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Several lessons learnt from a Bayesian analysis of basic macroeconomic time-series models are presented for the situation where some model parameters have substantial posterior probability near the boundary of the parameter region. This feature refers to near-instability within dynamic models, to forecasting with near-random walk models and to clustering of several economic series in a small number of groups within a data panel. Two canonical models are used: a linear regression model with autocorrelation and a simple variance components model. Several well-known time-series models like unit root and error correction models and further state space and panel data models are shown to be simple generalizations of these two canonical models for the purpose of posterior inference. A Bayesian model averaging procedure is presented in order to deal with models with substantial probability both near and at the boundary of the parameter region. Analytical, graphical, and empirical results using U.S. macroeconomic data, in particular on GDP growth, are presented.

A major stumbling block in multivariate discrete data analysis is the problem of evaluating the outcome probabilities that enter the likelihood function. Calculation of these probabilities involves high-dimensional integration, making simulation methods indispensable in both Bayesian and frequentist estimation and model choice. We review several existing probability estimators and then show that a broader perspective on the simulation problem can be afforded by interpreting the outcome probabilities through Bayes’ theorem, leading to the recognition that estimation can alternatively be handled by methods for marginal likelihood computation based on the output of Markov chain Monte Carlo (MCMC) algorithms. These techniques offer stand-alone approaches to simulated likelihood estimation but can also be integrated with traditional estimators. Building on both branches in the literature, we develop new methods for estimating response probabilities and propose an adaptive sampler for producing high-quality draws from multivariate truncated normal distributions. A simulation study illustrates the practical benefits and costs associated with each approach. The methods are employed to estimate the likelihood function of a correlated random effects panel data model of women's labor force participation.

Our paper discusses simulation-based Bayesian inference using information from previous draws to build the proposals. The aim is to produce samplers that are easy to implement, that explore the target distribution effectively, and that are computationally efficient and mix well.

The normal error distribution for the observations and log-volatilities in a stochastic volatility (SV) model is replaced by the Student-t distribution for robustness consideration. The model is then called the t-t SV model throughout this paper. The objectives of the paper are twofold. First, we introduce the scale mixtures of uniform (SMU) and the scale mixtures of normal (SMN) representations to the Student-t density and show that the setup of a Gibbs sampler for the t-t SV model can be simplified. For example, the full conditional distribution of the log-volatilities has a truncated normal distribution that enables an efficient Gibbs sampling algorithm. These representations also provide a means for outlier diagnostics. Second, we consider the so-called t SV model with leverage where the observations and log-volatilities follow a bivariate t distribution. Returns on exchange rates of Australian dollar to 10 major currencies are fitted by the t-t SV model and the t SV model with leverage, respectively.

Partitioned analysis is an increasingly popular approach for modeling complex systems with behaviors governed by multiple, interdependent physical phenomena. Yielding accurate representations of reality from partitioned models depends on the availability of all necessary constituent models representing relevant physical phenomena. However, there are many engineering problems where one or more of the constituents may be unavailable because of lack of knowledge regarding the underlying principles governing the behavior or the inability to experimentally observe the constituent behavior in an isolated manner through separate-effect experiments. This study aims to enable partitioned analysis in such situations with an incomplete representation of the full system by inferring the behavior of the missing constituent.

This paper presents a statistical method for inverse analysis infer missing constituent physics. The feasibility of the method is demonstrated using a physics-based visco-plastic self-consistent (VPSC) model that represents the mechanics of slip and twinning behavior in 5182 aluminum alloy. However, a constituent model to carry out thermal analysis representing the dependence of hardening parameters on temperature is unavailable. Using integral-effect experimental data, the proposed approach is used to infer an empirical constituent model, which is then coupled with VPSC to obtain an experimentally augmented partitioned model representing the thermo-mechanical properties of 5182 aluminum alloy.

Results demonstrate the capability of the method to enable model predictions dependent upon relevant operational conditions. The VPSC model is coupled with the empirical constituent, and the newly enabled thermal-dependent predictions are compared with experimental data.

The method developed in this paper enables the empirical inference of a functional representation of input parameter values in lieu of a missing constituent model. Through this approach, development of partitioned models in the presence of uncertainty regarding a constituent model is made possible.

This article is motivated by the lack of flexibility in Bayesian quantile regression for ordinal models where the error follows an asymmetric Laplace (AL) distribution. The inflexibility arises because the skewness of the distribution is completely specified when a quantile is chosen. To overcome this shortcoming, we derive the cumulative distribution function (and the moment-generating function) of the generalized asymmetric Laplace (GAL) distribution – a generalization of AL distribution that separates the skewness from the quantile parameter – and construct a working likelihood for the ordinal quantile model. The resulting framework is termed flexible Bayesian quantile regression for ordinal (FBQROR) models. However, its estimation is not straightforward. We address estimation issues and propose an efficient Markov chain Monte Carlo (MCMC) procedure based on Gibbs sampling and joint Metropolis–Hastings algorithm. The advantages of the proposed model are demonstrated in multiple simulation studies and implemented to analyze public opinion on homeownership as the best long-term investment in the United States following the Great Recession.

This chapter proposes an approach toward the estimation of cross-sectional sample selection models, where the shocks on the units of observation feature some interdependence through spatial or network autocorrelation. In particular, this chapter improves on prior Bayesian work on this subject by proposing a modified approach toward sampling the multivariate-truncated, cross-sectionally dependent latent variable of the selection equation. This chapter outlines the model and implementation approach and provides simulation results documenting the better performance of the proposed approach relative to existing ones.

In a Bayesian approach, we compare the forecasting performance of five classes of models: ARCH, GARCH, SV, SV-STAR, and MSSV using daily Tehran Stock Exchange (TSE) market data. To estimate the parameters of the models, Markov chain Monte Carlo (MCMC) methods is applied. The results show that the models in the fourth and the fifth class perform better than the models in the other classes.

The purpose of this paper is to present designs for an accelerated life test (ALT).

Bayesian methods and simulation Monte Carlo Markov Chain (MCMC) methods were used.

In the paper a Bayesian method based on MCMC for ALT under EW distribution (for life time) and Arrhenius models (relating the stress variable and parameters) was proposed. The paper can conclude that it is a reasonable alternative to the classical statistical methods since the implementation of the proposed method is simple, not requiring advanced computational understanding and inferences on the parameters can be made easily. By the predictive density of a future observation, a procedure was developed to plan ALT and also to verify if the conformance fraction of the manufactured process reaches some desired level of quality. This procedure is useful for statistical process control in many industrial applications.

The results may be applied in a semiconductor manufacturer.

The Exponentiated‐Weibull‐Arrhenius model has never before been used to plan an ALT.

This paper aims to illustrate how a Bayesian approach to yield fitting can be implemented in a non-parametric framework with automatic smoothing inferred from the data. It also briefly illustrates the advantages of such an approach using real data.

The paper uses an infinite dimensional (functional space) approach to inverse problems. Numerical computations are carried out using a Markov Chain Monte-Carlo algorithm with several tweaks to ensure good performance. The model explicitly uses bid-ask spreads to allow for observation errors and provides automatic smoothing based on them.

A non-parametric framework allows to capture complex shapes of zero-coupon yield curves typical for emerging markets. Bayesian approach allows to assess the precision of estimates, which is crucial for some applications. Examples of estimation results are reported for three different bond markets: liquid (German), medium liquidity (Chinese) and illiquid (Russian).

The result shows that infinite-dimensional Bayesian approach to term structure estimation is feasible. Market practitioners could use this approach to gain more insight into interest rates term structure. For example, they could now be able to complement their non-parametric term structure estimates with Bayesian confidence intervals, which would allow them to assess statistical significance of their results.

The model does not require parameter tuning during estimation. It has its own parameters, but they are to be selected during model setup.