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 
n.mu 
the number of possible 
... 
optional control arguments. See 
Value
A list will be returned with the following components:
mu 
the
vector of possible 
mu.prior 
the associated probability mass for the values in

likelihood 
the scaled likelihood function for

posterior 
the posterior probability of 
mean 
the posterior mean 
sd 
the posterior standard deviation 
qtls 
a selection of quantiles from the posterior density 
See Also
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)