Publikacje

Abstract:

We consider the theoretical problem of time series which arises when the distribution of the observed variable is
the de facto conditional distribution. The Kalman filter provides an effective solution to the linear Gaussian
filtering problem. However, when state/measurement functions are highly non-linear, and posterior probability
distribution of the state is non-Gaussian, the optimal linear filter and its modifications do not provide satisfactory
results. We propose the Sequential Monte Carlo method, known generically as particle filter, which combines
importance sampling and resampling schemes. In particular, we present a construction of an auxiliary particle
filter algorithm using the Pearson curves technique for approximation of importance weights of simulated
particles. The effectiveness of the method is discussed and illustrated by numerical results based on the
simulated stochastic volatility process SV

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On the particular construction of the SMC sampling method for Bayesian filtering