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The prior distribution for the unknown model parameters plays a crucial role in the process of statistical inference based on Bayesian methods. However, specifying suitable priors is often difficult even when detailed prior knowledge is…

The choice of the prior distribution is a key aspect of Bayesian analysis. For the spatial regression setting a subjective prior choice for the parameters may not be trivial, from this perspective, using the objective Bayesian analysis…

Priors in Bayesian analyses often encode informative domain knowledge that can be useful in making the inference process more efficient. Occasionally, however, priors may be unrepresentative of the parameter values for a given dataset,…

In real-world Bayesian inference applications, prior assumptions regarding the parameters of interest may be unrepresentative of their actual values for a given dataset. In particular, if the likelihood is concentrated far out in the wings…

We study Bayesian discriminative inference given a model family $p(c,\x, \theta)$ that is assumed to contain all our prior information but still known to be incorrect. This falls in between "standard" Bayesian generative modeling and…

This paper deals with Bayesian inference of a mixture of Gaussian distributions. A novel formulation of the mixture model is introduced, which includes the prior constraint that each Gaussian component is always assigned a minimal number of…

Prior information often takes the form of parameter constraints. Bayesian methods include such information through prior distributions having constrained support. By using posterior sampling algorithms, one can quantify uncertainty without…

Deep learning has revolutionized the last decade, being at the forefront of extraordinary advances in a wide range of tasks including computer vision, natural language processing, and reinforcement learning, to name but a few. However, it…

The Bayesian approach to inverse problems with functional unknowns, has received significant attention in recent years. An important component of the developing theory is the study of the asymptotic performance of the posterior distribution…

We consider Bayesian inference in inverse regression problems where the objective is to infer about unobserved covariates from observed responses and covariates. We establish posterior consistency of such unobserved covariates in Bayesian…

Bayes' theorem incorporates distinct types of information through the likelihood and prior. Direct observations of state variables enter the likelihood and modify posterior probabilities through consistent updating. Information in terms of…

In high-dimensions, the prior tails can have a significant effect on both posterior computation and asymptotic concentration rates. To achieve optimal rates while keeping the posterior computations relatively simple, an empirical Bayes…

In a bivariate meta-analysis the number of diagnostic studies involved is often very low so that frequentist methods may result in problems. Bayesian inference is attractive as informative priors that add small amount of information can…

We consider a popular family of constrained optimization problems arising in machine learning that involve optimizing a non-decomposable evaluation metric with a certain thresholded form, while constraining another metric of interest.…

Bayesian inference can often be sensitive to the choice of hyperparameters of the prior or likelihood, yet defining and quantifying this sensitivity in a principled and computationally feasible way remains challenging in practice.…

It is a relatively well-known fact that in problems of Bayesian model selection improper priors should, in general, be avoided. In this paper we derive a proper and parsimonious uniform prior for regression coefficients. We then use this…

Factor models are widely used for dimension reduction. Bayesian approaches to these models often place a prior on the factor loadings that allows for infinitely many factors, with loadings increasingly shrunk toward zero as the column index…

Unobserved confounding is a fundamental challenge for estimating causal effects. To address unobserved confounding, recent literature has turned to two different approaches -- proxy variables and the use of multiple treatments. The first…

In this work we apply the methodology of integral priors to handle Bayesian model selection in binomial regression models with a general link function. These models are very often used to investigate associations and risks in…

It is shown that a consistent application of Bayesian updating from a prior probability density to a posterior using evidence in the form of expectation constraints leads to exactly the same results as the application of the maximum entropy…