Bolstad (version 0.1-8)

normnp: Bayesian inference on a normal mean with a normal prior

Description

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

Usage

normnp(x, sigma.x, m.x = 0, s.x = 1, 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 normal distribution

m.x

the mean of the normal prior

s.x

the standard deviation of the normal prior

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:
• likelihood
  the scaled likelihood function of x given mu and sigma.x
• posterior
  the posterior probability of mu given x and sigma.x
• mu
  the vector of possible mu values used in the prior
• mu.prior
  the associated probability mass for the values in mu

See Also

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
normnp(x,1)

## find the posterior density with N(0.5,3) prior on mu
normnp(x,1,0.5,3)

## Find the posterior density for mu, given a random sample of 4 
## observations from N(mu,sigma^2=1), y = [2.99, 5.56, 2.83, 3.47], 
## and a N(3,sd=2)$ prior for mu
y<-c(2.99,5.56,2.83,3.47)
normnp(y,1,3,2)