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# Efficient Bayesian Methods for Counting Processes in Partially Observable Environments

*Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics*, PMLR 84:1906-1913, 2018.

#### Abstract

When sensors that count events are unreliable, the data sets that result cannot be trusted. We address this common problem by developing practical Bayesian estimators for a partially observable Poisson process (POPP). Unlike Bayesian estimation for a fully observable Poisson process (FOPP) this is non-trivial, since there is no conjugate density for a POPP and the posterior has a number of elements that grow exponentially in the number of observed intervals. We present two tractable approximations, which we combine in a switching filter. This switching filter enables efficient and accurate estimation of the posterior. We perform a detailed empirical analysis, using both simulated and real-world data.