On Unbiased Estimation of the Score Function for a Class of Partially Observed Diffusions

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In this talk we consider the problem of estimating the score function (or gradient of the log-likelihood) associated to a class of partially observed diffusion processes, with discretely observed, fixed length, data and finite dimensional parameters.We construct an estimator that is unbiased with no time-discretization bias. Using a simple Girsanov change of measure method to represent the score function, our methodology can be used for a wide class of diffusion processes and requires only access to a time-discretization method such as Euler-Maruyama.

Our approach is based upon a novel adaptation of the randomization schemes developed by Glynn and co-authors along with a new coupled Markov chain simulation scheme. The latter methodology is an original type of coupling of the coupled conditional particle filter. We prove that our estimator is unbiased and of finite variance. We then illustrate our methodology on several challenging statistical examples. This is a joint work with Jeremy Heng (ESSEC, Singapore) and Jeremie Houssineau (Warwick, UK).

Brief Biography

Ajay Jasra joined KAUST in July 2019 as a professor in Applied Mathematics and Computational Science. Before that, he held faculty positions at first Imperial College London (2008-2011) and then the National University of Singapore (2011-2019). He completed his PhD in statistics, in 2005, at Imperial College London under the supervision of Professor Chris Holmes (now at Oxford) and Professor David Stephens (now at McGill). Prof Jasra's work lies at the intersection of applied mathematics and statistics, with primary contributions to stochastic algorithms for data analysis. He is currently an associate editor at several journals including: Annals of Applied Probability, Stat and Statistics and Computing. He is also co-editor in chief of the AIMS journal Foundations of Data Science. 

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