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In Bayesian nonparametric inference, random discrete probability measures are commonly used as priors within hierarchical mixture models for density estimation and for inference on the clustering of the data. Recently, it has been shown…

Statistics Theory · Mathematics 2012-11-26 Stefano Favaro , Antonio Lijoi , Igor Prünster

Bayesian model comparison (BMC) offers a principled probabilistic approach to study and rank competing models. In standard BMC, we construct a discrete probability distribution over the set of possible models, conditional on the observed…

Machine Learning · Statistics 2023-02-22 Marvin Schmitt , Stefan T. Radev , Paul-Christian Bürkner

Bayesian model comparison is often based on the posterior distribution over the set of compared models. This distribution is often observed to concentrate on a single model even when other measures of model fit or forecasting ability…

Statistics Theory · Mathematics 2020-03-10 Oscar Oelrich , Shutong Ding , Måns Magnusson , Aki Vehtari , Mattias Villani

We obtain an asymptotic normality result that reveals the precise asymptotic behavior of the maximum likelihood estimators of parameters for a very general class of linear mixed models containing cross random effects. In achieving the…

Statistics Theory · Mathematics 2026-02-10 Jiming Jiang , Matt P. Wand , Swarnadip Ghosh

Bayesian statistics has two common measures of central tendency of a posterior distribution: posterior means and Maximum A Posteriori (MAP) estimates. In this paper, we discuss a connection between MAP estimates and posterior means. We…

Statistics Theory · Mathematics 2024-10-02 Michiko Okudo , Keisuke Yano

We consider the sparse high-dimensional linear regression model $Y=Xb+\epsilon$ where $b$ is a sparse vector. For the Bayesian approach to this problem, many authors have considered the behavior of the posterior distribution when, in truth,…

Statistics Theory · Mathematics 2017-04-11 Dana Yang

Consider semiparametric models that display local asymptotic exponentiality (Ibragimov and Has'minskii (1981)), an asymptotic property of the likelihood associated with discontinuities of densities. Our interest goes to estimation of the…

Statistics Theory · Mathematics 2013-12-19 Bas Kleijn , Bartek Knapik

Bayesian inference and the use of posterior or posterior predictive probabilities for decision making have become increasingly popular in clinical trials. The current practice in Bayesian clinical trials relies on a hybrid…

Methodology · Statistics 2024-04-30 Shirin Golchi , James Willard

We present asymptotic results for the regression-adjusted version of approximate Bayesian computation introduced by Beaumont(2002). We show that for an appropriate choice of the bandwidth, regression adjustment will lead to a posterior…

Statistics Theory · Mathematics 2017-11-29 Wentao Li , Paul Fearnhead

We study the properties of variational Bayes approximations for exponential family models with missing values. It is shown that the iterative algorithm for obtaining the variational Bayesian estimator converges locally to the true value…

Statistics Theory · Mathematics 2012-07-19 Bo Wang , D. Titterington

The Peaks Over Threshold (POT) method is the most popular statistical method for the analysis of univariate extremes. Even though there is a rich applied literature on Bayesian inference for the POT, the asymptotic theory for such proposals…

Statistics Theory · Mathematics 2025-04-01 Clément Dombry , Simone A. Padoan , Stefano Rizzelli

We study the consistency of sample mean-variance portfolios of arbitrarily high dimension that are based on Bayesian or shrinkage estimation of the input parameters as well as weighted sampling. In an asymptotic setting where the number of…

Portfolio Management · Quantitative Finance 2015-05-30 Francisco Rubio , Xavier Mestre , Daniel P. Palomar

The autoregressive moving average (ARMA) model is one of the most important models in time series analysis.We consider the Bayesian estimation of an unknown spectral density in the ARMA model.In the i.i.d. cases, Komaki showed that Bayesian…

Statistics Theory · Mathematics 2021-05-27 Fuyuhiko Tanaka , Fumiyasu Komaki

We study Bayesian linear regression models with skew-symmetric scale mixtures of normal error distributions. These kinds of models can be used to capture departures from the usual assumption of normality of the errors in terms of heavy…

Applications · Statistics 2016-01-12 Francisco J. Rubio , Marc G. Genton

We derive the precise asymptotic distributional behavior of Gaussian variational approximate estimators of the parameters in a single-predictor Poisson mixed model. These results are the deepest yet obtained concerning the statistical…

Statistics Theory · Mathematics 2012-02-24 Peter Hall , Tung Pham , M. P. Wand , S. S. J. Wang

Asymptotic equivalence results for nonparametric regression experiments have always assumed that the variances of the observations are known. In practice, however the variance of each observation is generally considered to be an unknown…

Statistics Theory · Mathematics 2007-11-06 Andrew V. Carter

Contemporary focus on selective inference has renewed interest in the theory of selection models. In this paper, we analyze the asymptotic properties of selection models built on independent and identically distributed observations. We show…

Statistics Theory · Mathematics 2026-03-16 Daniel G. Rasines , G. Alastair Young

Asymptotic equivalence in Le Cam's sense for nonparametric regression experiments is extended to the case of non-regular error densities, which have jump discontinuities at their endpoints. We prove asymptotic equivalence of such regression…

Statistics Theory · Mathematics 2011-01-28 Alexander Meister , Markus Reiß

Mathematical models of real life phenomena are highly nonlinear involving multiple parameters and often exhibiting complex dynamics. Experimental data sets are typically small and noisy, rendering estimation of parameters from such data…

Chaotic Dynamics · Physics 2017-05-11 Abhirup Ghosh , Samit Bhattacharyya , Somdatta Sinha , Amit Apte

Many modern experiments, such as microarray gene expression and genome-wide association studies, present the problem of estimating a large number of parallel effects. Bayesian inference is a popular approach for analyzing such data by…

Methodology · Statistics 2018-10-26 J G Liao , Arthur Berg , Timothy L McMurry