Summarization and Classification of Non-Poisson Point Processes

TL;DR

This paper introduces a novel approach for summarizing and classifying non-Poisson point processes using statistical learning and a broad set of descriptive statistics to evaluate model fit.

Contribution

It proposes a new classification-based method for assessing the fit of non-Poisson point process models, expanding the range of descriptive statistics used.

Findings

Effective classification of realizations achieved

Requires a wider set of descriptive statistics

Provides a new perspective on model fitting

Abstract

Fitting models for non-Poisson point processes is complicated by the lack of tractable models for much of the data. By using large samples of independent and identically distributed realizations and statistical learning, it is possible to identify absence of fit through finding a classification rule that can efficiently identify single realizations of each type. The method requires a much wider range of descriptive statistics than are currently in use, and a new concept of model fitting which is derive from how physical laws are judged to fit data.