Decoding complex relationships among large numbers of variables with relatively few observations is one of the crucial issues in science. One approach to this problem is Gaussian graphical modeling, which describes conditional independence of variables through the presence or absence of edges in the underly- ing graph. In this paper, we introduce a novel and efficient Bayesian framework for Gaussian graphical model determination which is a trans-dimensional Markov Chain Monte Carlo (MCMC) approach based on a continuous-time birth-death process. We cover the theory and computational details of the method. It is easy to implement and computationally feasible for high-dimensional graphs. We show our method outperforms alternative Bayesian approaches in terms of convergence, mixing in the graph space and computing time. Unlike frequentist approaches, it gives a principled and, in practice, sensible approach for structure learning. We illustrate the efficiency of the method on a broad range of simulated data. We then apply the method on large-scale real applications from human and mammary gland gene expression studies to show its empirical usefulness. In addition, we implemented the method in the R package BDgraph which is freely available at http://CRAN.R-project.org/package=BDgraphComment: Published at http://dx.doi.org/10.1214/14-BA889 in the Bayesian Analysis (http://projecteuclid.org/euclid.ba) by the International Society of Bayesian Analysis (http://bayesian.org/

Graphical models provide powerful tools to uncover complicated patterns in multivariate data and are commonly used in Bayesian statistics and machine learning. In this paper, we introduce an R package BDgraph which performs Bayesian structure learning for general undirected graphical models (decomposable and non-decomposable) with continuous, discrete, and mixed variables. The package efficiently implements recent improvements in the Bayesian literature, including that of Mohammadi and Wit (2015) and Dobra and Mohammadi (2018). To speed up computations, the computationally intensive tasks have been implemented in C++ and interfaced with R, and the package has parallel computing capabilities. In addition, the package contains several functions for simulation and visualization, as well as several multivariate datasets taken from the literature and are used to describe the package capabilities. The paper includes a brief overview of the statistical methods which have been implemented in the package. The main body of the paper explains how to use the package. Furthermore, we illustrate the package's functionality in both real and artificial examples.

Summary. Dupuytren disease is a fibroproliferative disorder with unknown aetiology that often progresses and eventually can cause permanent contractures of the fingers affected. We provide a computationally efficient Bayesian framework to discover potential risk factors and investigate which fingers are jointly affected. Our Bayesian approach is based on Gaussian copula graphical models, which provide a way to discover the underlying conditional independence structure of variables in multivariate data of mixed types. In particular, we combine the semiparametric Gaussian copula with extended rank likelihood to analyse multivariate data of mixed types with arbitrary marginal distributions. For structural learning, we construct a computationally efficient search algorithm by using a transdimensional Markov chain Monte Carlo algorithm based on a birth-death process. In addition, to make our statistical method easily accessible to other researchers, we have implemented our method in C++ and provide an interface with R software as an R package BDgraph, which is freely available from http://CRAN.Rproject.org/package=BDgraph.

Methods for selecting loglinear models were among Steve Fienberg's research interests since the start of his long and fruitful career. After we dwell upon the string of papers focusing on loglinear models that can be partly attributed to Steve's contributions and influential ideas, we develop a new algorithm for selecting graphical loglinear models that is suitable for analyzing hyper-sparse contingency tables. We show how multi-way contingency tables can be used to represent patterns of human mobility. We analyze a dataset of geolocated tweets from South Africa that comprises 46 million latitude/longitude locations of 476, 601 Twitter users that is summarized as a contingency table with 214 variables.

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