Evolutionary Sequential Monte Carlo Samplers for Change-Point Models

To evaluate a fitting of a statistical model to given data, calculating aconditional $p$ value by a Markov chain Monte Carlo method is one of the effective approaches. For this purpose, a Markov basis plays an important role because it guarantees the connectivity of the chain for unbiasedness of the estimation, and therefore is investigated in various settings such as incomplete tables or subtable sum constraints. In this paper, we consider the two-way change-point model for the ladder determinantal table, which is an extension of these two previous works. Our main result is based on the theory of Groebner basis for the distributive lattice. We give a numerical example for actual data.

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Bayesian Analysis

10.1093/oxfordhb/9780199286546.003.0021 ◽

2009 ◽

Author(s):

Andrew D. Martin

Keyword(s):

Social Sciences ◽

Monte Carlo ◽

Political Science ◽

Bayesian Methods ◽

Change Point ◽

Prior Information ◽

Mcmc Methods ◽

The Social ◽

Change Point Models ◽

The Bayesian Approach

This article surveys modern Bayesian methods of estimating statistical models. It first provides an introduction to the Bayesian approach for statistical inference, contrasting it with more conventional approaches. It then explains the Monte Carlo principle and reviews commonly used Markov Chain Monte Carlo (MCMC) methods. This is followed by a practical justification for the use of Bayesian methods in the social sciences, and a number of examples from the literature where Bayesian methods have proven useful are shown. The article finally provides a review of modern software for Bayesian inference, and a discussion of the future of Bayesian methods in political science. One area ripe for research is the use of prior information in statistical analyses. Mixture models and those with discrete parameters (such as change point models in the time-series context) are completely underutilized in political science.

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Bayesian Estimation of DSGE Models

10.23943/princeton/9780691161082.001.0001 ◽

2015 ◽

Cited By ~ 45

Author(s):

Edward P. Herbst ◽

Frank Schorfheide

Keyword(s):

Monte Carlo ◽

Sequential Monte Carlo ◽

Likelihood Function ◽

Academic Research ◽

Dynamic Stochastic General Equilibrium ◽

Computational Techniques ◽

Dsge Models ◽

Monte Carlo Techniques ◽

Dynamic Stochastic ◽

Theoretical Foundations

Dynamic stochastic general equilibrium (DSGE) models have become one of the workhorses of modern macroeconomics and are extensively used for academic research as well as forecasting and policy analysis at central banks. This book introduces readers to state-of-the-art computational techniques used in the Bayesian analysis of DSGE models. The book covers Markov chain Monte Carlo techniques for linearized DSGE models, novel sequential Monte Carlo methods that can be used for parameter inference, and the estimation of nonlinear DSGE models based on particle filter approximations of the likelihood function. The theoretical foundations of the algorithms are discussed in depth, and detailed empirical applications and numerical illustrations are provided. The book also gives invaluable advice on how to tailor these algorithms to specific applications and assess the accuracy and reliability of the computations. The book is essential reading for graduate students, academic researchers, and practitioners at policy institutions.

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