The Poisson Maximum Entropy Model for Homogeneous Poisson Processes

Choosing between Higher Moment Maximum Entropy Models and Its Application to Homogeneous Point Processes with Random Effects

“…The choice of the gamma distribution was motivated by mathematical convenience only since it is the conjugate prior of the Poisson distribution and results in the negative binomial (NB) posterior distribution. Moreover, in [4], we concluded that the 2-moment maximum entropy prior compared very favorably to the gamma prior in the prediction for HPPr. Here, we improve on these results by the use of the k-moment maximum entropy priors (k > 2).…”

“…This example has been previously analysed using 2-moment priors in [4]. We propose a suitable prediction model and study the performance of such a model using the discrepancy measure given by (10).…”

“…In this problem, the variation is usually handled in an empirical Bayesian fashion and the gamma prior is the most common choice. In [4], we compared the performance of the 2-moment maximum entropy prior to other commonly used ones, estimating the parameters by matching moments (MM) [4][5][6][7][8][9][10] as well as maximum likelihood (ML) [6].…”