We propose a comprehensive Bayesian approach for graphical model determination in observational studies that can accommodate binary, ordinal or continuous variables simultaneously. Our new models are called copula Gaussian graphical models (CGGMs) and embed graphical model selection inside a semiparametric Gaussian copula. The domain of applicability of our methods is very broad and encompasses many studies from social science and economics. We illustrate the use of the copula Gaussian graphical models in the analysis of a 16-dimensional functional disability contingency table.

We propose a method for post-processing an ensemble of multivariate forecasts in order to obtain a joint predictive distribution of weather. Our method utilizes existing univariate post-processing techniques, in this case ensemble Bayesian model averaging (BMA), to obtain estimated marginal distributions. However, implementing these methods individually offers no information regarding the joint distribution. To correct this, we propose the use of a Gaussian copula, which offers a simple procedure for recovering the dependence that is lost in the estimation of the ensemble BMA marginals. Our method is applied to 48 h forecasts of a set of five weather quantities using the eight-member University of Washington mesoscale ensemble. We show that our method recovers many well-understood dependencies between weather quantities and subsequently improves calibration and sharpness over both the raw ensemble and a method which does not incorporate joint distributional information. Copyright c 2012 Royal Meteorological Society Key Words: ensemble post-processing; joint predictive distributions; copula methods

We introduce efficient Markov chain Monte Carlo methods for inference and model determination in multivariate and matrix-variate Gaussian graphical models. Our framework is based on the G-Wishart prior for the precision matrix associated with graphs that can be decomposable or non-decomposable. We extend our sampling algorithms to a novel class of conditionally autoregressive models for sparse estimation in multivariate lattice data, with a special emphasis on the analysis of spatial data. These models embed a great deal of flexibility in estimating both the correlation structure across outcomes and the spatial correlation structure, thereby allowing for adaptive smoothing and spatial autocorrelation parameters. Our methods are illustrated using a simulated example and a real-world application which concerns cancer mortality surveillance. Supplementary materials with computer code and the datasets needed to replicate our numerical results together with additional tables of results are available online.

The literature on Foreign Direct Investment (FDI) determinants is remarkably diverse in terms of competing theories and empirical results. We utilize Bayesian Model Averaging (BMA) to resolve the model uncertainty that surrounds the validity of the competing FDI theories. Since the structure of existing FDI data is well known to induce selection bias, we extend BMA theory to HeckitBMA in order to address model uncertainty in the presence of selection bias. We show that more than half of the previously suggested FDI determinants are not robust and highlight theories that do receive robust support from the data. Our selection approach allows us to identify the determinants of the margins of FDI (intensive and extensive), which are shown to differ profoundly. Our results suggest a new emphasis in FDI theories that explicitly identify the dynamics of the intensive and extensive FDI margins.* We thank an anonymous referee, Christian Lorenczik, Monique Newiak, and Chris Papageorgiou for helpful suggestions. Assaf Razin and Hui Tong kindly shared their data. Lenkoski gratefully acknowledges support by the joint research project "Spatio/Temporal Graphical Models and Applications in Image Analysis" funded by the German Science Foundation (DFG), grant GRK 1653 as well as the MAThematics Centre Heidelberg (MATCH). Eicher thanks Max Soto Jimènez, the Instituto de Investigaciones en Ciencias Económicas, and the Department of Economics at the University of Costa Rica for their support and hospitality during the preparation of this paper. 1 IntroductionGlobal HeckitBMA reveals not only the determinants of the intensive and extensive margins of FDI ("the volume of investment flows" and "the decision to invest", respectively), it also permits us to estimate FDI determinants without having to constrain parameter estimates to be identical across both margins. There is no reason to suspect that the margins of FDI should feature identical determinants, nor that the same determinant has the identical impact for both margins. Our selection criterion is based on Razin,Rubinstein and Sadka (2004), who note that FDI involves fixed costs that give rise to two-part decisions: a marginal productivity condition that determines how much to invest, and a total profitability condition that indicates whether or not to invest abroad. Previous studies have confirmed the relevance of such FDI fixed costs. 4Our results show that the impact of model uncertainty on FDI estimates is substantial and that the Heckman selection methodology is necessary to obtain unbiased and consistent estimates. In the absence of explicit controls for model uncertainty, the conventional Heckit procedure suggests nearly three times as many FDI determinants asHeckitBMA at the extensive margin (32 vs 13) and a 50% more regressors at the intensive margin. This is not surprising, since Heckit is not designed to consider models associated with alternative theories. Instead, HeckitBMA discovers much more parsimonious models of FDI that score better as measured by the Bayesian I...

Spatial maps of extreme precipitation are a critical component of flood estimation in hydrological modeling, as well as in the planning and design of important infrastructure. This is particularly relevant in countries such as Norway that have a high density of hydrological power generating facilities and are exposed to significant risk of infrastructure damage due to flooding. In this work, we estimate a spatially coherent map of the distribution of extreme hourly precipitation in Norway, in terms of return levels, by linking generalized extreme value (GEV) distributions with latent Gaussian fields in a Bayesian hierarchical model. Generalized linear models on the parameters of the GEV distribution are able to incorporate location-specific geographic and meteorological information and thereby accommodate these effects on extreme precipitation. Our model incorporates a Bayesian model averaging component that directly assesses model uncertainty in the effect of the proposed covariates. Gaussian fields on the GEV parameters capture additional unexplained spatial heterogeneity and overcome the sparse grid on which observations are collected. Our framework is able to appropriately characterize both the spatial variability of the distribution of extreme hourly precipitation in Norway, and the associated uncertainty in these estimates.

We describe a comprehensive framework for performing Bayesian inference for Gaussian graphical models based on the G-Wishart prior with a special focus on efficiently including nondecomposable graphs in the model space. We develop a new approximation method to the normalizing constant of a G-Wishart distribution based on the Laplace approximation. We review recent developments in stochastic search algorithms and propose a new method, the mode oriented stochastic search (MOSS), that extends these techniques and proves superior at quickly finding graphical models with high posterior probability. We then develop a novel stochastic search technique for multivariate regression models and conclude with a real-world example from the recent covariance estimation literature. Supplemental materials are available online.

The G-Wishart distribution is the conjugate prior for precision matrices that encode the conditional independence of a Gaussian graphical model. Although the distribution has received considerable attention, posterior inference has proven computationally challenging, in part owing to the lack of a direct sampler. In this note, we rectify this situation. The existence of a direct sampler offers a host of new possibilities for the use of G-Wishart variates. We discuss one such development by outlining a new transdimensional model search algorithm-which we term double reversible jump-that leverages this sampler to avoid normalizing constant calculation when comparing graphical models. We conclude with two short studies meant to investigate our algorithm's validity.

Economic modeling in the presence of endogeneity is subject to model uncertainty at both the instrument and covariate level. We propose a Two-Stage Bayesian Model Averaging (2SBMA) methodology that extends the Two-Stage Least Squares (2SLS) estimator. By constructing a Two-Stage Unit Information Prior in the endogenous variable model, we are able to efficiently combine established methods for addressing model uncertainty in regression models with the classic technique of 2SLS. To assess the validity of instruments in the 2SBMA context, we develop Bayesian tests of the identification restriction that are based on model averaged posterior predictive p-values. A simulation study showed that 2SBMA has the ability to recover structure in both the instrument and covariate set, and substantially improves the sharpness of resulting coefficient estimates in comparison to 2SLS using the full specification in an automatic fashion. Due to the increased parsimony of the 2SBMA estimate, the Bayesian Sargan test had a power of 50 percent in detecting a violation of the exogeneity assumption, while the method based on 2SLS using the full specification had negligible power. We apply our approach to the problem of development accounting, and find support not only for institutions, but also for geography and integration as development determinants, once both model uncertainty and endogeneity have been jointly addressed.