We propose a sparse high-dimensional time series chain graphical model for reconstructing genetic networks from gene expression data parametrized by a precision matrix and autoregressive coefficient matrix. We consider the time steps as blocks or chains. The proposed approach explores patterns of contemporaneous and dynamic interactions by efficiently combining Gaussian graphical models and Bayesian dynamic networks. We use penalized likelihood inference with a smoothly clipped absolute deviation penalty to explore the relationships among the observed time course gene expressions. The method is illustrated on simulated data and on real data examples from Arabidopsis thaliana and mammary gland time course microarray gene expressions.

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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.