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, n.mu = 100, ret = FALSE)
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 is is by default,
then a flat prior is used and m.x and s.x are ignored |
n.mu |
the number of possible mu values in the prior |
ret |
this argument is deprecated. |
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)
[Package
Bolstad version 0.2-17
Index]