Multidimensional replica-exchange method for free-energy calculations

We have developed a new simulation algorithm for free-energy calculations. The method is a multidimensional extension of the replica-exchange method. While pairs of replicas with different temperatures are exchanged during the simulation in the original replica-exchange method, pairs of replicas with different temperatures and/or different parameters of the potential energy are exchanged in the new algorithm. This greatly enhances the sampling of the conformational space and allows accurate calculations of free energy in a wide temperature range from a single simulation run, using the weighted histogram analysis method.Comment: 13 pages, (ReVTeX), 9 figures. J. Chem. Phys. 113 (2000), in pres

Bayesian Analysis of Markov Switching Vector Error Correction Model

This paper introduces a Bayesian approach to a Markov switching vector error correction model that allows for regime shifts in the intercept terms, the lag terms, the adjustment terms and the variance-covariance matrix. The proposed Bayesian method allows for estimation of the cointegrating vector within a nonlinear framework through Gibbs sampling so that it generates more efficient estimation than classical approaches that require a multi-stage maximum likelihood procedure. The Bayes factors are applied to test for Markov switching and model specifications. We apply the proposed model to U.S. term structure of interest rates allowing the risk premium and other parameters in the model to change with regime.Bayesian inference, Nonlinear cointegration, Markov switching model, Gibbs sampling, Bayes factor

A Monte Carlo comparison of Bayesian testing for cointegration rank

This article considers a Bayesian testing for cointegration rank, using an approach developed by Strachan and van Dijk (2007), that is based on Koop, Leon-Gonzalez, and Strachan (2006). The Bayes factors are calculated for selecting cointegrating rank. We calculate the Bayes factors using two methods - the Schwarz BIC approximation and Chib's (1995) algorithm for calculating the marginal likelihood. We run Monte Carlo simulations to compare the two methods.

Bayesian analysis of a vector autoregressive model with multiple structural breaks

This paper develops a Bayesian approach for analyzing a vector autoregressive model with multiple structural breaks based on MCMC simulation methods, extending a method developed for the univariate case by Wang and Zivot (2000). It derives the conditional posterior densities using an independent Normal-Wishart prior. The number of structural breaks is chosen by the posterior model probability based on the marginal likelihood, calculated here by the method of Chib (1995) rather than the Gelfand-Dey (1994) method used by Wang and Zivot. Monte Carlo simulations demonstrate that the approach provides generally accurate estimation for the number of structural breaks as well as their locations.Bayesian inference Structural break Cointegration Bayes factor

A perturbative method for nonequilibrium steady state of open quantum systems

We develop a method of calculating the nonequilibrium steady state (NESS) of an open quantum system that is weakly coupled to reservoirs in different equilibrium states. We describe the system using a Redfield-type quantum master equation (QME). We decompose the Redfield QME into a Lindblad-type QME and the remaining part $\mathcal{R}$. Regarding the steady state of the Lindblad QME as the unperturbed solution, we perform a perturbative calculation with respect to $\mathcal{R}$ to obtain the NESS of the Redfield QME. The NESS thus determined is exact up to the first order in the system-reservoir coupling strength (pump/loss rate), which is the same as the order of validity of the QME. An advantage of the proposed method in numerical computation is its applicability to systems larger than those in methods of directly solving the original Redfield QME. We apply the method to a noninteracting fermion system to obtain an analytical expression of the NESS density matrix. We also numerically demonstrate the method in a nonequilibrium quantum spin chain.Comment: 15 pages, 3 figures. To appear in J. Phys. Soc. Jp