Efficient Bayesian Methods for Counting Processes in Partially Observable Environments

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.