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Additive regression models with interactions are widely studied in the literature, using methods such as splines or Gaussian process regression. However, these methods can pose challenges for estimation and model selection, due to the…

Statistics Theory · Mathematics 2023-06-14 Wicher Bergsma , Haziq Jamil

We examine the connection between training error and generalization error for arbitrary estimating procedures, working in an overparameterized linear model under general priors in a Bayesian setup. We find determining factors inherent to…

Machine Learning · Statistics 2026-02-11 Chen Cheng , Rina Foygel Barber

This paper develops some objective priors for certain parameters of the bivariate normal distribution. The parameters considered are the regression coefficient, the generalized variance, and the ratio of the conditional variance of one…

Statistics Theory · Mathematics 2008-12-18 Malay Ghosh , Upasana Santra , Dalho Kim

We derive some simple relations that demonstrate how the posterior convergence rate is related to two driving factors: a "penalized divergence" of the prior, which measures the ability of the prior distribution to propose a nonnegligible…

Statistics Theory · Mathematics 2014-11-12 Wenxin Jiang

Regression models with fat-tailed error terms are an increasingly popular choice to obtain more robust inference to the presence of outlying observations. This article focuses on Bayesian inference for the Student-$t$ linear regression…

Methodology · Statistics 2013-11-11 Catalina A. Vallejos , Mark F. J. Steel

We propose an efficient way to sample from a class of structured multivariate Gaussian distributions which routinely arise as conditional posteriors of model parameters that are assigned a conditionally Gaussian prior. The proposed…

Computation · Statistics 2016-06-28 Anirban Bhattacharya , Antik Chakraborty , Bani K. Mallick

The problem of estimating a parametric or nonparametric regression function in a model with normal errors is considered. For this purpose, a novel objective prior for the regression function is proposed, defined as the distribution…

Statistics Theory · Mathematics 2019-12-13 Wicher Bergsma

We consider evaluating improper priors in a formal Bayes setting according to the consequences of their use. Let $\Phi$ be a class of functions on the parameter space and consider estimating elements of $\Phi$ under quadratic loss. If the…

Statistics Theory · Mathematics 2011-09-07 Brian P. Shea , Galin L. Jones

Many real-world classification problems are significantly class-imbalanced to detriment of the class of interest. The standard set of proper evaluation metrics is well-known but the usual assumption is that the test dataset imbalance equals…

Machine Learning · Computer Science 2020-04-16 Jan Brabec , Tomáš Komárek , Vojtěch Franc , Lukáš Machlica

To date, we have seen the emergence of a large literature on multivariate disease mapping. That is, incidence of (or mortality from) multiple diseases is recorded at the scale of areal units where incidence (mortality) across the diseases…

Methodology · Statistics 2026-04-17 Garazi Retegui , María Dolores Ugarte , Jaione Etxeberria , Alan E. Gelfand

The problem of developing binary classifiers from positive and unlabeled data is often encountered in machine learning. A common requirement in this setting is to approximate posterior probabilities of positive and negative classes for a…

Machine Learning · Statistics 2016-01-11 Shantanu Jain , Martha White , Michael W. Trosset , Predrag Radivojac

Bayesian modeling and analysis of the MEG and EEG modalities provide a flexible framework for introducing prior information complementary to the measured data. This prior information is often qualitative in nature, making the translation of…

Mathematical Physics · Physics 2008-11-20 Daniela Calvetti , Harri Hakula , Sampsa Pursiainen , Erkki Somersalo

Applied researchers often find themselves making statistical inferences in settings that would seem to require multiple comparisons adjustments. We challenge the Type I error paradigm that underlies these corrections. Moreover we posit that…

Applications · Statistics 2009-07-16 Andrew Gelman , Jennifer Hill , Masanao Yajima

To get Bayesian neural networks to perform comparably to standard neural networks it is usually necessary to artificially reduce uncertainty using a "tempered" or "cold" posterior. This is extremely concerning: if the prior is accurate,…

Machine Learning · Statistics 2021-04-28 Laurence Aitchison

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

In the presence of modeling errors, the mainstream Bayesian methods seldom give a realistic account of uncertainties as they commonly underestimate the inherent variability of parameters. This problem is not due to any misconception in the…

Applications · Statistics 2020-05-19 Omid Sedehi , Costas Papadimitriou , Lambros S. Katafygiotis

There is growing interest in Bayesian clinical trial designs with informative prior distributions, e.g. for extrapolation of adult data to pediatrics, or use of external controls. While the classical type I error is commonly used to…

Methodology · Statistics 2023-09-06 Nicky Best , Maxine Ajimi , Beat Neuenschwander , Gaelle Saint-Hilary , Simon Wandel

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…

Statistics Theory · Mathematics 2020-04-10 Jose A. Ordoñez , Marcos O. Prates , Larissa A. Matos , Victor H. Lachos

We study full Bayesian procedures for high-dimensional linear regression. We adopt data-dependent empirical priors introduced in [1]. In their paper, these priors have nice posterior contraction properties and are easy to compute. Our paper…

Statistics Theory · Mathematics 2022-02-14 Xiao Fang , Malay Ghosh

Additional training of a deep learning model can cause negative effects on the results, turning an initially positive sample into a negative one (degradation). Such degradation is possible in real-world use cases due to the diversity of…

Machine Learning · Computer Science 2022-05-19 Akihito Yoshii , Susumu Tokumoto , Fuyuki Ishikawa