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BIRS Workshop Lecture Videos

Approximate filtering of intensity process for Poisson count data Santitissadeekorn, Naratip


We develop a sequential data assimilation algorithm for count data modelled by a doubly stochastic Poisson process. We apply an approximation technique similar to the extended Kalman filter to develop a sub-optimal discrete-time filtering algorithm, called the extended Poisson-Kalman lter (ExPKF), where only the mean and covariance are sequentially updated using count data via the Poisson likelihood function. The ExPKF, however, is inconvenient to use when the calculation of the Hessian is difficult. Thus, we also develop an ensemble-based filter based on the Gamma prior assumption; hence, ensemble Poisson-Gamma filter (EnPGF). The implementation of EnPGF is performed in the same manner as the serial-update version of EnKF. The performances of ExPKF and EnPGF are demonstrated in several synthetic experiments where the true solution is known. For the application to real-world data, we use ExPKF to approximate the uncertainty of urban crime intensity and parameters for Hawkes process and highlight the advantage of filtering scheme (over the non-filtering scheme) to track parameter changes.

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