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We describe a method for estimating the marginal likelihood, based on Chib (1995) and Chib and Jeliazkov (2001), when simulation from the posterior distribution of the model parameters is by the accept–reject Metropolis–Hastings (ARMH) algorithm. The method is developed for one‐block and multiple‐block ARMH algorithms and does not require the (typically) unknown normalizing constant of the proposal density. The problem of calculating the numerical standard error of the estimates is also considered and a procedure based on batch means is developed. Two examples, dealing with a multinomial logit model and a Gaussian regression model with non‐conjugate priors, are provided to illustrate the efficiency and applicability of the method.

This volume of Advances in Econometrics 34 focusses on Bayesian model comparison. It reflects the recent progress in model building and evaluation that has been achieved in the Bayesian paradigm and provides new state-of-the-art techniques, methodology, and findings that should stimulate future research

"Bayesian Inference in the Social Sciences builds upon the recent growth in Bayesian methodology and examines an array of topics in model formulation, estimation, and applications. Particular emphasis is placed on an interdisciplinary coverage, model checking, and modern computational tools such as Markov chain Monte Carlo. The book's broad interdisciplinary coverage provides exposure to recent and trending developments in a diverse, yet closely integrated, set of research topics in the social sciences. This approach facilitates the transmission of new ideas, developments, and methodology from one discipline to another, while at the same time maintaining manageability, coherence, and a clear focus"--

This volume of Advances in econometrics is devoted to Bayesian model comparison. It reflects the recent progress in model building and evaluation that has been achieved in the Bayesian paradigm and provides new state-of-the-art techniques, methodology, and findings that should stimulate future research. The volume contains articles that should appeal to readers with computational, modeling, theoretical, and applied interests. Methodological issues include parallel computation, Hamiltonian Monte Carlo, dynamic model selection, small sample comparison of structural models, Bayesian thresholding methods in hierarchical graphical models, adaptive reversible jump MCMC, LASSO estimators, parameter expansion algorithms, the implementation of parameter and non-parameter-based approaches to variable selection, a survey of key results in objective Bayesian model selection methodology, and a careful look at the modeling of endogeneity in discrete data settings. Important contemporary questions are examined in applications in macroeconomics, finance, banking, labor economics, industrial organization, and transportation, among others, in which model uncertainty is a central consideration.

This volume of Advances in econometrics is devoted to Bayesian model comparison. It reflects the recent progress in model building and evaluation that has been achieved in the Bayesian paradigm and provides new state-of-the-art techniques, methodology, and findings that should stimulate future research. The volume contains articles that should appeal to readers with computational, modeling, theoretical, and applied interests. Methodological issues include parallel computation, Hamiltonian Monte Carlo, dynamic model selection, small sample comparison of structural models, Bayesian thresholding methods in hierarchical graphical models, adaptive reversible jump MCMC, LASSO estimators, parameter expansion algorithms, the implementation of parameter and non-parameter-based approaches to variable selection, a survey of key results in objective Bayesian model selection methodology, and a careful look at the modeling of endogeneity in discrete data settings. Important contemporary questions are examined in applications in macroeconomics, finance, banking, labor economics, industrial organization, and transportation, among others, in which model uncertainty is a central consideration.

In this paper, we consider the analysis of models for univariate and multivariate ordinal outcomes in the context of the latent variable inferential framework of Albert and Chib (1993). We review several alternative modeling and identification schemes and evaluate how each aids or hampers estimation by Markov chain Monte Carlo simulation methods. For each identification scheme we also discuss the question of model comparison by marginal likelihoods and Bayes factors. In addition, we develop a simulation-based framework for analyzing covariate effects that can provide interpretability of the results despite the nonlinearities in the model and the different identification restrictions that can be implemented. The methods are employed to analyze problems in labor economics (educational attainment), political economy (voter opinions), and health economics (consumers' reliance on alternative sources of medical information).

We present a simulation technique for sorting out the size, shape, and location of the uncovered set to estimate the set of enactable outcomes in "real-world" social choice situations, such as the contemporary Congress. The uncovered set is a well-known but underexploited solution concept in the literature on spatial voting games and collective choice mechanisms. We explain this solution concept in nontechnical terms, submit some theoretical observations to improve our theoretical grasp of it, and provide a simulation technique that makes it possible to estimate this set and thus enable a series of tests of its empirical relevance.

Foreword / Ivan Jeliazkov and Justin Tobias -- 1. A Semiparametric Stochastic Frontier Model with Correlated Effects / Gholamreza Hajargasht and William Griffiths -- 2. A Bayesian Stochastic Frontier Model with Endogenous Regressors: An Application to the Effect of Division of Labor in Japanese Water Supply Organizations / Eri Nakamura, Takuya Urakami and Kazuhiko Kakamu -- 3. An Alternate Parameterization for Bayesian Nonparametric / Semiparametric Regression / Joshua Chan and Justin Tobias -- 4. Variable Selection in Sparse Semiparametric Single Index Models / Jianghao Chu, Tae-Hwy Lee and Aman Ullah -- 5. Fully Nonparametric Bayesian Additive Regression Trees / Edward George, Prakash Laud, Brent Logan, Robert McCulloch and Rodney Sparapani -- 6. Bayesian A/B Inference / John Geweke -- 7. Scalable semiparametric inference for the means of heavy-tailed distributions / Hedibert Lopes, Matthew Taddy and Matthew Gardner -- 8. Estimation and Applications of Quantile Regression for Binary Longitudinal Data / Mohammad Arshad Rahman and Angela Vossmeyer -- 9. On Quantile Estimator in Volatility Model with Non-negative Error Density and Bayesian Perspective / Debajit Dutta, Subhra Sankar Dhar and Amit Mitra -- 10. Flexible Bayesian Quantile Regression in Ordinal Models / Mohammad Arshad Rahman and Shubham Karnawat -- 11. A Reaction / Dale Poirier.

Volume 38 of Advances in Econometrics collects twelve innovative and thought-provoking contributions to the literature on Regression Discontinuity designs, covering a wide range of methodological and practical topics such as identification, interpretation, implementation, falsification testing, estimation and inference

Advances in Econometrics is a research annual whose editorial policy is to publish original research articles that contain enough details so that economists and econometricians who are not experts in the topics will find them accessible and useful in their research. Volume 37 exemplifies this focus by highlighting key research from new developments in econometrics.