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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…

Bayesian methods are a popular choice for statistical inference in small-data regimes due to the regularization effect induced by the prior. In the context of density estimation, the standard nonparametric Bayesian approach is to target the…

Competing risks occur in survival analysis when multiple causes of death are present. They play a prominent role in several domains extending beyond biostatistics to encompass epidemiology, actuarial sciences, and reliability theory. This…

In this paper we propose a general method to derive an upper bound for the contraction rate of the posterior distribution for nonparametric inverse problems. We present a general theorem that allows us to derive con- traction rates for the…

One-step ahead prediction for the multinomial model is considered. The performance of a predictive density is evaluated by the average Kullback-Leibler divergence from the true density to the predictive density. Asymptotic approximations of…

We consider a novel paradigm for Bayesian testing of hypotheses and Bayesian model comparison. Our alternative to the traditional construction of posterior probabilities that a given hypothesis is true or that the data originates from a…

We consider the statistical linear inverse problem of making inference on an unknown source function in an elliptic partial differential equation from noisy observations of its solution. We employ nonparametric Bayesian procedures based on…

This work advances randomized exploration in reinforcement learning (RL) with function approximation modeled by linear mixture MDPs. We establish the first prior-dependent Bayesian regret bound for RL with function approximation; and refine…

We consider decision-making problems involving the optimization of linear objective functions with uncertain coefficients. The probability distribution of the coefficients--which are assumed to be stochastic in nature--is unknown to the…

Bayesian inference can quantify uncertainty in the predictions of neural networks using posterior distributions for model parameters and network output. By looking at these posterior distributions, one can separate the origin of uncertainty…

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…

We propose a principled framework for nonparametric empirical Bayes (EB) estimation, based on the idea that the prior should be consistent with the observed posterior and that Bayesian updating should be stable. Focusing on discretized…

We consider nonparametric estimation of a mixed discrete-continuous distribution under anisotropic smoothness conditions and possibly increasing number of support points for the discrete part of the distribution. For these settings, we…

Composition methodologies in the current literature are mainly to promote estimation efficiency via direct composition, either, of initial estimators or of objective functions. In this paper, composite estimation is investigated for both…

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…

A family of random probabilities is defined and studied. This family contains the Dirichlet process as a special case, corresponding to an inner point in the appropriate parameter space. The extension makes it possible to have random means…

Due to their conjugate posteriors, Gaussian process priors are attractive for estimating the drift of stochastic differential equations with continuous time observations. However, their performance strongly depends on the choice of the…

We study asymptotically minimax predictive distributions in an infinite sequence model. First, we discuss the connection between the prediction in the infinite sequence model and the prediction in the function model. Second, we construct an…

We describe the semantic foundations for elicitation of generalized additively independent (GAI) utilities using the minimax regret criterion, and propose several new query types and strategies for this purpose. Computational feasibility is…

The increasing ease of data capture and storage has led to a corresponding increase in the choice of data, the type of analysis performed on that data, and the complexity of the analysis performed. The main contribution of this paper is to…