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Many modern applications of Bayesian inference, such as in cosmology, are based on complicated forward models with high-dimensional parameter spaces. This considerably limits the sampling of posterior distributions conditioned on observed…
Prior distributions for high-dimensional linear regression require specifying a joint distribution for the unobserved regression coefficients, which is inherently difficult. We instead propose a new class of shrinkage priors for linear…
The Bayesian approach to inverse problems typically relies on posterior sampling approaches, such as Markov chain Monte Carlo, for which the generation of each sample requires one or more evaluations of the parameter-to-observable map or…
Principal component regression uses principal components as regressors. It is particularly useful in prediction settings with high-dimensional covariates. The existing literature treating of Bayesian approaches is relatively sparse. We…
Given data from a Poisson point process with intensity $(x,y) \mapsto n \mathbf{1}(f(x)\leq y),$ frequentist properties for the Bayesian reconstruction of the support boundary function $f$ are derived. We mainly study compound Poisson…
We consider chance constrained optimization where it is sought to optimize a function while complying with constraints, both of which are affected by uncertainties. The high computational cost of realistic simulations strongly limits the…
A common problem in natural sciences is the comparison of competing models in the light of observed data. Bayesian model comparison provides a statistically sound framework for this comparison based on the evidence each model provides for…
In the recent paper [5], a Bayesian approach for constructing confidence intervals in monotone regression problems is proposed, based on credible intervals. We view this method from a frequentist point of view, and show that it corresponds…
Uncovering genuine relationships between a response variable of interest and a large collection of covariates is a fundamental and practically important problem. In the context of Gaussian linear models, both the Bayesian and non-Bayesian…
When using complex Bayesian models to combine information, the checking for consistency of the information being combined is good statistical practice. Here a new method is developed for detecting prior-data conflicts in Bayesian models…
In this article, we investigate posterior convergence of nonparametric binary and Poisson regression under possible model misspecification, assuming general stochastic process prior with appropriate properties. Our model setup and objective…
The nonparametric regression model with normal errors has been extensively studied, both from the frequentist and Bayesian viewpoint. A central result in Bayesian nonparametrics is that under assumptions on the prior, the data-generating…
The concepts of Bayesian prediction, model comparison, and model selection have developed significantly over the last decade. As a result, the Bayesian community has witnessed a rapid growth in theoretical and applied contributions to…
We consider the problem of isotonic regression, where the underlying signal $x$ is assumed to satisfy a monotonicity constraint, that is, $x$ lies in the cone $\{ x\in\mathbb{R}^n : x_1 \leq \dots \leq x_n\}$. We study the isotonic…
To design Bayesian studies, criteria for the operating characteristics of posterior analyses - such as power and the type I error rate - are often assessed by estimating sampling distributions of posterior probabilities via simulation. In…
Bayesian coresets approximate a posterior distribution by building a small weighted subset of the data points. Any inference procedure that is too computationally expensive to be run on the full posterior can instead be run inexpensively on…
In this paper, we propose a new Bayesian inference method for a high-dimensional sparse factor model that allows both the factor dimensionality and the sparse structure of the loading matrix to be inferred. The novelty is to introduce a…
We propose Bayesian Conformal Prediction (BCP), a framework that combines Bayesian posterior predictive distributions with PAC-style conformal risk control to produce prediction sets with finite-sample coverage guarantees. Standard…
We consider priors for several nonparametric Bayesian models which use finite random series with a random number of terms. The prior is constructed through distributions on the number of basis functions and the associated coefficients. We…
For a classification problem described by the joint density $P(\omega,x)$, models of $P(\omega\eq\omega'|x,x')$ (the ``Bayesian similarity measure'') have been shown to be an optimal similarity measure for nearest neighbor classification.…