Related papers: Insufficient Gibbs Sampling
The current standard Bayesian approach to model calibration, which assigns a Gaussian process prior to the discrepancy term, often suffers from issues of unidentifiability and computational complexity and instability. When the goal is to…
Approximate Bayesian computation (ABC) methods perform inference on model-specific parameters of mechanistically motivated parametric statistical models when evaluating likelihoods is difficult. Central to the success of ABC methods is…
This work presents a tractable approach to multi-object posterior computation under a generic measurement likelihood function. While filtering is a popular solution, valuable historical information is discarded. Posterior inference, which…
We consider the problem of parametric statistical inference when likelihood computations are prohibitively expensive but sampling from the model is possible. Several so-called likelihood-free methods have been developed to perform inference…
This paper develops a new empirical Bayesian inference algorithm for solving a linear inverse problem given multiple measurement vectors (MMV) of under-sampled and noisy observable data. Specifically, by exploiting the joint sparsity across…
Gibbs states are familiar from statistical mechanics, yet their use is not limited to that domain. For instance, they also feature in the maximum entropy reconstruction of quantum states from incomplete measurement data. Outside the…
Gibbs sampling is a workhorse for Bayesian inference but has several limitations when used for parameter estimation, and is often much slower than non-sampling inference methods. SAME (State Augmentation for Marginal Estimation)…
Univariate and multivariate general linear regression models, subject to linear inequality constraints, arise in many scientific applications. The linear inequality restrictions on model parameters are often available from phenomenological…
Count data with zero inflation and large outliers are ubiquitous in many scientific applications. However, posterior analysis under a standard statistical model, such as Poisson or negative binomial distribution, is sensitive to such…
Estimation of parameters that obey specific constraints is crucial in statistics and machine learning; for example, when parameters are required to satisfy boundedness, monotonicity, or linear inequalities. Traditional approaches impose…
Gaussian process regression in its most simplified form assumes normal homoscedastic noise and utilizes analytically tractable mean and covariance functions of predictive posterior distribution using Gaussian conditioning. Its…
In high-dimensional Bayesian statistics, various methods have been developed, including prior distributions that induce parameter sparsity to handle many parameters. Yet, these approaches often overlook the rich spectral structure of the…
We propose a general framework for obtaining probabilistic solutions to PDE-based inverse problems. Bayesian methods are attractive for uncertainty quantification but assume knowledge of the likelihood model or data generation process. This…
High-dimensional and complex discrete distributions often exhibit multimodal behavior due to inherent discontinuities, posing significant challenges for sampling. Gradient-based discrete samplers, while effective, frequently become trapped…
Gibbs partition models are the largest class of infinite exchangeable partitions of the positive integers generalizing the product form of the probability function of the two-parameter Poisson-Dirichlet family. Recently those models have…
In this article, we develop a semiparametric Bayesian estimation and model selection approach for partially linear additive models in conditional quantile regression. The asymmetric Laplace distribution provides a mechanism for Bayesian…
Gibbs sampling on factor graphs is a widely used inference technique, which often produces good empirical results. Theoretical guarantees for its performance are weak: even for tree structured graphs, the mixing time of Gibbs may be…
Gibbs random fields play an important role in statistics. However they are complicated to work with due to an intractability of the likelihood function and there has been much work devoted to finding computational algorithms to allow…
We present a modified Gibbs sampler for general state spaces. We establish that this modification can lead to substantial gains in statistical efficiency while maintaining the overall quality of convergence. We illustrate our results in two…
This paper considers properties of an optimization based sampler for targeting the posterior distribution when the likelihood is intractable and auxiliary statistics are used to summarize information in the data. Our reverse sampler…