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Bayesian methods are developed for the multivariate nonparametric regression problem where the domain is taken to be a compact Riemannian manifold. In terms of the latter, the underlying geometry of the manifold induces certain symmetries…

Statistics Theory · Mathematics 2007-06-13 Jean-François Angers , Peter T. Kim

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…

Numerical Analysis · Mathematics 2024-01-05 Khalil A Hall-Hooper , Arvind K Saibaba , Julianne Chung , Scot M Miller

We put forward a novel calibration of p values, the "Adaptive Robust Lower Bound" (ARLB) which maps p values into approximations of posterior probabilities taking into account the effect of sample sizes. We build on the Robust Lower Bound…

Methodology · Statistics 2017-11-17 Luis R. Pericchi , Maria-Eglee Perez

The models used to describe the kinetics of ruminal degradation are usually nonlinear models where the dependent variable is the proportion of degraded food. The method of least squares is the standard approach used to estimate the unknown…

Applications · Statistics 2021-07-21 Diego Salmerón

Parameter estimation is a fundamental problem in science and engineering. In many safety-critical applications, one is not only interested in a {\it point} estimator, but also the uncertainty bound that can self-assess the accuracy of the…

Statistics Theory · Mathematics 2025-08-05 Qin Lu , Yaakov Bar-Shalom , Peter Willett

In this paper, we address the theoretical limitations in reconstructing sparse signals (in a known complete basis) using compressed sensing framework. We also divide the CS to non-blind and blind cases. Then, we compute the Bayesian…

Information Theory · Computer Science 2010-05-25 Hadi Zayyani , Massoud Babaie-Zadeh , Christian Jutten

The classical parametric and semiparametric Bernstein -- von Mises (BvM) results are reconsidered in a non-classical setup allowing finite samples and model misspecification. In the case of a finite dimensional nuisance parameter we obtain…

Statistics Theory · Mathematics 2020-01-24 Maxim Panov , Vladimir Spokoiny

Randomized experiments are the gold standard for evaluating the effects of changes to real-world systems. Data in these tests may be difficult to collect and outcomes may have high variance, resulting in potentially large measurement error.…

Machine Learning · Statistics 2018-06-27 Benjamin Letham , Brian Karrer , Guilherme Ottoni , Eytan Bakshy

Bayesian methods have proven themselves to be successful across a wide range of scientific problems and have many well-documented advantages over competing methods. However, these methods run into difficulties for two major and prevalent…

Methodology · Statistics 2022-07-29 John R. Lewis , Steven N. MacEachern , Yoonkyung Lee

Bayesian approaches for handling covariate measurement error are well established, and yet arguably are still relatively little used by researchers. For some this is likely due to unfamiliarity or disagreement with the Bayesian inferential…

Methodology · Statistics 2017-08-01 Jonathan W. Bartlett , Ruth H. Keogh

Bayesian estimation is increasingly popular for performing model based inference to support policymaking. These data are often collected from surveys under informative sampling designs where subject inclusion probabilities are designed to…

Methodology · Statistics 2018-07-13 Luis G. Leon-Novelo , Terrance D. Savitsky

This paper studies the minimum mean squared error (MMSE) of estimating $\mathbf{X} \in \mathbb{R}^d$ from the noisy observation $\mathbf{Y} \in \mathbb{R}^k$, under the assumption that the noise (i.e., $\mathbf{Y}|\mathbf{X}$) is a member…

Information Theory · Computer Science 2022-05-13 Ian Zieder , Alex Dytso , Martina Cardone

Using instruments comprising ordered responses to items are ubiquitous for studying many constructs of interest. However, using such an item response format may lead to items with response categories infrequently endorsed or unendorsed…

Methodology · Statistics 2024-05-02 R. Noah Padgett , Grant B. Morgan , Tim Lomas

This paper studies a problem of Bayesian parameter estimation for a sequence of scaled counting processes whose weak limit is a Brownian motion with an unknown drift. The main result of the paper is that the limit of the posterior…

Statistics Theory · Mathematics 2015-03-19 Asaf Cohen

We derive lower bounds on the Bayes risk in decentralized estimation, where the estimator does not have direct access to the random samples generated conditionally on the random parameter of interest, but only to the data received from…

Information Theory · Computer Science 2016-07-05 Aolin Xu , Maxim Raginsky

Bayesian coresets speed up posterior inference in the large-scale data regime by approximating the full-data log-likelihood function with a surrogate log-likelihood based on a small, weighted subset of the data. But while Bayesian coresets…

Machine Learning · Statistics 2024-10-18 Trevor Campbell

Minimum Bayes-risk (MBR) decoding has recently gained renewed attention in text generation. MBR decoding considers texts sampled from a model as pseudo-references and selects the text with the highest similarity to the others. Therefore,…

Computation and Language · Computer Science 2024-04-02 Atsumoto Ohashi , Ukyo Honda , Tetsuro Morimura , Yuu Jinnai

Minimum Bayes Risk (MBR) decoding has been shown to be a powerful alternative to beam search decoding in a variety of text generation tasks. MBR decoding selects a hypothesis from a pool of hypotheses that has the least expected risk under…

Artificial Intelligence · Computer Science 2024-06-13 Yuu Jinnai , Tetsuro Morimura , Ukyo Honda , Kaito Ariu , Kenshi Abe

In practical nonlinear filtering, the assessment of achievable filtering performance is important. In this paper, we focus on the problem of efficiently approximate the posterior Cramer-Rao lower bound (CRLB) in a recursive manner. By using…

Applications · Statistics 2010-05-31 Ming Lei , Pierre Del Moral , Christophe Baehr

The bootstrap provides a simple and powerful means of assessing the quality of estimators. However, in settings involving large datasets---which are increasingly prevalent---the computation of bootstrap-based quantities can be prohibitively…

Methodology · Statistics 2012-06-29 Ariel Kleiner , Ameet Talwalkar , Purnamrita Sarkar , Michael I. Jordan