Boom (version 0.9.15)

normal.inverse.wishart.prior: Normal inverse Wishart prior

Description

The NormalInverseWishartPrior is the conjugate prior for the mean and variance of the multivariate normal distribution. The model says that $$\Sigma^{-1} \sim Wishart(\nu, S) \mu|\sigma \sim N(\mu_0, \Sigma/\kappa)$$

The \(Wishart(S, \nu)\) distribution is parameterized by S, the inverse of the sum of squares matrix, and the scalar degrees of freedom parameter nu.

The distribution is improper if \(\nu < dim(S)\).

Usage

NormalInverseWishartPrior(mean.guess,
                          mean.guess.weight = .01,
                          variance.guess,
                          variance.guess.weight = nrow(variance.guess) + 1)

Arguments

mean.guess

The mean of the prior distribution. This is \(\mu_0\) in the description above.

mean.guess.weight

The number of observations worth of weight assigned to mean.guess. This is \(\kappa\) in the description above.

variance.guess

A prior estimate at the value of \(\Sigma\). This is \(S^{-1}/\nu\) in the notation above.

variance.guess.weight

The number of observations worth of weight assigned to variance.guess. This is \(df\).

Author

Steven L. Scott

References

Gelman, Carlin, Stern, Rubin (2003), "Bayesian Data Analysis", Chapman and Hall.