Posterior Contraction Rates for Gaussian Cox Processes with Non-identically Distributed Data

Grant, James and Leslie, David Stuart (2019) Posterior Contraction Rates for Gaussian Cox Processes with Non-identically Distributed Data. Working Paper. UNSPECIFIED.

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Abstract

This paper considers the posterior contraction of non-parametric Bayesian inference on non-homogeneous Poisson processes. We consider the quality of inference on a rate function λ, given non-identically distributed realisations, whose rates are transformations of λ. Such data arises frequently in practice due, for instance, to the challenges of making observations with limited resources or the effects of weather on detectability of events. We derive contraction rates for the posterior estimates arising from the Sigmoidal Gaussian Cox Process and Quadratic Gaussian Cox Process models. These are popular models where λ is modelled as a logistic and quadratic transformation of a Gaussian Process respectively. Our work extends beyond the existing analyses by providing rates at which the posterior mass placed far from the true λ shrinks for certain finite numbers of observations.

Item Type: Monograph (Working Paper)
Departments: Faculty of Science and Technology > Mathematics and Statistics
Lancaster University Management School > Management Science
ID Code: 139512
Deposited By: ep_importer_pure
Deposited On: 10 Dec 2019 15:50
Refereed?: No
Published?: Published
Last Modified: 24 Feb 2020 00:27
URI: https://eprints.lancs.ac.uk/id/eprint/139512

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