相关论文: Enhanced gradient-based MCMC in discrete spaces

Computing the marginal likelihood or evidence is one of the core challenges in Bayesian analysis. While there are many established methods for estimating this quantity, they predominantly rely on using a large number of posterior samples…

In this paper, we propose a new stochastic optimization algorithm for Bayesian inference based on multilevel Monte Carlo (MLMC) methods. In Bayesian statistics, biased estimators of the model evidence have been often used as stochastic…

Deterministic-scan and random-scan component-wise Markov chain Monte Carlo algorithms, such as Gibbs samplers and conditional Metropolis-Hastings, are popular approaches for sampling from multivariate distributions. A long-standing open…

Bayesian experimental design (BED) is to answer the question that how to choose designs that maximize the information gathering. For implicit models, where the likelihood is intractable but sampling is possible, conventional BED methods…

Sampling from the lattice Gaussian distribution plays an important role in various research fields. In this paper, the Markov chain Monte Carlo (MCMC)-based sampling technique is advanced in several fronts. Firstly, the spectral gap for the…

Despite the abundance of methods for variable selection and accommodating spatial structure in regression models, there is little precedent for incorporating spatial dependence in covariate inclusion probabilities for regionally varying…

Recently, gradient-based discrete sampling has emerged as a highly efficient, general-purpose solver for various combinatorial optimization (CO) problems, achieving performance comparable to or surpassing the popular data-driven approaches.…

Modeling binary and categorical data is one of the most commonly encountered tasks of applied statisticians and econometricians. While Bayesian methods in this context have been available for decades now, they often require a high level of…

We combine the newly-constructed Galerkin difference basis with the energy-based discontinuous Galerkin method for wave equations in second order form. The approximation properties of the resulting method are excellent and the allowable…

Stochastic gradient Markov Chain Monte Carlo (SGMCMC) is considered the gold standard for Bayesian inference in large-scale models, such as Bayesian neural networks. Since practitioners face speed versus accuracy tradeoffs in these models,…

We study the convergence properties of the Gibbs Sampler in the context of posterior distributions arising from Bayesian analysis of conditionally Gaussian hierarchical models. We develop a multigrid approach to derive analytic expressions…

Bayesian inference via standard Markov Chain Monte Carlo (MCMC) methods is too computationally intensive to handle large datasets, since the cost per step usually scales like $\Theta(n)$ in the number of data points $n$. We propose the…

Hamiltonian Monte Carlo (HMC) is a powerful Markov Chain Monte Carlo (MCMC) method for sampling from complex high-dimensional continuous distributions. However, in many situations it is necessary or desirable to combine HMC with other…

Sampling from a target distribution is a fundamental problem. Traditional Markov chain Monte Carlo (MCMC) algorithms, such as the unadjusted Langevin algorithm (ULA), derived from the overdamped Langevin dynamics, have been extensively…

We explore the use of higher-order tail area approximations for Bayesian simulation. These approximations give rise to an alternative simulation scheme to MCMC for Bayesian computation of marginal posterior distributions for a scalar…

Identifying the active factors that have significant impacts on the output of the complex system is an important but challenging variable selection problem in computer experiments. In this paper, a Bayesian hierarchical Gaussian process…

Gaussian processes allow for flexible specification of prior assumptions of unknown dynamics in state space models. We present a procedure for efficient Bayesian learning in Gaussian process state space models, where the representation is…

Although discrete mixture modeling has formed the backbone of the literature on Bayesian density estimation, there are some well known disadvantages. We propose an alternative class of priors based on random nonlinear functions of a uniform…

Latent Gaussian models (LGMs) are a popular class of Bayesian hierarchical models that include Gaussian processes, as well as certain spatial models and mixed-effect models. Efficient Bayesian inference of LGMs often requires marginalizing…

Gaussian graphical models can capture complex dependency structures among variables. For such models, Bayesian inference is attractive as it provides principled ways to incorporate prior information and to quantify uncertainty through the…