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Abstract 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.
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Anytime-valid and asymptotically efficient inference driven by predictive recursion
Summary Distinguishing two models is a fundamental and practically important statistical problem. Error rate control is crucial to the testing logic, but in complex nonparametric settings can be difficult to achieve, especially when the stopping rule that determines the data collection process is not available. This paper proposes an $ e $-process construction based on the predictive recursion algorithm originally designed to recursively fit nonparametric mixture models. The resulting predictive recursion $ e $-process affords anytime-valid inference and is asymptotically efficient in the sense that its growth rate is first-order optimal relative to the predictive recursion’s mixture model.
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- PAR ID:
- 10582636
- Publisher / Repository:
- Oxford University Press
- Date Published:
- Journal Name:
- Biometrika
- Volume:
- 112
- Issue:
- 2
- ISSN:
- 1464-3510
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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