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February 2022 Thinned completely random measures with applications in competing risks models
John W. Lau, Edward Cripps
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Bernoulli 28(1): 638-662 (February 2022). DOI: 10.3150/21-BEJ1361

Abstract

We present a posterior analysis of kernel mixtures of thinned completely random measures (CRMs) for multivariate intensities, in the context of competing risks models. The construction of the thinned CRMs is derived from a common Poisson random measure that includes the thinning probabilities in its intensity and is transferable to existing Poisson partition calculus results for the posterior analysis (James (2002; Ann. Statist. 33 (2005) 1771–1799)). We derive the posterior thinned CRMs, provide generalizations of both the Blackwell and MacQueen Pólya urn formula and the (weighted) Chinese restaurant process for the variates and partitions generated from the thinned CRMs, and we outline strategies for the further development of Monte Carlo simulation for estimation.

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John W. Lau. Edward Cripps. "Thinned completely random measures with applications in competing risks models." Bernoulli 28 (1) 638 - 662, February 2022. https://doi.org/10.3150/21-BEJ1361

Information

Received: 1 May 2020; Revised: 1 April 2021; Published: February 2022
First available in Project Euclid: 10 November 2021

Digital Object Identifier: 10.3150/21-BEJ1361

Keywords: Bayesian non-parametrics , completely random measures , thinning

Rights: Copyright © 2022 ISI/BS

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Vol.28 • No. 1 • February 2022
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