Related papers: Besting Good--Turing: Optimality of Non-Parametric…

Selective classification enhances the reliability of predictive models by allowing them to abstain from making uncertain predictions. In this work, we revisit the design of optimal selection functions through the lens of the Neyman--Pearson…

When classical particle filtering algorithms are used for maximum likelihood parameter estimation in nonlinear state-space models, a key challenge is that estimates of the likelihood function and its derivatives are inherently noisy. The…

We address the problem of data clustering by introducing an unsupervised, parameter free approach based on maximum likelihood principle. Starting from the observation that data sets belonging to the same cluster share a common information,…

Mixed-effect models are widely used for the analysis of correlated data such as longitudinal data and repeated measures. In this article, we study an approach to the nonparametric estimation of mixed-effect models. We consider models with…

Likelihood-based inference for multivariate extreme-value models is often unreliable or infeasible when likelihoods are intractable or supports are discrete. This challenge is particularly acute for multivariate discrete generalized Pareto…

Capturing aleatoric uncertainty is a critical part of many machine learning systems. In deep learning, a common approach to this end is to train a neural network to estimate the parameters of a heteroscedastic Gaussian distribution by…

This article introduces a framework for evaluating statistical decisions under both prior ambiguity and likelihood misspecification. We begin with an ambiguity set - a frequentist model that pairs a possibly misspecified likelihood with…

It has historically been a challenge to perform Bayesian inference in a design-based survey context. The present paper develops a Bayesian model for sampling inference in the presence of inverse-probability weights. We use a hierarchical…

Predicting the outcomes of quantum measurements is a cornerstone of quantum information theory and a key resource for quantum technologies. Here, we introduce a comprehensive framework for quantifying the predictability of measurements on a…

Many mathematical imaging problems are posed as non-convex optimization problems. When numerically tractable global optimization procedures are not available, one is often interested in testing ex post facto whether or not a locally…

A simple derivation of the optimal state estimation of a quantum bit was obtained by using the no-signaling principle. In particular, the no-signaling principle determines a unique form of the guessing probability independently of figures…

Simulation-based inference enables learning the parameters of a model even when its likelihood cannot be computed in practice. One class of methods uses data simulated with different parameters to infer models of the likelihood-to-evidence…

Accurate simulation of complex physical systems enables the development, testing, and certification of control strategies before they are deployed into the real systems. As simulators become more advanced, the analytical tractability of the…

We present a general non-parametric statistical inference theory for integrals of quantiles without assuming any specific sampling design or dependence structure. Technical considerations are accompanied by examples and discussions,…

This paper studies an approximation method for the log-likelihood function of a nonlinear diffusion process using the bridge of the diffusion. The main result (Theorem \refthm:approx) shows that this approximation converges uniformly to the…

Neural estimators are simulation-based estimators for the parameters of a family of statistical models, which build a direct mapping from the sample to the parameter vector. They benefit from the versatility of available network…

We study the problem of estimating, in the sense of optimal transport metrics, a measure which is assumed supported on a manifold embedded in a Hilbert space. By establishing a precise connection between optimal transport metrics, optimal…

When prior information is lacking, the go-to strategy for probabilistic inference is to combine a "default prior" and the likelihood via Bayes's theorem. Objective Bayes, (generalized) fiducial inference, etc. fall under this umbrella. This…

Turing's estimator allows one to estimate the probabilities of outcomes that either do not appear or only rarely appear in a given random sample. We perform a simulation study to understand the finite sample performance of several related…

This paper considers an empirical likelihood inference for parameters defined by general estimating equations, when data are missing at random. The efficiency of existing estimators depends critically on correctly specifying the conditional…