estimation_methods.Rmd
library(iNZightBayes)The ‘iNZightBayes’ package uses simple Bayesian estimation methods to obtain summaries for some common problems, such as a sample mean or proportion, ANOVA (multiple means), and linear regression.
Here we are calculating the mean \(\mu\) and variance \(\sigma^2\) of a single numeric variable \(y\) with length \(n\), using a Gibbs sampler. The model is \[p(\mu,\sigma^2|y) \propto p(y|\mu,\sigma^2) p(\mu) p(\sigma^2)\] where the prior on \(\mu\) is Normal with mean \(\mu_0\) and variance \(\sigma_0^2\), and the prior on \(\sigma^2\) is Inverse-Gamma with parameters \(\alpha\) and \(\beta\). The likelihood for \(y\) is Normal with mean \(\mu\) and variance \(\sigma^2\).
Since these are conjugate, the full conditionals needed for Gibbs sampling are \[p(\mu^{(i+1)}|\sigma^2, \ldots) = \ldots\]