normal.inverse.wishart.prior {Boom}

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(s)

Steven L. Scott [e-mail]

References

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