Approximate Bayesian inference methods for mixture filtering with known model of switching

Bayesian inference has proven itself to be a practically useful tool for many scientific fields. The exact Bayesian inference is, however, possible in only a narrow class of probabilistic models enjoying the conjugacy principle. It is rather typical that the principle does not hold, and therefore the approximate Bayesian inference methods are taken into account. The present paper compares some of these techniques on a mixture filtering problem. The methods are presented in a generic way, considering that the mixture components are members of the exponential family of probability distributions and that the Markov model of switching between the mixture components is known. A particular instance of the methods is given for a mixture of normal linear state space models, and experiments evaluating the estimation precision and computational time are performed.