This methodology is extended to the class of GARMA models with Generalized Autoregressive Conditionally Heteroskedastic (GARCH) errors. Finally, a unit root test of the index of a Gegenbauer polynomial in terms of the psedo maximum likelihood estimator is also considered.

Joint work with Professors M.S. Peiris, T. Proietti and Q. Wang.

This lecture presents a comprehensive treatment of mean field particle simulation models and interdisciplinary research topics, including sequential Monte Carlo methodologies, genetic particle algorithms, genealogical tree-based algorithms, and quantum and diffusion Monte Carlo methods.

Along with covering refined convergence analysis of particle algorithms, we also discuss applications related to parameter estimation in hidden Markov chain models, stochastic optimization, nonlinear filtering and multiple target tracking, stochastic optimization, calibration and uncertainty propagation in numerical codes, rare event simulation, financial mathematics, and free energy and quasi-invariant measures arising in computational physics and dynamic population biology.

This presentation shows how mean field particle simulation has revolutionized the field of Monte Carlo integration and stochastic algorithms. It will help theoretical probability researchers, applied statisticians, biologists, statistical physicists, and computer scientists work better across their own disciplinary boundaries.

This model is known as Kingman's paintbox, put forward by Kingman in 1976 to study random infinite partitions. In the infinite version of the above model, the X_i's are jumps of a subordinator. In 1992, Perman, Pitman and Yor derived various distributional properties of this infinite size-biased permutation. Their work found applications in species sampling, oil and gas discovery, topic modeling in Bayesian statistics, amongst many others.

In this talk, we will derive distributional properties of finite i.i.d size-biased permutation, both for fixed and asymptotic n. We have multiple derivations using tools from Perman-Pitman-Yor, as well as the induced order statistics literature. Their comparisons lead to new results, as well as simpler proofs of existing ones. Our main contribution describes the asymptotic distribution of the last few terms in a finite i.i.d size-biased permutation via a Poisson coupling with its few smallest order statistics. For example, we will answer the question: what is the asymptotic probability that the smallest block is discovered last?

Enquiries about the Statistics Seminar should be directed to the organizer John Ormerod.

Last updated on 22 July 2014.