Nonparametric Bayesian inference for Levy subordinators - VVSOR - VVSOR

Vereniging voor Statistiek en Operations Research

Nonparametric Bayesian inference for Levy subordinators

We cordially invite you to the last Bayes club meeting of this semester, taking place on the 30th November (Friday) between 4 pm and 5 pm in Leiden (room 403, Mathematical Institute).

Speaker: Moritz Schauer (Leiden)
Title: Nonparametric Bayesian inference for Levy subordinators
Time: 16:00-17:00, 30th of November, 2018
Location: room 403, Snellius building, Niels Bohrweg 1

Abstract: Given discrete-time observations over a growing time interval, we consider a non-parametric Bayesian approach to estimation of the Lévy density of a Lévy process belonging to a flexible class of infinite 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 an infinite-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 non-parametric Bayesian procedure is consistent: in the low-frequency data setting, with observations equi-spaced in time and intervals between successive observations remaining fixed, the posterior asymptotically, as the sample size grows to infinity, concentrates around the Lévy density under which the data have been generated. Finally, we test our method on an insurance dataset.

 

Joint work with Denis Belomestny, Shota Gugushvili, Peter Spreij