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In variational inference, the benefits of Bayesian models rely on accurately capturing the true posterior distribution. We propose using neural samplers that specify implicit distributions, which are well-suited for approximating complex…

This article surveys computational methods for posterior inference with intractable likelihoods, that is where the likelihood function is unavailable in closed form, or where evaluation of the likelihood is infeasible. We review recent…

Bayesian synthetic likelihood (BSL) is a popular method for performing approximate Bayesian inference when the likelihood function is intractable. In synthetic likelihood methods, the likelihood function is approximated parametrically via…

Scientists continue to develop increasingly complex mechanistic models to reflect their knowledge more realistically. Statistical inference using these models can be challenging since the corresponding likelihood function is often…

A common problem in disciplines of applied Statistics research such as Astrostatistics is of estimating the posterior distribution of relevant parameters. Typically, the likelihoods for such models are computed via expensive experiments…

We study Bayesian methods for large-scale linear inverse problems, focusing on the challenging task of hyperparameter estimation. Typical hierarchical Bayesian formulations that follow a Markov Chain Monte Carlo approach are possible for…

We consider the fractional posterior distribution that is obtained by updating a prior distribution via Bayes theorem with a fractional likelihood function, a usual likelihood function raised to a fractional power. First, we analyze the…

In all areas of human knowledge, datasets are increasing in both size and complexity, creating the need for richer statistical models. This trend is also true for economic data, where high-dimensional and nonlinear/nonparametric inference…

Observational astrophysics consists of making inferences about the Universe by comparing data and models. The credible intervals placed on model parameters are often as important as the maximum a posteriori probability values, as the…

We propose a general method to carry out a valid Bayesian analysis of a finite-dimensional `targeted' parameter in the presence of a finite-dimensional nuisance parameter. We apply our methods to causal inference based on estimating…

Models with intractable normalizing functions arise frequently in statistics. Common examples of such models include exponential random graph models for social networks and Markov point processes for ecology and disease modeling. Inference…

Empirical Bayes (EB) improves the accuracy of simultaneous inference "by learning from the experience of others" (Efron, 2012). Classical EB theory focuses on latent variables that are iid draws from a fitted prior (Efron, 2019). Modern…

We present a novel approach to the inference of spectral functions from Euclidean time correlator data that makes close contact with modern Bayesian concepts. Our method differs significantly from the maximum entropy method (MEM). A new set…

Models for which the likelihood function can be evaluated only up to a parameter-dependent unknown normalising constant, such as Markov random field models, are used widely in computer science, statistical physics, spatial statistics, and…

The prior distribution on parameters of a sampling distribution is the usual starting point for Bayesian uncertainty quantification. In this paper, we present a different perspective which focuses on missing observations as the source of…

Many modern experiments, such as microarray gene expression and genome-wide association studies, present the problem of estimating a large number of parallel effects. Bayesian inference is a popular approach for analyzing such data by…

Selection bias arises when the probability that an observation enters a dataset depends on variables related to the quantities of interest, leading to systematic distortions in estimation and uncertainty quantification. For example, in…

Ising models originated in statistical physics and are widely used in modeling spatial data and computer vision problems. However, statistical inference of this model remains challenging due to intractable nature of the normalizing constant…

The Bayesian predictive density has complex representation and does not belong to any finite-dimensional statistical model except for in limited situations. In this paper, we introduce its simple approximate representation employing its…

We propose a posterior for Bayesian Likelihood-Free Inference (LFI) based on generalized Bayesian inference. To define the posterior, we use Scoring Rules (SRs), which evaluate probabilistic models given an observation. In LFI, we can…