This paper describes the general linear synthesis blind source separation problem and presents a Bayesian statistical approach with correlated sources. This is a generalization of the methods in Rowe (1999). The blind separation of sources model is extended to the general case where the mixing matrix is allowed to change over time, the sources are allowed to be time delayed, and both the observ...

We study the computational complexity of Markov chain Monte Carlo (MCMC) methods for high-dimensional Bayesian linear regression under sparsity constraints. We first show that a Bayesian approach can achieve variable-selection consistency under relatively mild conditions on the design matrix. We then demonstrate that the statistical criterion of posterior concentration need not imply the comput...

In this paper we address the following question: “Can we approximately sample from a Bayesian posterior distribution if we are only allowed to touch a small mini-batch of data-items for every sample we generate?”. An algorithm based on the Langevin equation with stochastic gradients (SGLD) was previously proposed to solve this, but its mixing rate was slow. By leveraging the Bayesian Central Li...

We study the computational complexity of Markov chain Monte Carlo (MCMC) methods for high-dimensional Bayesian linear regression under sparsity constraints. We first show that a Bayesian approach can achieve variable-selection consistency under relatively mild conditions on the design matrix. We then demonstrate that the statistical criterion of posterior concentration need not imply the comput...

A structured mathematical model of anaerobic conversion of complex organic materials in non-ideally cyclic-batch reactors for biogas production has been developed. The  model is based on multiple-reaction stoichiometry (enzymatic hydrolysis, acidogenesis, acetogenesis and methanogenesis), microbial growth kinetics, conventional material balances in the liquid and gas phases for a cyclic-bat...

Abstract Yang et al. proved that the symmetric random walk Metropolis–Hastings algorithm for Bayesian variable selection is rapidly mixing under mild high-dimensional assumptions. We propose a novel Markov chain Monte Carlo (MCMC) sampler using an informed proposal scheme, which we prove achieves much faster time independent of number covariates, assumptions To best our knowledge, this first re...

Binary response regression is a useful technique for analyzing categorical data. Popular binary models use special link functions such as the logit or the probit link. In this article, the inverse link function H is modeled to be a scale mixture of cumulative distribution functions. Two different models for H are proposed: (i) H is a finite normal scale mixture with a Dirichlet distribution pri...

Bayesian inference often poses difficult computational problems. Even when off-the-shelf Markov chain Monte Carlo (MCMC) methods are available to the problem at hand, mixing issues might compromise the quality of the results. We introduce a framework for situations where the model space can be naturally divided into two components: i. a baseline black-box probability distribution for the observ...