normdp {Bolstad}R Documentation

Bayesian inference on a normal mean with a discrete prior

Description

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

Usage

normdp(x, sigma.x = NULL, mu = NULL, mu.prior = NULL, n.mu = 50,
        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 normal distribution
mu a vector of possibilities for the probability of success in a single trial. If mu is NULL then a uniform prior is used.
mu.prior the associated prior probability mass.
n.mu the number of possible mu values in the prior
ret if true then the likelihood and posterior are returned as a list.

Value

If ret is true, then a list will be returned with the following components:

mu the vector of possible mu values used in the prior
mu.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

normnp 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 uniform prior on mu
normdp(x,1)

## find the posterior density with a non-uniform prior on mu
mu<-seq(-3,3,by=0.1)
mu.prior<-runif(length(mu))
mu.prior<-sort(mu.prior/sum(mu.prior))
normdp(x,1,mu,mu.prior)

## Let mu have the discrete distribution with 5 possible
## values, 2, 2.5, 3, 3.5 and 4, and associated prior probability of
## 0.1, 0.2, 0.4, 0.2, 0.1 respectively. Find the posterior 
## distribution after a drawing random sample of n = 5 observations 
## from a N(mu,1) distribution y = [1.52, 0.02, 3.35, 3.49, 1.82]
mu<-seq(2,4,by=0.5)
mu.prior<-c(0.1,0.2,0.4,0.2,0.1)
y<-c(1.52,0.02,3.35,3.49,1.82)
normdp(y,1,mu,mu.prior)

[Package Bolstad version 0.2-14 Index]