MIT media Lab note (1998)

A common question in statistical modeling is ``which out of a continuum of
models are likely to have generated this data?'' For the Gaussian class of
models, this question can be answered completely and exactly. This paper
derives the exact posterior distribution over the mean and variance of the
generating distribution, i.e. `p(m, V | X)`, as well as the
marginals `p(m | X)` and `p(V | X)`. It also derives
`p(X | Gaussian)`, the probability that the data came from any
Gaussian whatsoever. From this we can get the posterior predictive density
`p(x | X)`, which has the most practical importance. The analysis
is done for noninformative priors and for arbitrary conjugate priors. The
presentation borrows from MacKay (1995). The paper concludes with a
simulated classification experiment demonstrating the advantage of the
Bayesian method over maximum-likelihood and unbiased estimation.

Last modified: Fri Dec 10 14:30:48 GMT 2004