Anastasia Papavasiliou

 Adaptive filtering with particles

Abstract: Suppose that we have a partially observed Markov chain with
transition kernel depending on an unknown parameter theta. For each time
point, we want to compute the conditional distribution of the Markov chain
given observations up to that point, while simultaneously get an estimate
of theta. I will show how to compute the conditional probability
recursively, using the Interactive Particle Filter and prove that the
estimator of theta will converge to the true value of the parameter, under
certain conditions. This method has a wide variety of applicatinos,
ranging from finance to Independent Component Analysis.