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

In Bolstad: Functions for Elementary Bayesian Inference

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

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,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)

Bolstad documentation built on Jan. 8, 2021, 2:03 a.m.