The problem of simulating from distributions with intractable normalizing constants has received much attention in recent literature. In this article, we propose an asymptotic algorithm, the so-called double Metropolis–Hastings (MH) sampler, for tackling this problem. Unlike other auxiliary variable algorithms, the double MH sampler removes the need for exact sampling, the auxiliary variables being generated using MH kernels, and thus can be applied to a wide range of problems for which exact sampling is not available. For the problems for which exact sampling is available, it can typically produce the same accurate results as the exchange algorithm, but using much less CPU time. The new method is illustrated by various spatial models.

Understanding the underlying relationship between crash injury severity and factors such as driver’s characteristics, vehicle type, and roadway conditions is very important for improving traffic safety. Most previous studies on this topic used traditional statistical models such as ordered probit (OP), multinomial logit, and nested logit models. This research introduces the Bayesian inference and investigates the application of a Bayesian ordered probit (BOP) model in driver’s injury severity analysis. The OP and BOP models are compared based on datasets with different sample sizes from the 2003 National Automotive Sampling System General Estimates System (NASSGES). The comparison results show that these two types of models produce similar results for large sample data. When the sample data size is small, with proper prior setting, the BOP model can produce more reasonable parameter estimations and better prediction performance than the OP model. This research also shows that the BOP model provides a flex...

Recent advances in high-throughput biotechnologies have provided an unprecedented opportunity for biomarker discovery, which, from a statistical point of view, can be cast as a variable selection problem. This problem is challenging due to the high-dimensional and nonlinear nature of omics data and, in general, it suffers three difficulties: (i) an unknown functional form of the nonlinear system, (ii) variable selection consistency, and (iii) high-demanding computation. To circumvent the first difficulty, we employ a feed-forward neural network to approximate the unknown nonlinear function motivated by its universal approximation ability. To circumvent the second difficulty, we conduct structure selection for the neural network, which induces variable selection, by choosing appropriate prior distributions that lead to the consistency of variable selection. To circumvent the third difficulty, we implement the population stochastic approximation Monte Carlo algorithm, a parallel adaptive Markov Chain Monte Carlo algorithm, on the OpenMP platform that provides a linear speedup for the simulation with the number of cores of the computer. The numerical results indicate that the proposed method can work very well for identification of relevant variables for high-dimensional nonlinear systems. The proposed method is successfully applied to identification of the genes that are associated with anticancer drug sensitivities based on the data collected in the cancer cell line encyclopedia study. Supplementary materials for this article are available online.

Deep learning has been the engine powering many successes of data science. However, the deep neural network (DNN), as the basic model of deep learning, is often excessively over-parameterized, causing many difficulties in training, prediction and interpretation. We propose a frequentist-like method for learning sparse DNNs and justify its consistency under the Bayesian framework: the proposed method could learn a sparse DNN with at most $O(n/\hspace{0.17em}\text{log}\hspace{0.17em}(n))$ connections and nice theoretical guarantees such as posterior consistency, variable selection consistency and asymptotically optimal generalization bounds. In particular, we establish posterior consistency for the sparse DNN with a mixture Gaussian prior, show that the structure of the sparse DNN can be consistently determined using a Laplace approximation-based marginal posterior inclusion probability approach, and use Bayesian evidence to elicit sparse DNNs learned by an optimization method such as stochastic gradient descent in multiple runs with different initializations. The proposed method is computationally more efficient than standard Bayesian methods for large-scale sparse DNNs. The numerical results indicate that the proposed method can perform very well for large-scale network compression and high-dimensional nonlinear variable selection, both advancing interpretable machine learning.