normnp {Bolstad} | R Documentation |
Evaluates and plots the posterior density for mu, the mean of a normal distribution, with a normal prior on mu
normnp( x, m.x = 0, s.x = 1, sigma.x = NULL, mu = NULL, n.mu = max(100, length(mu)), ... )
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 mu values in the prior |
... |
optional control arguments. See |
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 |
## 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)