Erlang mixture modeling for Poisson process intensities
| Autor: | Athanasios Kottas, Hyotae Kim |
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| Rok vydání: | 2021 |
| Předmět: |
FOS: Computer and information sciences
Statistics and Probability Gamma process Density estimation Poisson distribution Erlang (unit) Point process Theoretical Computer Science Methodology (stat.ME) symbols.namesake Computational Theory and Mathematics Prior probability symbols Applied mathematics Statistics Probability and Uncertainty Scale parameter Gaussian process Statistics - Methodology Mathematics |
| Zdroj: | Statistics and Computing. 32 |
| ISSN: | 1573-1375 0960-3174 |
| Popis: | We develop a prior probability model for temporal Poisson process intensities through structured mixtures of Erlang densities with common scale parameter, mixing on the integer shape parameters. The mixture weights are constructed through increments of a cumulative intensity function which is modeled nonparametrically with a gamma process prior. Such model specification provides a novel extension of Erlang mixtures for density estimation to the intensity estimation setting. The prior model structure supports general shapes for the point process intensity function, and it also enables effective handling of the Poisson process likelihood normalizing term resulting in efficient posterior simulation. The Erlang mixture modeling approach is further elaborated to develop an inference method for spatial Poisson processes. The methodology is examined relative to existing Bayesian nonparametric modeling approaches, including empirical comparison with Gaussian process prior based models, and is illustrated with synthetic and real data examples. |
| Databáze: | OpenAIRE |
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