Abdolreza Mohammadi

Bayesian Structure Learning in Sparse Gaussian Graphical Models

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=BDgraph

Bayesian inference and prediction in an M/G/1 with optional second service

In this article, we exploit the Bayesian inference and prediction for an M/G/1 queuing model with optional second re-service. In this model, a service unit attends customers arriving following a Poisson process and demanding service according to a general distribution and some of customers need to re-service with probability “p”. First, we introduce a mixture of truncated Normal distributions on interval (− ∞, 0) to approximate the service and re-service time densities. Then, given observations of the system, we propose a Bayesian procedure based on birth-death MCMC methodology to estimate some performance measures. Finally, we apply the theories in practice by providing a numerical example based on real data which have been obtained from a hospital.

GAUSSIAN GRAPHICAL MODELS FOR ASSESSING MULTIMODAL REGIONAL ASSOCIATIONS IN PRODROMAL ALZHEIMER’S DISEASE

p<0.0001). Faster decline in gamma and lambda values was strongly associated with steeper decline in the MMSE (b6SE(gamma)1⁄40.1260.02; b6SE(lambda)1⁄40.1460.02; all p<0.0001) and logical memory delayed recall over time (b6SE(gamma)1⁄40.0560.02; b6SE(lambda)1⁄40.0660.02; all p<0.005). Effects remained similar when additionally correcting for hippocampal volume. Conclusions:Decline in grey matter connectivity measures over time was associated with cognitive decline over time in prodromal AD. These results suggest that brain connectivity may provide a biological substrate that underlies cognitive decline in AD. Future research will further investigate the potential of grey matter network measures to serve as surrogate markers for disease progression monitoring.

Contributed discussion on article by Pratola

Pratola (2016) introduces a novel proposal mechanism for the Metropolis–Hastings step of a Markov chain Monte Carlo (MCMC) sampler that allows efficient traversal of the space of latent stochastic partitions defined by binary regression trees. Here we discuss two considerations: the first is the use of the new proposal mechanism within a population Markov chain Monte Carlo sampler (Geyer, 1991) to further increase sampling efficiency in the presence of greatly separated posterior modes, the second is a prior model that favors parsimony for the problem of variable selection.