Classification of Mixtures of Spatial Point Processes via Partial Bayes Factors

Walsh, Adrian; Raftery, Adrian E.

doi:10.21236/ada459757

Cited by 3 publications

(4 citation statements)

References 5 publications

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“…Another relevant instance outside the ABC domain is provided in Dickey and Gunel (1978), who exhibit the above differences in the Bayes factors when using a non-sufficient statistic, including an example where the limiting Bayes factor, as the sample size grows to infinity, is 0 or ∞. Similarly, Walsh and Raftery (2005) compare point processes via Bayes factors constructed on summary statistics. They discuss those summary statistics (second order statistics and some based on Voronoï tesselations) depending on the misclassification rates of the corresponding Bayes factors through a simulation study.…”

Section: Summary Statisticsmentioning

confidence: 99%

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Relevant Statistics for Bayesian Model Choice

Marin

Pillai

Robert

et al. 2013

Journal of the Royal Statistical Society Series B: Statistical Methodology

113

132

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International audienceThe choice of the summary statistics that are used in Bayesian inference and in particular in approximate Bayesian computation algorithms has bearings on the validation of the resulting inference. Those statistics are nonetheless customarily used in approximate Bayesian computation algorithms without consistency checks. We derive necessary and sufficient conditions on summary statistics for the corresponding Bayes factor to be convergent, namely to select the true model asymptotically. Those conditions, which amount to the expectations of the summary statistics differing asymptotically under the two models, are quite natural and can be exploited in approximate Bayesian computation settings to infer whether or not a choice of summary statistics is appropriate, via a Monte Carlo validation

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Section: Summary Statisticsmentioning

confidence: 99%

“…However, the connection with the genuine Bayes factor was not pursued. (A connection with the ABC setting appears in the conclusion of Walsh and Raftery (), though, with a reference to Diggle and Gratton (), which is often credited as one originator of the method. )…”

Section: Introductionmentioning

confidence: 99%

Relevant Statistics for Bayesian Model Choice

Marin

Pillai

Robert

et al. 2013

Journal of the Royal Statistical Society Series B: Statistical Methodology

113

132

View full text Add to dashboard Cite

show abstract

“…Additionally, the superposition of arrival processes is used to analyze voice data in (Sriram & Whitt, 1986). More recently, Bayesian-based methods are proposed for classifying source processes from superposed observations (Walsh & Raftery, 2005), and their learning algorithms can be implemented based on MCMC (Redenbach et al, 2015) or variational inference (Rajala et al, 2016). However, all of these research fruits are based on simple point processes, like Poisson and renewal processes.…”

Section: Superposed Point Processesmentioning

confidence: 99%

Benefits from Superposed Hawkes Processes

Xu,

Luo,

Chen

et al. 2017

Preprint

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The superposition of temporal point processes has been studied for many years, although the usefulness of such models for practical applications has not be fully developed. We investigate superposed Hawkes process as an important class of such models, with properties studied in the framework of least squares estimation. The superposition of Hawkes processes is demonstrated to be beneficial for tightening the upper bound of excess risk under certain conditions, and we show the feasibility of the benefit in typical situations. The usefulness of superposed Hawkes processes is verified on synthetic data, and its potential to solve the cold-start problem of recommendation systems is demonstrated on realworld data.

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“…In the point pattern literature, the term classification usually refers to the procedure of labelling individual points within a single pattern generated by a superposition of several point processes (Dasgupta and Raftery, 1998;Redenbach et al, 2015;Walsh and Raftery, 2005). This corresponds to the typical setting of spatial statistics, where a single point pattern, obtained by some physical measurement, is analyzed.…”

Section: Introductionmentioning

confidence: 99%

Supervised Nonparametric Classification in the Context of Replicated Point Patterns

Koňasová¹,

Dvořák²

2022

Image Anal Stereol

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A spatial point pattern is a collection of points in space, representing, e.g. observed locations of trees, bird nests, centers of cells in a histological sample, etc. When several independent realizations of the underlying stochastic process are observed, these realizations are referred to as replicated point patterns. The main objective of this paper is to classify a newly observed pattern into one of the existing classes using a supervised nonparametric classification method, namely the Bayes classifier in combination with the k-nearest neighbors algorithms and the kernel regression method. The dissimilarity between a pair of patterns is defined using the functional summaries extracted from the point patterns via the Cramér-von Mises or Kolmogorov-Smirnov type formula. A set of simulation experiments is presented to investigate the performance of the proposed classifier with a dissimilarity measure based on functional summaries, such as the pair correlation function. The application of such a classifier to a real point pattern dataset is also illustrated.

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Classification of Mixtures of Spatial Point Processes via Partial Bayes Factors

Cited by 3 publications

References 5 publications

Relevant Statistics for Bayesian Model Choice

Relevant Statistics for Bayesian Model Choice

Benefits from Superposed Hawkes Processes

Supervised Nonparametric Classification in the Context of Replicated Point Patterns

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