## 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,
m.x = 0,
s.x = 1,
sigma.x = NULL,
mu = NULL,
n.mu = max(100, length(mu)),
...
)


### Arguments

 x a vector of observations from a normal distribution with unknown mean and known std. deviation. m.x the mean of the normal prior s.x the standard deviation of the normal prior sigma.x the population std. deviation of the normal distribution. If this value is NULL, which it is by default, then a flat prior is used and m.x and s.x are ignored mu a vector of prior possibilities for the true mean. If this is null, then a set of values centered on the sample mean is used. n.mu the number of possible \mu values in the prior ... optional control arguments. See Bolstad.control

### Value

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 mean the posterior mean sd the posterior standard deviation qtls a selection of quantiles from the posterior density

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,sigma=1)

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

## 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,3,2,1)