This model has two * hyperparameters*:
the inverse of the common variance to the components
and the inverse of the variance
of the prior probability .
In the empirical Bayesian method, hyperparameters are estimated
by maximizing the * evidence* for the hyperparameters:

For the BSOM model, however, it is difficult to calculate this integral exactly, thus we need to use an approximated integral. Here, we use a Gaussian approximation (Laplace method) at the MAP estimates [5]. Now, the approximated log evidence is given by

where is the negative Hessian of the log posterior probability at the MAP estimates. The formula to calculate this Hessian is given in [2].

Wed Nov 27 14:16:58 JST 1996