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## The approximating posterior distribution

The approximating posterior distribution needed in ensemble learning is over all the possible hidden state sequences and the parameter values . The approximation is chosen to be of a factorial form

 (5.13)

The approximation is a discrete distribution and it factorises as

 (5.14)

The parameters of this distribution are the discrete probabilities and .

The distribution is also formed as a product of independent distribution for different parameters. The parameters with Dirichlet priors have posterior approximations of a single Dirichlet distribution like for

 (5.15)

or a product of Dirichlet distributions as for

 (5.16)

These will actually be the optimal choices among all possible distributions, assuming the factorisation .

The parameters with Gaussian priors have Gaussian posterior approximations of the form

 (5.17)

All these parameters are assumed to be independent.

Next: Bayesian nonlinear state-space model Up: Bayesian continuous density hidden Previous: The model   Contents
Antti Honkela 2001-05-30