Staff Publications

Staff Publications

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    'Staff publications' is the digital repository of Wageningen University & Research

    'Staff publications' contains references to publications authored by Wageningen University staff from 1976 onward.

    Publications authored by the staff of the Research Institutes are available from 1995 onwards.

    Full text documents are added when available. The database is updated daily and currently holds about 240,000 items, of which 72,000 in open access.

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Record number 559699
Title Nonparametric Bayesian inference for Gamma-type Lévy subordinators
Author(s) Belomestny, Denis; Gugushvili, Shota; Schauer, Moritz; Spreij, Peter
Source Communications in Mathematical Sciences 17 (2019)3. - ISSN 1539-6746 - p. 781 - 816.
DOI https://doi.org/10.4310/CMS.2019.v17.n3.a8
Department(s) Mathematical and Statistical Methods - Biometris
Publication type Refereed Article in a scientific journal
Publication year 2019
Keyword(s) Bridge sampling - Data augmentation - Gamma process - Lévy density - Lévy process - MCMC - Metropolis-Hastings algorithm - Nonparametric Bayesian estimation - Posterior consistency - Reversible jump MCMC - Subordinator - θ-subordinator
Abstract

Given discrete time observations over a growing time interval, we consider a nonparametric Bayesian approach to estimation of the Lévy density of a Lévy process belonging to a exible class of in finite activity subordinators. Posterior inference is performed via MCMC, and we circumvent the problem of the intractable likelihood via the data augmentation device, that in our case relies on bridge process sampling via Gamma process bridges. Our approach also requires the use of a new in fiite-dimensional form of a reversible jump MCMC algorithm. We show that our method leads to good practical results in challenging simulation examples. On the theoretical side, we establish that our nonparametric Bayesian procedure is consistent: in the low frequency data setting, with equispaced in time observations and intervals between successive observations remaining fixed, the posterior asymptotically, as the sample size n → ∞, concentrates around the Lévy density under which the data have been generated. Finally, we test our method on a classical insurance dataset.

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