Fast Integrations of Poisson Distributions for Dead Sensor Marginalization

In dual-phase xenon time-projection chamber there are arrays of photosensors arranged to allow for inference of the positions of interactions within the detector. If there is a gap in data left by a broken or saturated photosensors, the inference of the position is less precise and less accurate. As we are unable to repair or replace photosensors once the experiment has begun, we develop methods to estimate what would have been detected. Our group is developing a probabilistic graphical model of the correlations between the number of photons detected by adjacent photosensors that represents the probability distribution over photons detected as a Poisson distribution. To determine the posterior probability distribution over number of photons detected by a sensor then requires integration over a multivariate Poisson distribution, which is computationally intractable for high-dimensions. In this work, we present an approach more to quickly calculate and integrate over a multidimensional Poisson distribution. Our approach uses zarr, a Python array compression package, to manage large multi-dimensional arrays and approximates the log factorial to quickly calculate the Poisson distribution without overflow.