Variance reduction for Markov chains with application to MCMC
In this paper we propose a novel variance reduction approach for additive functionals of Markov chains based on minimization of an estimate for the asymptotic variance of these functionals over suitable classes of control variates. A distinctive feature of the proposed approach is its ability to significantly reduce the overall finite sample variance. This feature is theoretically demonstrated by means of a deep non asymptotic analysis of a variance reduced functional as well as by a thorough simulation study. In particular we apply our method to various MCMC Bayesian estimation problems where it favourably compares to the existing variance reduction approaches.
In his book, Rowan Wilken, lecturer at the University of Swinburne, Australia, makes an attempt at providing a theoretical frame for a three-dimensional problem: the relation between new technologies, communities and places. His main goal is to sculpt an understanding of the relationship between place and community, both of which are transcended by what he calls 'teletechnologies' such as mobile phones, internet and their eventual derivatives. Looking for ‘productive theoretical possibilities to make sense of the complex interactions and interconnections between teletechnologies, place, and community’ appears to be a very difficult task.
What factors best explain the low incidence of skills training in a late industrial society like Russia? This research undertakes a multilevel analysis of the role of occupational structure against the probability of training. The explanatory power of occupation-specific determinants and skills polarisation are evaluated, using a representative 2012 sample from the Russian Longitudinal Monitoring Survey. Applying a two-level Bayesian logistic regression model, we show that the incidence of training in Russia is significantly contextualised within the structure of occupations and the inequalities between them. The study shows that extremely high wage gaps within managerial class jobs can discourage training, an unusual finding. Markets accumulating interchangeable and disposable labour best explain the low incidence of training; workers within generic labour are less likely to develop their skills formally, except in urban markets. Although we did not find strong evidence of skills polarisation, Russians are yet to live in a knowledge economy.
Given discrete time observations over a growing time interval, we consider a nonparametric Bayesian approach to estimation of the Levy density of a Levy 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 a new 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 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 tends to infinity, concentrates around the Levy density under which the data have been generated. Finally, we test our method on a classical insurance dataset.
This proceedings publication is a compilation of selected contributions from the “Third International Conference on the Dynamics of Information Systems” which took place at the University of Florida, Gainesville, February 16–18, 2011. The purpose of this conference was to bring together scientists and engineers from industry, government, and academia in order to exchange new discoveries and results in a broad range of topics relevant to the theory and practice of dynamics of information systems. Dynamics of Information Systems: Mathematical Foundation presents state-of-the art research and is intended for graduate students and researchers interested in some of the most recent discoveries in information theory and dynamical systems. Scientists in other disciplines may also benefit from the applications of new developments to their own area of study.