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Bayesian analysis has become an indispensable tool across many different cosmological fields including the study of gravitational waves, the Cosmic Microwave Background and the 21-cm signal from the Cosmic Dawn among other phenomena. The…

Instrumentation and Methods for Astrophysics · Physics 2023-12-19 Harry T. J. Bevins , William J. Handley , Pablo Lemos , Peter H. Sims , Eloy de Lera Acedo , Anastasia Fialkov , Justin Alsing

We consider the task of estimating a conditional density using i.i.d. samples from a joint distribution, which is a fundamental problem with applications in both classification and uncertainty quantification for regression. For joint…

Statistics Theory · Mathematics 2023-06-16 Blair Bilodeau , Dylan J. Foster , Daniel M. Roy

This article is devoted to the study of overlap measures of densities of two exponential populations. Various Overlapping Coefficients, namely: Matusita's measure $\rho$, Morisita's measure $\lambda$ and Weitzman's measure $\Delta$. A new…

Methodology · Statistics 2017-04-11 Hamza Dhaker , Papa Ngom , Malick Mbodj

We study the problem of nonparametric estimation of density functions with a product form on the domain $\triangle=\{( x_1, \ldots, x_d)\in \mathbb{R}^d, 0\leq x_1\leq \dots \leq x_d \leq 1\}$. Such densities appear in the random truncation…

Statistics Theory · Mathematics 2016-04-22 Cristina Butucea , Jean-François Delmas , Anne Dutfoy , Richard Fischer

Recent work has focused on the problem of nonparametric estimation of information divergence functionals. Many existing approaches are restrictive in their assumptions on the density support set or require difficult calculations at the…

Information Theory · Computer Science 2021-07-30 Kevin R. Moon , Kumar Sricharan , Kristjan Greenewald , Alfred O. Hero

We investigate Bayesian nonparametric density estimation via orthogonal polynomial expansions in weighted Sobolev spaces. A core challenge is establishing minimax optimal posterior convergence rates, especially for densities on unbounded…

Statistics Theory · Mathematics 2026-03-20 Yiqi Luo , Xue Luo

Optimum designs for parameter estimation in generalized regression models are standardly based on the Fisher information matrix (cf. Atkinson et al (2014) for a recent exposition). The corresponding optimality criteria are related to the…

Statistics Theory · Mathematics 2015-07-28 Katarína Burclová , Andrej Pázman

Approximate Bayesian inference on the basis of summary statistics is well-suited to complex problems for which the likelihood is either mathematically or computationally intractable. However the methods that use rejection suffer from the…

Computation · Statistics 2010-05-04 M. G. B. Blum , O. Francois

In this paper, we address the problem of estimating a multidimensional density $f$ by using indirect observations from the statistical model $Y=X+\varepsilon$. Here, $\varepsilon$ is a measurement error independent of the random vector $X$…

Statistics Theory · Mathematics 2015-05-15 Gilles Rebelles

This paper provides a unified perspective for the Kullback-Leibler (KL)-divergence and the integral probability metrics (IPMs) from the perspective of maximum likelihood density-ratio estimation (DRE). Both the KL-divergence and the IPMs…

Machine Learning · Computer Science 2022-02-01 Masahiro Kato , Masaaki Imaizumi , Kentaro Minami

Variational Inference is a powerful tool in the Bayesian modeling toolkit, however, its effectiveness is determined by the expressivity of the utilized variational distributions in terms of their ability to match the true posterior…

Machine Learning · Statistics 2019-05-10 Artem Sobolev , Dmitry Vetrov

In this paper we propose a Bayesian, information theoretic approach to dimensionality reduction. The approach is formulated as a variational principle on mutual information, and seamlessly addresses the notions of sufficiency, relevance,…

Data Analysis, Statistics and Probability · Physics 2007-05-23 David R. Wolf , Edward I. George

We show that rate-adaptive multivariate density estimation can be performed using Bayesian methods based on Dirichlet mixtures of normal kernels with a prior distribution on the kernel's covariance matrix parameter. We derive sufficient…

Statistics Theory · Mathematics 2013-08-22 Weining Shen , Surya T. Tokdar , Subhashis Ghosal

The problem of adaptive sampling for estimating probability mass functions (pmf) uniformly well is considered. Performance of the sampling strategy is measured in terms of the worst-case mean squared error. A Bayesian variant of the…

Methodology · Statistics 2020-12-09 Dhruva Kartik , Neeraj Sood , Urbashi Mitra , Tara Javidi

We consider Bayesian nonparametric density estimation using a Pitman-Yor or a normalized inverse-Gaussian process kernel mixture as the prior distribution for a density. The procedure is studied from a frequentist perspective. Using the…

Statistics Theory · Mathematics 2013-02-15 Catia Scricciolo

Group-invariant probability distributions appear in many data-generative models in machine learning, such as graphs, point clouds, and images. In practice, one often needs to estimate divergences between such distributions. In this work, we…

Machine Learning · Computer Science 2026-02-05 Behrooz Tahmasebi , Stefanie Jegelka

In the sparse normal means model, convergence of the Bayesian posterior distribution associated to spike and slab prior distributions is considered. The key sparsity hyperparameter is calibrated via marginal maximum likelihood empirical…

Statistics Theory · Mathematics 2018-10-17 Ismaël Castillo , Romain Mismer

We deal with the problem of the adaptive estimation of the $\mathbb{L}_2$-norm of a probability density on $\mathbb{R}^d$, $d\geq 1$, from independent observations. The unknown density is assumed to be uniformly bounded and to belong to the…

Statistics Theory · Mathematics 2024-05-28 Galatia Cleanthous , Athanasios G. Georgiadis , Oleg V. Lepski

In some misspecified settings, the posterior distribution in Bayesian statistics may lead to inconsistent estimates. To fix this issue, it has been suggested to replace the likelihood by a pseudo-likelihood, that is the exponential of a…

Statistics Theory · Mathematics 2019-12-12 Badr-Eddine Chérief-Abdellatif , Pierre Alquier

There is a growing interest in learning how the distribution of a response variable changes with a set of predictors. Bayesian nonparametric dependent mixture models provide a flexible approach to address this goal. However, several…

Computation · Statistics 2020-05-06 Tommaso Rigon , Daniele Durante