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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

The objective Bayesian treatment of a model representing two independent Poisson processes, labelled as "signal" and "background" and both contributing additively to the total number of counted events, is considered. It is shown that the…

Data Analysis, Statistics and Probability · Physics 2015-04-16 Diego Casadei

We present a continuation method that entails generating a sequence of transition probability density functions from the prior to the posterior in the context of Bayesian inference for parameter estimation problems. The characterization of…

Computation · Statistics 2019-11-27 Ben Mansour Dia

It is shown that the first-order term of the asymptotic bias of the posterior mean is removed by a suitable choice of a prior density. In regular statistical models including exponential families, and linear and logistic regression models,…

Methodology · Statistics 2024-10-22 Miyata Yoichi , Yanagimoto Takemi

A mixture of multivariate contaminated normal distributions is developed for model-based clustering. In addition to the parameters of the classical normal mixture, our contaminated mixture has, for each cluster, a parameter controlling the…

Methodology · Statistics 2016-05-20 Antonio Punzo , Paul D. McNicholas

Reference priors are theoretically attractive for the analysis of geostatistical data since they enable automatic Bayesian analysis and have desirable Bayesian and frequentist properties. But their use is hindered by computational hurdles…

Methodology · Statistics 2022-01-27 Victor De Oliveira , Zifei Han

This paper is concerned with general nonlinear regression models where the predictor variables are subject to Berkson-type measurement errors. The measurement errors are assumed to have a general parametric distribution, which is not…

Statistics Theory · Mathematics 2009-08-21 Liqun Wang

We develop a code length principle which is invariant to the choice of parameterization on the model distributions. An invariant approximation formula for easy computation of the marginal distribution is provided for gaussian likelihood…

Information Theory · Computer Science 2007-07-13 Eirik Fossgaard

We consider the problem of distributed estimation under the Bayesian criterion and explore the design of optimal quantizers in such a system. We show that, for a conditionally unbiased and efficient estimator at the fusion center and when…

Information Theory · Computer Science 2015-06-22 Aditya Vempaty , Hao He , Biao Chen , Pramod K. Varshney

In this paper we leverage on probability over Riemannian manifolds to rethink the interpretation of priors and posteriors in Bayesian inference. The main mindshift is to move away from the idea that "a prior distribution establishes a…

Statistics Theory · Mathematics 2021-06-03 Jesus Cerquides

Simultaneous predictive densities for independent Poisson observables are investigated. The observed data and the target variables to be predicted are independently distributed according to different Poisson distributions parametrized by…

Statistics Theory · Mathematics 2021-05-27 Fumiyasu Komaki

We review common situations in Bayesian latent variable models where the prior distribution that a researcher specifies differs from the prior distribution used during estimation. These situations can arise from the positive definite…

Methodology · Statistics 2024-11-19 Edgar C. Merkle , Oludare Ariyo , Sonja D. Winter , Mauricio Garnier-Villarreal

Pre-conditioning is a well-known concept that can significantly improve the convergence of optimization algorithms. For noise-free problems, where good pre-conditioners are not known a priori, iterative linear algebra methods offer one way…

Machine Learning · Computer Science 2019-02-21 Filip de Roos , Philipp Hennig

The negative binomial distribution has been widely used as a more flexible model than the Poisson distribution for count data. However, when the true data-generating process is Poisson, it is often challenging to distinguish it from a…

Statistics Theory · Mathematics 2026-04-07 Yingying Yang , Niloufar Dousti Mousavi , Zhou Yu , Jie Yang

We consider nonparametric Bayesian inference in a multidimensional diffusion model with reflecting boundary conditions based on discrete high-frequency observations. We prove a general posterior contraction rate theorem in $L^2$-loss, which…

Statistics Theory · Mathematics 2025-08-12 Marc Hoffmann , Kolyan Ray

We consider the problem of estimating the unconditional distribution of a post-model-selection estimator. The notion of a post-model-selection estimator here refers to the combined procedure resulting from first selecting a model (e.g., by…

Statistics Theory · Mathematics 2007-11-08 Hannes Leeb , Benedikt M. Poetscher

Estimating how uncertain an AI system is in its predictions is important to improve the safety of such systems. Uncertainty in predictive can result from uncertainty in model parameters, irreducible data uncertainty and uncertainty due to…

Machine Learning · Statistics 2018-12-03 Andrey Malinin , Mark Gales

This paper addresses Bayesian inference related to partial differential equations (PDEs), particularly nonparametric regression constrained by PDEs. To effectively encode prior information, we propose a novel framework that learns a…

Statistics Theory · Mathematics 2026-02-09 Junxiong Jia , Deyu Meng , Zongben Xu , Fang Yao

We develop a new method for generating prediction sets that combines the flexibility of conformal methods with an estimate of the conditional distribution $P_{Y \mid X}$. Existing methods, such as conformalized quantile regression and…

Machine Learning · Statistics 2024-10-10 Vincent Plassier , Alexander Fishkov , Mohsen Guizani , Maxim Panov , Eric Moulines

When complex Bayesian models exhibit implausible behaviour, one solution is to assemble available information into an informative prior. Challenges arise as prior information is often only available for the observable quantity, or some…

Methodology · Statistics 2026-03-18 Andrew A. Manderson , Robert J. B. Goudie