Markov Chain Monte Carlo Technology

In the past fifteen years computational statistics has been enriched by a powerful, somewhat abstract method of generating variates from a target probability distribution that is based on Markov chains whose stationary distribution is the probability distribution of interest. This class of methods, popularly referred to as Markov chain Monte Carlo methods, or simply MCMC methods, have been influential in the modern practice of Bayesian statistics where these methods are used to summarize the posterior distributions that arise in the context of the Bayesian prior-posterior analysis (Tanner and Wong, 1987; Gelfand and Smith, 1990; Smith and Roberts, 1993; Tierney, 1994; Besaget al., 1995; Chib and Greenberg, 1995, 1996; Gilks et al., 1996; Tanner, 1996; Gammerman, 1997; Robert and Casella, 1999; Carlin and Louis, 2000; Chen et al., 2000; Chib, 2001; Congdon, 2001; Liu, 2001; Robert, 2001; Gelman at al, 2003). MCMC methods have proved useful in practically all aspects of Bayesian inference, for example, in the context of prediction problems and in the computation of quantities, such as the marginal likelihood, that are used for comparing competing Bayesian models. --

Non-Markovian Regime Switching with Endogenous States and Time-Varying State Strengths

This article presents a non-Markovian regime switching model in which the regime states depend on the sign of an autoregressive latent variable. The magnitude of the latent variable indexes the `strength' of the state or how deeply the system is embedded in the current regime. The autoregressive nature of this non-Markovian regime switching implies time-varying state transition probabilities, even in the absence of an exogenous covariate. Furthermore, with time-varying regime strengths, the expected duration of a regime is time-varying. In this framework, it is natural to allow the autoregressive latent variable to be endogenous so that regimes are determined jointly with the observed data. We apply the model to GDP growth, as in Hamilton (1989), Albert and Chib (1993) and Filardo and Gordon (1998) to illustrate the relation of the regimes to NBER-dated recessions and the time-varying expected durations of regimesRegime switching; Markov Chain Monte Carlo

Posterior inference on the degrees of freedom parameter in multivariate-t regression models

Economics

Regression models under competing covariance matrices: A Bayesian perspective

Economics

A Bayesian note on competing correlation structures in the dynamic linear regression model

Economics

Multivariate stochastic volatility (Revised in May 2007, Handbook of Financial Time Series (Published in "Handbook of Financial Time Series" (eds T.G. Andersen, R.A. Davis, Jens-Peter Kreiss and T. Mikosch), 365-400. Springer-Verlag: New York. April 2009. )

The success of univariate stochastic volatility (SV) models in relation to univariate GARCH models has spurred an enormous interest in generalizations of SV models to a multivariate setting. A large number of multivariate SV (MSV) models are now available along with clearly articulated estimation recipes. Our goal in this paper is to provide the first detailed summary of the various model formulations, along with connections and differences, and discuss how the models are estimated. We aim to show that the developments and achievements in this area represent one of the great success stories of financial econometrics.

Estimation of heterogeneous preferences, with an application to demand for internet services

This paper presents a structural econometric framework for discrete and continuous consumer choices in which unobserved intrapersonal and interpersonal preference heterogeneity is modeled explicitly. It outlines a simulation-assisted estimation methodology applicable in this framework. This methodology is illustrated in an application to analyze data from the U.C. Berkeley Internet Demand Experiment