normdp {Bolstad}  R Documentation 
Bayesian inference on a normal mean with a discrete prior
Description
Evaluates and plots the posterior density for \mu
, the mean of a
normal distribution, with a discrete prior on \mu
Usage
normdp(x, sigma.x = NULL, mu = NULL, mu.prior = NULL, n.mu = 50, ...)
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 
mu 
a vector of possibilities for the probability of success in a single trial. If mu is NULL then a uniform prior is used. 
mu.prior 
the associated prior probability mass. 
n.mu 
the number of possible 
... 
additional arguments that are passed to 
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 
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 uniform prior on mu
normdp(x,1)
## find the posterior density with a nonuniform prior on mu
mu = seq(3,3,by=0.1)
mu.prior = runif(length(mu))
mu.prior = sort(mu.prior/sum(mu.prior))
normdp(x,1,mu,mu.prior)
## Let mu have the discrete distribution with 5 possible
## values, 2, 2.5, 3, 3.5 and 4, and associated prior probability of
## 0.1, 0.2, 0.4, 0.2, 0.1 respectively. Find the posterior
## distribution after a drawing random sample of n = 5 observations
## from a N(mu,1) distribution y = [1.52, 0.02, 3.35, 3.49, 1.82]
mu = seq(2,4,by=0.5)
mu.prior = c(0.1,0.2,0.4,0.2,0.1)
y = c(1.52,0.02,3.35,3.49,1.82)
normdp(y,1,mu,mu.prior)