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The paper solves the problem of optimal portfolio choice when the parameters of the asset returns distribution, like the mean vector and the covariance matrix are unknown and have to be estimated by using historical data of the asset…

Statistical Finance · Quantitative Finance 2023-04-19 David Bauder , Taras Bodnar , Nestor Parolya , Wolfgang Schmid

Data uncertainty in practical person reID is ubiquitous, hence it requires not only learning the discriminative features, but also modeling the uncertainty based on the input. This paper proposes to learn the sample posterior and the class…

Computer Vision and Pattern Recognition · Computer Science 2020-07-20 Yan Zhang , Zhilin Zheng , Binyu He , Li Sun

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…

Methodology · Statistics 2020-07-09 Yan Dora Zhang , Brian P. Naughton , Howard D. Bondell , Brian J. Reich

Uncertainty quantification is essential when dealing with ill-conditioned inverse problems due to the inherent nonuniqueness of the solution. Bayesian approaches allow us to determine how likely an estimation of the unknown parameters is…

Machine Learning · Statistics 2020-01-16 Ali Siahkoohi , Gabrio Rizzuti , Felix J. Herrmann

In this paper we adopt the familiar sparse, high-dimensional linear regression model and focus on the important but often overlooked task of prediction. In particular, we consider a new empirical Bayes framework that incorporates data in…

Statistics Theory · Mathematics 2020-07-28 Ryan Martin , Yiqi Tang

We study the stability of posterior predictive inferences to the specification of the likelihood model and perturbations of the data generating process. In modern big data analyses, useful broad structural judgements may be elicited from…

Methodology · Statistics 2024-04-30 Jack Jewson , Jim Q. Smith , Chris Holmes

We introduce a novel Bayesian estimator for the class proportion in an unlabeled dataset, based on the targeted learning framework. Our procedure requires the specification of a prior (and outputs a posterior) only for the target of…

Methodology · Statistics 2019-11-26 Iván Díaz , Oleksander Savenkov , Hooman Kamel

We study full Bayesian procedures for high-dimensional linear regression under sparsity constraints. The prior is a mixture of point masses at zero and continuous distributions. Under compatibility conditions on the design matrix, the…

Statistics Theory · Mathematics 2015-10-15 Ismaël Castillo , Johannes Schmidt-Hieber , Aad van der Vaart

When prior information is lacking, the go-to strategy for probabilistic inference is to combine a "default prior" and the likelihood via Bayes's theorem. Objective Bayes, (generalized) fiducial inference, etc. fall under this umbrella. This…

Methodology · Statistics 2026-01-05 Ryan Martin

When dealing with Bayesian inference the choice of the prior often remains a debatable question. Empirical Bayes methods offer a data-driven solution to this problem by estimating the prior itself from an ensemble of data. In the…

Methodology · Statistics 2020-05-13 Ilja Klebanov , Alexander Sikorski , Christof Schütte , Susanna Röblitz

The main object of Bayesian statistical inference is the determination of posterior distributions. Sometimes these laws are given for quantities devoid of empirical value. This serious drawback vanishes when one confines oneself to…

Statistical Finance · Quantitative Finance 2008-12-02 Federico Bassetti

The power-expected-posterior (PEP) prior is an objective prior for Gaussian linear models, which leads to consistent model selection inference, under the M-closed scenario, and tends to favor parsimonious models. Recently, two new forms of…

Methodology · Statistics 2019-11-22 Dimitris Fouskakis , Ioannis Ntzoufras , Konstantinos Perrakis

The classical Bayesian posterior arises naturally as the unique solution of several different optimization problems, without the necessity of interpreting data as conditional probabilities and then using Bayes' Theorem. For example, the…

Statistics Theory · Mathematics 2012-03-02 Theodore P. Hill , Marco Dall'Aglio

In this article, we investigate posterior convergence in nonparametric regression models where the unknown regression function is modeled by some appropriate stochastic process. In this regard, we consider two setups. The first setup is…

Statistics Theory · Mathematics 2020-05-04 Debashis Chatterjee , Sourabh Bhattacharya

We investigate the asymptotic behavior of Bayesian posterior distributions under independent and identically distributed ($i.i.d.$) misspecified models. More specifically, we study the concentration of the posterior distribution on…

Statistics Theory · Mathematics 2015-12-04 R. V. Ramamoorthi , Karthik Sriram , Ryan Martin

The remarkable generalization performance of large-scale models has been challenging the conventional wisdom of the statistical learning theory. Although recent theoretical studies have shed light on this behavior in linear models and…

Machine Learning · Statistics 2024-06-18 Tomoya Wakayama

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…

Machine Learning · Computer Science 2024-01-24 Sebastian W. Ober

Bayesian inference provides a principled probabilistic framework for quantifying uncertainty by updating beliefs based on prior knowledge and observed data through Bayes' theorem. In Bayesian deep learning, neural network weights are…

Machine Learning · Computer Science 2024-10-22 Yijie Zhang

Standard Bayesian inference is known to be sensitive to model misspecification, leading to unreliable uncertainty quantification and poor predictive performance. However, finding generally applicable and computationally feasible methods for…

Methodology · Statistics 2020-07-31 Jonathan H. Huggins , Jeffrey W. Miller

Utility preference robust optimization (PRO) has recently been proposed to deal with optimal decision making problems where the decision maker's (DM) preference over gains and losses is ambiguous. In this paper, we take a step further to…

Optimization and Control · Mathematics 2024-03-11 Jian Hu , Dali Zhang , Huifu Xu , Sainan Zhang