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

normnp {Bolstad}

R Documentation

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

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)