nvaricp: Bayesian inference for a normal standard deviation with a...

In Bolstad: Functions for Elementary Bayesian Inference

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 sigma 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))

Bolstad documentation built on Jan. 8, 2021, 2:03 a.m.