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STRONEGGER, WJ.
WHEN IS A SEQUENCE OF SUFFICIENT SIGMA-ALGEBRAS A FILTER SYSTEM
SYST CONTROL LETT. 1991; 16(6): 473-477. Doi: 10.1016/0167-6911(91)90119-Y
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Leading authors Med Uni Graz: Stronegger Willibald
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Abstract:: A very general formulation was given by van Schuppen in 1979 for stochastic dynamic systems (SDS) in terms of sigma-algebra families but not in the same generality for the corresponding filter system. As usual filters were defined indirectly as SDS solving the filtering problem, i.e. the recursive computation of the conditional state distribution. Adopting a Bayesian point of view we are able to establish a connection between statistical notions and discrete time filtering on a measure theoretic level. We show that sufficiency alone is not enough to make a sequence of statistics a filter and that the additional condition required is transitivity. We conclude that a transitive sequence of sufficient statistics is a SDS, namely a filter system.
Find related publications in this database (Keywords): STOCHASTIC DYNAMIC SYSTEMS; ADEQUACY; TRANSITIVITY; SUFFICIENCY; FILTERING; BAYESIAN MODELS