Random Walk Metropolis-Hastings Algorithm Research Articles

Computationally Efficient Poisson Time-Varying Autoregressive Models through Bayesian Lattice Filters

Estimation of time-varying autoregressive models for count-valued time series can be computationally challenging. In this direction, we propose a time-varying Poisson autoregressive (TV-Pois-AR) model that accounts for the changing intensity of the Poisson process. Our approach can capture the latent dynamics of the time series and therefore make superior forecasts. To speed up the estimation of the TV-AR process, our approach uses the Bayesian Lattice Filter. In addition, the No-U-Turn Sampler (NUTS) is used, instead of a random walk Metropolis–Hastings algorithm, to sample intensity-related parameters without a closed-form full conditional distribution. The effectiveness of our approach is evaluated through model-based and empirical simulation studies. Finally, we demonstrate the utility of the proposed model through an example of COVID-19 spread in New York State and an example of US COVID-19 hospitalization data.

New Computer Experiment Designs Using Continuum Random Cluster Point Process

In this paper, we propose a new approach for building computer experiment designs using the continuum random cluster point process, also referred to as the connected component Markov point process. Our method involves generating designs through the Markov Chain Monte Carlo method (MCMC) and the Random Walk Metropolis Hastings algorithm (RWMH algorithm), which can be easily scaled to meet various objectives. We have conducted a comprehensive study on the convergence of the Markov chain and compared our approach with existing computer experiment designs. Overall, our approach offers a novel and flexible solution for constructing computer experiment designs.

Dimension-Free Mixing for High-Dimensional Bayesian Variable Selection

AbstractYang et al. proved that the symmetric random walk Metropolis–Hastings algorithm for Bayesian variable selection is rapidly mixing under mild high-dimensional assumptions. We propose a novel Markov chain Monte Carlo (MCMC) sampler using an informed proposal scheme, which we prove achieves a much faster mixing time that is independent of the number of covariates, under the assumptions of Yang et al. To the best of our knowledge, this is the first high-dimensional result which rigorously shows that the mixing rate of informed MCMC methods can be fast enough to offset the computational cost of local posterior evaluation. Motivated by the theoretical analysis of our sampler, we further propose a new approach called ‘two-stage drift condition’ to studying convergence rates of Markov chains on general state spaces, which can be useful for obtaining tight complexity bounds in high-dimensional settings. The practical advantages of our algorithm are illustrated by both simulation studies and real data analysis.

Applying Bayesian method to investigate determinants of non performing loans of banks in Vietnam

This study was conducted to determine the factors affecting non-performing loans of commercial banks in Vietnam for the period 2007 - 2018. The study applies the Bayesian approach and the Random-walk Metropolis-Hastings algorithm to evaluate the impact of micro and macro factors on non-performing loans of commercial banks. The dependent variable is non-performing loans, which is measured by the ratio of non-performing loans divided by total outstanding loans; the independent variables in terms of bank characteristics are non-performing loans of the previous year, profitability, bank size, bak loans, and bank capital; the macro variables are inflation and GDP growth. Research data was collected from financial statements of 30 Vietnamese commercial banks and the General Statistics Office of Vietnam from 2007 to 2018. To increase the reliability and efficiency of the model as well as reasonable Bayes inference, a convergence test of the MCMC chain was performed. The result of this study shows that non-performing loans of the previous year, bank size, bank loan, bank capital, and inflation have positive impacts on bank non-performing loans. In addition, bank profitability and GDP growth rate are factors that have the opposite effects. Based on the research results, the author proposes policy implications for the decision-makers to help banks reduce non-performing loans and promote banks to operate effectively and more efficiently.

Bayesian Inference in Extremes Using the Four-Parameter Kappa Distribution

Maximum likelihood estimation (MLE) of the four-parameter kappa distribution (K4D) is known to be occasionally unstable for small sample sizes and to be very sensitive to outliers. To overcome this problem, this study proposes Bayesian analysis of the K4D. Bayesian estimators are obtained by virtue of a posterior distribution using the random walk Metropolis–Hastings algorithm. Five different priors are considered. The properties of the Bayesian estimators are verified in a simulation study. The empirical Bayesian method turns out to work well. Our approach is then compared to the MLE and the method of the L-moments estimator by calculating the 20-year return level, the confidence interval, and various goodness-of-fit measures. It is also compared to modeling using the generalized extreme value distribution. We illustrate the usefulness of our approach in an application to the annual maximum wind speeds in Udon Thani, Thailand, and to the annual maximum sea-levels in Fremantle, Australia. In the latter example, non-stationarity is modeled through a trend in time on the location parameter. We conclude that Bayesian inference for K4D may be substantially useful for modeling extreme events.

How Much Better Is Commitment Policy Than Discretionary Policy? Evidence From Six Developed Economies

Abstract Much has been written on how an active central bank produces inflation outcomes above and beyond what commitment policy would produce. This paper contributes to this body of literature by simulating from the state estimates of both commitment and discretionary policy equilibria in a familiar dynamic New–Keynesian framework. Optimal interest rate and inflation rate policies are derived under the two regimes for six developed economies. The model is estimated using Bayesian methods employing a random-walk Metropolis–Hastings algorithm. Optimal inflation and interest rate policies for each of the economies are simulated. Results suggest that the simulated inflation induced by discretionary policy is not significantly different from commitment policy after 2000 for five of the six countries (including the U.S). Simulated commitment interest rate policy is on average 1.9% higher at the center of the distribution, suggesting that discretionary interest rate policy is on average more often loose compared to commitment interest rate policy. Simulations of the average inflation deviation and welfare loss of discretion policy indicate are greatest when the central bank exhibits low preference for inflation targeting and high preference for output stability.

Bayesian estimation of generalized partition of unity copulas

Abstract This paper proposes a Bayesian estimation algorithm to estimate Generalized Partition of Unity Copulas (GPUC), a class of nonparametric copulas recently introduced by [18]. The first approach is a random walk Metropolis-Hastings (RW-MH) algorithm, the second one is a random blocking random walk Metropolis-Hastings algorithm (RBRW-MH). Both approaches are Markov chain Monte Carlo methods and can cope with ˛at priors. We carry out simulation studies to determine and compare the efficiency of the algorithms. We present an empirical illustration where GPUCs are used to nonparametrically describe the dependence of exchange rate changes of the crypto-currencies Bitcoin and Ethereum.

A novel Bayesian approach for variable selection in linear regression models

A novel Bayesian approach to the problem of variable selection in multiple linear regression models is proposed. In particular, a hierarchical setting which allows for direct specification of a priori beliefs about the number of nonzero regression coefficients as well as a specification of beliefs that given coefficients are nonzero is presented. This is done by introducing a new prior for a random set which holds the indices of the predictors with nonzero regression coefficients. To guarantee numerical stability, a g-prior with an additional ridge parameter is adopted for the unknown regression coefficients. In order to simulate from the joint posterior distribution an intelligent random walk Metropolis–Hastings algorithm which is able to switch between different models is proposed. For the model transitions a novel proposal, which prefers to add a priori or empirically important predictors to the model and further tries to remove less important ones, is used. Testing the algorithm on real and simulated data illustrates that it performs at least on par and often even better than other well-established methods. Finally, it is proven that under some nominal assumptions, the presented approach is consistent in terms of model selection.

Fast Li-ion conduction at grain boundaries in (La,Li)NbO3 polycrystals

We have investigated optimum synthesis condition and the lithium-ion conductivity of lithium lanthanum niobate (LLNbO) polycrystals which is a candidate for solid-state electrolyte in all solid-state Li-ion secondary batteries. The LLNbO polycrystals sintered at 1470 K for 12 h show the highest sintered density, the largest average grain size and the largest ionic conductivity in both the bulk and at the grain boundary. Unlike the other oxide electrolytes, the Li-ion conductivity at the grain boundary is three-times larger than that in the bulk, which is statistically confirmed by using random walk Metropolis Hastings algorithm. We also evaluated the activation energies for Li-ion conduction in LLNbO polycrystals and we found the activation energy at the grain boundary is also 1.5 times lower than that in the bulk. Atomic resolution electron microscopy elucidates that the conventional (La,Li)TiO3 has a strong La-enrichment at the grain boundary, while in LLNbO no significant La-enrichment was observed at the grain boundaries. The present results suggest that the local atomic configurations at the grain boundary strongly affects the Li-ion conductivity and it is therefore important to control the local atomic structures in polycrystalline electrolytes.

Random walk Metropolis algorithm in high dimension with non-Gaussian target distributions

High-dimensional asymptotics of the random walk Metropolis–Hastings algorithm are well understood for a class of light-tailed target distributions. Although this idealistic assumption is instructive, it may not always be appropriate, especially for complicated target distributions. We here study heavy-tailed target distributions for the random walk Metropolis algorithms. When the number of dimensions is d, the rate of consistency is d2 and the calculation cost is O(d3), which might be too expensive in high dimension.

Unique fitting of electrochemical impedance spectra by random walk Metropolis Hastings algorithm

A curve fitting is the most important process in the analysis of electrochemical impedance spectra to evaluate the ionic conductivity of materials. To analyze the impedance spectra, a gradient method such as steepest descent has been used so far. However, the parameter solution by using the gradient method is often trapped into local minima, and the curve fitting strongly depends on the initial parameters. In this study, to avoid the local minima issue, we propose a random walk Metropolis Hastings algorithm to analyze impedance spectra, where we can provide a unique solution of the impedance spectra. As an example, we measured the solid-state oxide electrolyte of (La0.62Li0.15)TiO3, (La0.53Li0.40)TiO3 and (La0.31Li0.07)NbO3 polycrystal and we uniquely identify the respective lithium ion conductivity at the bulk and the grain boundary by using the random walk Metropolis Hastings algorithm. The present algorithm is free from the choice of the initial values of the fitting parameters and moreover the estimated accuracy of the Li-ion conductivity is better than 5%.

A Bayesian Beta-Mixture Model for Nonparametric IRT (BBM-IRT)

Item response models typically assume that the item characteristic (step) curves follow a logistic or normal cumulative distribution function, which are strictly monotone functions of person test ability. Such assumptions can be overly-restrictive for real item response data. We propose a simple and more flexible Bayesian nonparametric IRT model for dichotomous items, which constructs monotone item characteristic (step) curves by a finite mixture of beta distributions, which can support the entire space of monotone curves to any desired degree of accuracy. A simple adaptive random-walk Metropolis-Hastings algorithm is proposed to estimate the posterior distribution of the model parameters. The Bayesian IRT model is illustrated through the analysis of item response data from a 2015 TIMSS test of math performance.

Comparison of the Sampling Efficiency in Spatial Autoregressive Model

A random walk Metropolis-Hastings algorithm has been widely used in sampling the parameter of spatial interaction in spatial autoregressive model from a Bayesian point of view. In addition, as an alternative approach, the griddy Gibbs sampler is proposed by [1] and utilized by [2]. This paper proposes an acceptance-rejection Metropolis-Hastings algorithm as a third approach, and compares these three algorithms through Monte Carlo experiments. The experimental results show that the griddy Gibbs sampler is the most efficient algorithm among the algorithms whether the number of observations is small or not in terms of the computation time and the inefficiency factors. Moreover, it seems to work well when the size of grid is 100.

SEQUENTIAL MONTE CARLO SAMPLING FOR DSGE MODELS

SUMMARYWe develop a sequential Monte Carlo (SMC) algorithm for estimating Bayesian dynamic stochastic general equilibrium (DSGE) models; wherein a particle approximation to the posterior is built iteratively through tempering the likelihood. Using two empirical illustrations consisting of the Smets and Wouters model and a larger news shock model we show that the SMC algorithm is better suited for multimodal and irregular posterior distributions than the widely used random walk Metropolis–Hastings algorithm. We find that a more diffuse prior for the Smets and Wouters model improves its marginal data density and that a slight modification of the prior for the news shock model leads to drastic changes in the posterior inference about the importance of news shocks for fluctuations in hours worked. Unlike standard Markov chain Monte Carlo (MCMC) techniques; the SMC algorithm is well suited for parallel computing. Copyright © 2014 John Wiley & Sons, Ltd.

Sequential Monte Carlo Sampling for DSGE Models

SUMMARY We develop a sequential Monte Carlo (SMC) algorithm for estimating Bayesian dynamic stochastic general equilibrium (DSGE) models; wherein a particle approximation to the posterior is built iteratively through tempering the likelihood. Using two empirical illustrations consisting of the Smets and Wouters model and a larger news shock model we show that the SMC algorithm is better suited for multimodal and irregular posterior distributions than the widely used random walk Metropolis–Hastings algorithm. We find that a more diffuse prior for the Smets and Wouters model improves its marginal data density and that a slight modification of the prior for the news shock model leads to drastic changes in the posterior inference about the importance of news shocks for fluctuations in hours worked. Unlike standard Markov chain Monte Carlo (MCMC) techniques; the SMC algorithm is well suited for parallel computing. Copyright © 2014 John Wiley & Sons, Ltd.

Sequential Monte Carlo Sampling for DSGE Models

We develop a sequential Monte Carlo (SMC) algorithm for estimating Bayesian dynamic stochastic general equilibrium (DSGE) models, wherein a particle approximation to the posterior is built iteratively through tempering the likelihood. Using three examples--an artificial state-space model, the Smets and Wouters (2007) model, and Schmitt-Grohe and Uribe's (2012) news shock model--we show that the SMC algorithm is better suited for multimodal and irregular posterior distributions than the widely-used random-walk Metropolis-Hastings algorithm. We find that a more diffuse prior for the Smets and Wouters (2007) model improves its marginal data density and that a slight modification of the prior for the news shock model leads to important changes in the posterior inference about the importance of news shocks for fluctuations in hours worked. Unlike standard Markov chain Monte Carlo (MCMC) techniques, the SMC algorithm is well suited for parallel computing.

Asteroid orbital inversion using a virtual-observation Markov-chain Monte Carlo method

A novel virtual-observation Markov-chain Monte Carlo method (MCMC) is presented for the asteroid orbital inverse problem posed by small to moderate numbers of astrometric observations. In the method, the orbital-element proposal probability density is chosen to mimic the convolution of the a posteriori density by itself: first, random errors are simulated for each observation, resulting in a set of virtual observations; second, least-squares orbital elements are derived for the virtual observations using the Nelder–Mead downhill simplex method; third, repeating the procedure gives a difference between two sets of what can be called virtual least-squares elements; and, fourth, the difference obtained constitutes a symmetric proposal in a random-walk Metropolis–Hastings algorithm, avoiding the explicit computation of the proposal density. In practice, the proposals are based on a large number of pre-computed sets of orbital elements. Virtual-observation MCMC is thus based on the characterization of the phase-space volume of solutions before the actual MCMC sampling. Virtual-observation MCMC is compared to MCMC orbital ranging, a random-walk Metropolis–Hastings algorithm based on sampling with the help of Cartesian positions at two observation dates, in the case of the near-Earth asteroid (85640) 1998 OX4. In the present preliminary comparison, the methods yield similar results for a 9.1-day observational time interval extracted from the full current astrometry of the asteroid. In the future, both of the methods are to be applied to the astrometric observations of the Gaia mission.

Sequential Monte Carlo Sampling for DSGE Models

We develop a sequential Monte Carlo (SMC) algorithm for estimating Bayesian dynamic stochastic general equilibrium (DSGE) models, wherein a particle approximation to the posterior is built iteratively through tempering the likelihood. Using three examples consisting of an artificial state-space model, the Smets and Wouters (2007) model, and Schmitt-Grohe and Uribe's (2012) news shock model we show that the SMC algorithm is better suited for multi-modal and irregular posterior distributions than the widely-used random walk Metropolis-Hastings algorithm. Unlike standard Markov chain Monte Carlo (MCMC) techniques, the SMC algorithm is well suited for parallel computing.

Efficient parallelisation of Metropolis–Hastings algorithms using a prefetching approach

Prefetching is a simple and general method for single-chain parallelisation of the Metropolis–Hastings algorithm based on the idea of evaluating the posterior in parallel and ahead of time. Improved Metropolis–Hastings prefetching algorithms are presented and evaluated. It is shown how to use available information to make better predictions of the future states of the chain and increase the efficiency of prefetching considerably. The optimal acceptance rate for the prefetching random walk Metropolis–Hastings algorithm is obtained for a special case and it is shown to decrease in the number of processors employed. The performance of the algorithms is illustrated using a well-known macroeconomic model. Bayesian estimation of DSGE models, linearly or nonlinearly approximated, is identified as a potential area of application for prefetching methods. The generality of the proposed method, however, suggests that it could be applied in other contexts as well.