NormalNormalPosterior {bpp} R Documentation

Normal-Normal Posterior in conjugate normal model, for known sigma

Description

Compute the posterior distribution in a conjugate normal model for known variance: Let X_1, \ldots, X_n be a sample from a N(\mu, \sigma^2) distribution, with \sigma assumed known. We assume a prior distribution on \mu, namely N(\nu, \tau^2). The posterior distribution is then \mu|x \sim N(\mu_p, \sigma_p^2) with

\mu_p = (1 / (\sigma^2 / n) + \tau^{-2})^{-1} (\bar{x} / (\sigma^2/n) + \nu / \tau^2)

and

\sigma_p = (1 / (\sigma^2/n) + \tau^{-2})^{-1}.

These formulas are available e.g. in Held (2014, p. 182).

Usage

NormalNormalPosterior(datamean, sigma, n, nu, tau)

Arguments

 datamean Mean of the data. sigma (Known) standard deviation of the data. n Number of observations. nu Prior mean. tau Prior standard deviation.

Value

A list with the entries:

 postmean Posterior mean. postsigma Posterior standard deviation.

Author(s)

Kaspar Rufibach (maintainer)
kaspar.rufibach@roche.com

References

Held, L., Sabanes-Bove, D. (2014). Applied Statistical Inference. Springer.

Examples

## data:
n <- 25
sd0 <- 3
x <- rnorm(n, mean = 2, sd = sd0)

## prior:
nu <- 0
tau <- 2

## posterior:
NormalNormalPosterior(datamean = mean(x), sigma = sd0,
n = n, nu = nu, tau = tau)


[Package bpp version 1.0.4 Index]