Improved prediction for independent Poisson processes under Kullback-Leibler loss

09/29/2022

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by   Xiao Li, et al.

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We consider simultaneous predictive distributions for independent Poisson observables and evaluate the performance of predictive distributions using Kullback–Leibler loss. We show that Bayesian predictive distributions based on priors constructed by superharmonic functions satisfying several conditions dominate the Bayesian predictive distribution based on the Jeffreys prior. The case that the observed data and target variables to be predicted are independent Poisson processes with different durations is also discussed.