# NormalNormalPosterior: Normal-Normal Posterior in conjugate normal model, for known... In bpp: Computations Around Bayesian Predictive Power

## Description

Compute the posterior distribution in a conjugate normal model for known variance: Let X_1, …, X_n be a sample from a N(μ, σ^2) distribution, with σ assumed known. We assume a prior distribution on μ, namely N(ν, τ^2). The posterior distribution is then μ|x \sim N(μ_p, σ_p^2) with

μ_p = (1 / (σ^2 / n) + τ^{-2})^{-1} (\bar{x} / (σ^2/n) + ν / τ^2)

and

σ_p = (1 / (σ^2/n) + τ^{-2})^{-1}.

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

## Usage

 1 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

  1 2 3 4 5 6 7 8 9 10 11 12 ## 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) 

bpp documentation built on Jan. 13, 2022, 5:09 p.m.