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Many two-sample problems call for a comparison of two distributions from an exponential family. Density ratio estimation methods provide ways to solve such problems through direct estimation of the differences in natural parameters. The…

Statistics Theory · Mathematics 2025-02-19 Erika Banzato , Mathias Drton , Kian Saraf-Poor , Hongjian Shi

This article concerns testing for equality of distribution between groups. We focus on screening variables with shared distributional features such as common support, modes and patterns of skewness. We propose a Bayesian testing method…

Methodology · Statistics 2016-02-19 Eric F. Lock , David B. Dunson

When analyzing modern machine learning algorithms, we may need to handle kernel density estimation (KDE) with intricate kernels that are not designed by the user and might even be irregular and asymmetric. To handle this emerging challenge,…

Statistics Theory · Mathematics 2021-06-09 Hau-Tieng Wu , Nan Wu

We investigate predictive densities for multivariate normal models with unknown mean vectors and known covariance matrices. Bayesian predictive densities based on shrinkage priors often have complex representations, although they are…

Methodology · Statistics 2022-12-08 Michiko Okudo , Fumiyasu Komaki

Recent work has attempted to directly approximate the `function-space' or predictive posterior distribution of Bayesian models, without approximating the posterior distribution over the parameters. This is appealing in e.g. Bayesian neural…

Machine Learning · Statistics 2020-11-19 David R. Burt , Sebastian W. Ober , Adrià Garriga-Alonso , Mark van der Wilk

Kernel estimation of a probability density function supported on the unit interval has proved difficult, because of the well known boundary bias issues a conventional kernel density estimator would necessarily face in this situation.…

Methodology · Statistics 2013-03-19 Gery Geenens

In this paper, we consider the problem of estimating the density function of a Chi-squared variable on the basis of observations of another Chi-squared variable and a normal variable under the Kullback-Leibler divergence. We assume that…

Statistics Theory · Mathematics 2021-07-22 Yasuyuki Hamura , Tatsuya Kubokawa

This paper deals with a method for the approximation of a spectral density function among the solutions of a generalized moment problem a` la Byrnes/Georgiou/Lindquist. The approximation is pursued with respect to the Kullback-Leibler…

Optimization and Control · Mathematics 2009-11-04 Augusto Ferrante , Federico Ramponi , Francesco Ticozzi

Shape restriction, like monotonicity or convexity, imposed on a function of interest, such as a regression or density function, allows for its estimation without smoothness assumptions. The concept of $k$-monotonicity encompasses a family…

Statistics Theory · Mathematics 2023-06-09 Kang Wang , Subhashis Ghosal

We introduce a density basis of the trigonometric polynomials that is suitable to mixture modelling. Statistical and geometric properties are derived, suggesting it as a circular analogue to the Bernstein polynomial densities. Nonparametric…

Methodology · Statistics 2019-02-26 Olivier Binette , Simon Guillotte

The practice of employing empirical likelihood (EL) components in place of parametric likelihood functions in the construction of Bayesian-type procedures has been well-addressed in the modern statistical literature. We rigorously derive…

Methodology · Statistics 2018-08-21 Albert Vexler , Li Zou , Alan D. Hutson

In this paper, we discuss a property of the Kullback--Leibler divergence measured between two models of the family of the location-scale distributions. We show that, if model $M_1$ and model $M_2$ are represented by location-scale…

Statistics Theory · Mathematics 2016-04-08 Cristiano Villa

We derive necessary conditions for localization of continuous frames in terms of generalized Beurling densities. As an important application we provide necessary density conditions for sampling and interpolation in a very large class of…

Functional Analysis · Mathematics 2023-05-02 Mishko Mitkovski , Aaron Ramirez

Modern datasets across many disciplines increasingly consist of time-evolving, potentially infinite-dimensional random objects, such as dynamic functional data, which are naturally modeled in Hilbert spaces. In these settings,…

Machine Learning · Statistics 2026-05-08 Daniel López-Montero , Antonio Álvarez-López , Marcos Matabuena

Bayesian sequence prediction is a simple technique for predicting future symbols sampled from an unknown measure on infinite sequences over a countable alphabet. While strong bounds on the expected cumulative error are known, there are only…

Machine Learning · Computer Science 2013-07-02 Tor Lattimore , Marcus Hutter , Peter Sunehag

We study the maximum likelihood estimator of density of $n$ independent observations, under the assumption that it is well approximated by a mixture with a large number of components. The main focus is on statistical properties with respect…

Statistics Theory · Mathematics 2017-01-19 Arnak S. Dalalyan , Mehdi Sebbar

A generalized Kullback-Leibler relative entropy is introduced starting with the symmetric Jackson derivative of the generalized overlap between two probability distributions. The generalization retains much of the structure possessed by the…

Statistical Mechanics · Physics 2015-05-13 Takuya Yamano

The prediction of the variance-covariance matrix of the multivariate normal distribution is important in the multivariate analysis. We investigated Bayesian predictive distributions for Wishart distributions under the Kullback-Leibler…

Statistics Theory · Mathematics 2022-09-26 Hidemasa Oda , Fumiyasu Komaki

In this paper, we use the class of Wasserstein metrics to study asymptotic properties of posterior distributions. Our first goal is to provide sufficient conditions for posterior consistency. In addition to the well-known Schwartz's…

Statistics Theory · Mathematics 2021-07-01 Minwoo Chae , Pierpaolo De Blasi , Stephen G. Walker

We investigate the convergence properties of popular data-augmentation samplers for Bayesian probit regression. Leveraging recent results on Gibbs samplers for log-concave targets, we provide simple and explicit non-asymptotic bounds on the…

Computation · Statistics 2025-05-21 Filippo Ascolani , Giacomo Zanella