmixp {Bolstad}R Documentation

Bayesian inference on a normal mean with a mixture of normal priors

Description

Evaluates and plots the posterior density for mu, the mean of a normal distribution, with a mixture of normal priors on mu

Usage

normmixp(x, sigma.x, prior0, prior1, p = 0.5, n.mu = 100, ret = FALSE)

Arguments

x a vector of observations from a normal distribution with unknown mean and known std. deviation.
sigma.x the population std. deviation of the observations
prior0 the vector of length 2 which contains the means and standard deviation of your precise prior
prior1 the vector of length 2 which contains the means and standard deviation of your vague prior
n.mu the number of possible mu values in the prior
p the mixing proportion for the two component normal priors
ret this argument is deprecated.

Value

A list will be returned with the following components:
mu the vector of possible mu values used in the prior
prior the associated probability mass for the values in mu
likelihood the scaled likelihood function for mu given x and sigma.x
posterior the posterior probability of mu given x and sigma.x

See Also

binomixp normdp normgcp

Examples

## generate a sample of 20 observations from a N(-0.5,1) population
x = rnorm(20,-0.5,1)

## find the posterior density with a N(0,1) prior on mu - a 50:50 mix of
## two N(0,1) densities
normmixp(x,1,c(0,1),c(0,1))

## find the posterior density with 50:50 mix of a N(0.5,3) prior and a
## N(0,1) prior on mu
normmixp(x,1,c(0.5,3),c(0,1))

## Find the posterior density for mu, given a random sample of 4 
## observations from N(mu,1), y = [2.99, 5.56, 2.83, 3.47], 
## and a 80:20 mix of a N(3,2) prior and a N(0,100) prior for mu
x = c(2.99,5.56,2.83,3.47)
normmixp(x,1,c(3,2),c(0,100),0.8)

[Package Bolstad version 0.2-17 Index]