Bayesian inference for a normal standard deviation with a scaled inverse chi-squared distribution

Description

Evaluates and plots the posterior density for \sigma, the standard deviation of a Normal distribution where the mean \mu is known

Usage

nvaricp(y, mu, S0, kappa, ...)


Arguments

 y a random sample from a normal(\mu,\sigma^2) distribution. mu the known population mean of the random sample. S0 the prior scaling factor. kappa the degrees of freedom of the prior. ... additional arguments that are passed to Bolstad.control

Value

A list will be returned with the following components:

 sigma the vaules of \sigma for which the prior, likelihood and posterior have been calculated prior the prior density for \sigma likelihood the likelihood function for \sigma given y posterior the posterior density of \mu given y S1 the posterior scaling constant kappa1 the posterior degrees of freedom

Examples


## Suppose we have five observations from a normal(mu, sigma^2)
## distribution mu = 200 which are 206.4, 197.4, 212.7, 208.5.
y = c(206.4, 197.4, 212.7, 208.5, 203.4)

## We wish to choose a prior that has a median of 8. This happens when
## S0 = 29.11 and kappa = 1
nvaricp(y,200,29.11,1)

##  Same as the previous example but a calculate a 95% credible
## interval for sigma. NOTE this method has changed
results = nvaricp(y,200,29.11,1)
quantile(results, probs = c(0.025, 0.975))