Breadcrumb
Optimal filtering and the dual process
Fri 08 March 2013, 14:15
Omiros Papaspiliopoulos
Universitat Pompeu Fabra
Organisers: Nick Whiteley, Feng Yu
ABSTRACT
Joint work with Matteo Ruggiero (University of Turin)
In this talk I will present ongoing work on a class of partially observed Markov models for which the so-called filtering distributions belong in mixtures of known finite dimensional distributions, the parameters and weights of which can be computed sequentially. This class contains as special case the models for which the well-known Baum or Kalman filters can be used for the computation of the filtering distributions, and involves high and infinite-dimensional unobserved signals. The filters for this class are computable because the law of the unobserved signals in these models admits a representation in terms of an auxiliary discrete state-space, continuous-time Markov chain. This auxiliary process is directly related with the so-called dual process in population genetics, and as we show the processes in the class we identify are related to the so-called Fleming-Viot process.