In experiments with a noble liquid time-projection chamber there are arrays of photosensors positioned to allow for inference of the locations of interactions within the detector. If there is a gap in data left by a broken or saturated photosensor, inference of the position is less precise and less accurate. As it is not practical to repair or replace photosensors once the experiment has begun, methods to estimate what would have been detected are used. To determine the correlations between the number of photons detected by adjacent photosensors, we developed a method using a probabilistic graphical model with the probability distribution over number of photons represented as a Poisson distribution. Estimation of the number of photons that would have been detected by a broken photosensor then requires integration over a multivariate Poisson distribution, which is computationally intractable for high dimensions. In this work, we present an approach to more quickly calculate and integrate a multidimensional Poisson distribution. Our approach utilizes zarr, a Python array compression package, to manage large multi-dimensional arrays and an approximation of the log factorial to efficiently calculate the Poisson distribution without errors caused by integer overflow.
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