Particle methods for optimal filter derivative: Application to parameter estimation

Particle filtering techniques are a popular set of simulationbased methods to perform optimal state estimation in non linear non Gaussian dynamic models. However, in applications related to control and identification, it is often necessary to be able to compute the derivative of the optimal filter with respect to parameters of the dynamic model. Several methods have already been proposed in the literature. In experiments, the approximation errors increase with the dataset length. We propose here original particle methods to approximate numerically the filter derivative. In simulations, these methods do not suffer from the problem mentioned. Applications to batch and recursive parameter estimation are presented

Particle approximations of the score and observed information matrix in state space models with application to parameter estimation

Particle methods are popular computational tools for Bayesian inference in nonlinear non-Gaussian state space models. For this class of models, we present two particle algorithms to compute the score vector and observed information matrix recursively. The first algorithm is implemented with computational complexity and the second with complexity , where N�is the number of particles. Although cheaper, the performance of the �method degrades quickly, as it relies on the approximation of a sequence of probability distributions whose dimension increases linearly with time. In particular, even under strong mixing assumptions, the variance of the estimates computed with the �method increases at least quadratically in time. The more expensive �method relies on a nonstandard particle implementation and does not suffer from this rapid degradation. It is shown how both methods can be used to perform batch and recursive parameter estimation. Copyright 2011, Oxford University Press.

ONLINE PARAMETER ESTIMATION FOR PARTIALLY OBSERVED DIFFUSIONS

This paper proposes novel particle methods for online parameter estimation for partially observed diffusions. We consider diffusions observed with error under a non-linear mapping and multivariate diffusions where only a subset of the components is observed. The proposed methods rely on the commonly used idea of data augmentation and are based on obtaining particle approximations to the derivatives of the optimal filter. The performance of our algorithms is assessed using several financial applications. 1