Related papers: Bounding Wasserstein distance with couplings
Markov chain Monte Carlo (MCMC) simulations are modeled as driven by true random numbers. We consider variance bounding Markov chains driven by a deterministic sequence of numbers. The star-discrepancy provides a measure of efficiency of…
Bayesian hierarchical modeling is a popular approach to capturing unobserved heterogeneity across individual units. However, standard estimation methods such as Markov chain Monte Carlo (MCMC) can be impracticable for modeling outcomes from…
In this paper, we present a method for computing the marginal likelihood, also known as the model likelihood or Bayesian evidence, from Markov Chain Monte Carlo (MCMC), or other sampled posterior distributions. In order to do this, one…
In the following article we provide an exposition of exact computational methods to perform parameter inference from partially observed network models. In particular, we consider the duplication attachment (DA) model which has a likelihood…
Modern computational advances have enabled easy parallel implementations of Markov chain Monte Carlo (MCMC). However, almost all work in estimating the variance of Monte Carlo averages, including the efficient batch means (BM) estimator,…
In the context of Bayesian inversion for scientific and engineering modeling, Markov chain Monte Carlo sampling strategies are the benchmark due to their flexibility and robustness in dealing with arbitrary posterior probability density…
Using Markov chain Monte Carlo to sample from posterior distributions was the key innovation which made Bayesian data analysis practical. Notoriously, however, MCMC is hard to tune, hard to diagnose, and hard to parallelize. This…
We propose a Monte Carlo algorithm to sample from high dimensional probability distributions that combines Markov chain Monte Carlo and importance sampling. We provide a careful theoretical analysis, including guarantees on robustness to…
Linear regression with measurement error in the covariates is a heavily studied topic, however, the statistics/econometrics literature is almost silent to estimating a multi-equation model with measurement error. This paper considers a…
Bayesian inference promises to ground and improve the performance of deep neural networks. It promises to be robust to overfitting, to simplify the training procedure and the space of hyperparameters, and to provide a calibrated measure of…
Calculating a Monte Carlo standard error (MCSE) is an important step in the statistical analysis of the simulation output obtained from a Markov chain Monte Carlo experiment. An MCSE is usually based on an estimate of the variance of the…
Sampling from distributions play a crucial role in aiding practitioners with statistical inference. However, in numerous situations, obtaining exact samples from complex distributions is infeasible. Consequently, researchers often turn to…
In this paper we propose an efficient stochastic optimization algorithm to search for Bayesian experimental designs such that the expected information gain is maximized. The gradient of the expected information gain with respect to…
Markov Chain Monte Carlo (MCMC) methods sample from unnormalized probability distributions and offer guarantees of exact sampling. However, in the continuous case, unfavorable geometry of the target distribution can greatly limit the…
Bayesian Neural Networks (BNNs) provide a promising framework for modeling predictive uncertainty and enhancing out-of-distribution robustness (OOD) by estimating the posterior distribution of network parameters. Stochastic Gradient Markov…
As modern neural networks get more complex, specifying a model with high predictive performance and sound uncertainty quantification becomes a more challenging task. Despite some promising theoretical results on the true posterior…
Along with Markov chain Monte Carlo (MCMC) methods, variational inference (VI) has emerged as a central computational approach to large-scale Bayesian inference. Rather than sampling from the true posterior $\pi$, VI aims at producing a…
For big data analysis, high computational cost for Bayesian methods often limits their applications in practice. In recent years, there have been many attempts to improve computational efficiency of Bayesian inference. Here we propose an…
The availability of data sets with large numbers of variables is rapidly increasing. The effective application of Bayesian variable selection methods for regression with these data sets has proved difficult since available Markov chain…
Markov chain Monte Carlo (MCMC) produces a correlated sample for estimating expectations with respect to a target distribution. A fundamental question is when should sampling stop so that we have good estimates of the desired quantities?…