Abstract
In this paper a comparative evaluation study on popular non-homogeneous Poisson models for count data is performed. For the study the standard homogeneous Poisson model (HOM) and three non-homogeneous variants, namely a Poisson changepoint model (CPS), a Poisson free mixture model (MIX), and a Poisson hidden Markov model (HMM) are implemented in both conceptual frameworks: a frequentist and a Bayesian framework. This yields eight models in total, and the goal of the presented study is to shed some light onto their relative merits and shortcomings. The first major objective is to cross-compare the performances of the four models (HOM, CPS, MIX and HMM) independently for both modelling frameworks (Bayesian and frequentist). Subsequently, a pairwise comparison between the four Bayesian and the four frequentist models is performed to elucidate to which extent the results of the two paradigms (‘Bayesian vs. frequentist’) differ. The evaluation study is performed on various synthetic Poisson data sets as well as on real-world taxi pick-up counts, extracted from the recently published New York City Taxi database.
Highlights
The Poisson distribution is one of the most popular statistical standard tools for analysing count data, i.e. integer-valued samples
The study was performed on various synthetic data sets and on taxi pick-up counts, extracted from the recently published New York City Taxi (NYCT) database, described in Sect
If the data is informative enough, in both frameworks (Bayesian and frequentist) all three non-homogeneous models can approximate all kinds of non-homogeneity, unless there is a clear mismatch between the model and the underlying data
Summary
The Poisson distribution is one of the most popular statistical standard tools for analysing (homogeneous) count data, i.e. integer-valued samples. (iii) Third, the three approaches can be formulated and implemented in both conceptual frameworks: the standard ‘frequentist’ framework and the Bayesian framework Despite this popularity, the performances of the resulting non-homogeneous models have never been systematically compared with each other in the statistical literature. This paper tries to fill this gap and presents a comparative evaluation study on nonhomogeneous Poisson count data, for which those three well-known statistical models (changepoint models, mixture models and hidden Markov models) are implemented in both conceptual frameworks: the frequentist framework and the Bayesian framework. The non-stationarity is implemented intrinsically by temporal changepoints, at which the Poisson process spontaneously changes its values Within this introductory text no literature references have been given, since detailed descriptions of all those generic statistical concepts, mentioned so far, can be found in many standard textbooks on Statistics, and in principle, will be familiar for most of the readers.
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