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The concept of data depth leads to a center-outward ordering of multivariate data, and it has been effectively used for developing various data analytic tools. While different notions of depth were originally developed for finite…

We present a novel approach to Bayesian inference and general Bayesian computation that is defined through a sequential decision loop. Our method defines a recursive partitioning of the sample space. It neither relies on gradients nor…

Indirect inference estimators (i.e., simulation-based minimum distance estimators) in a parametric model that are based on auxiliary non-parametric maximum likelihood density estimators are shown to be asymptotically normal. If the…

This paper proposes various nonparametric tools based on measure transportation for directional data. We use optimal transports to define new notions of distribution and quantile functions on the hypersphere, with meaningful quantile…

Probabilistic regression models the entire predictive distribution of a response variable, offering richer insights than classical point estimates and directly allowing for uncertainty quantification. While diffusion-based generative models…

Estimation of response functions is an important task in dynamic medical imaging. This task arises for example in dynamic renal scintigraphy, where impulse response or retention functions are estimated, or in functional magnetic resonance…

In this paper a method of obtaining smooth analytical estimates of probability densities, radial distribution functions and potentials of mean force from sampled data in a statistically controlled fashion is presented. The approach is…

If two random variables X and A are functionally related via f(X)=A for some strictly monotone continuously differentiable function f:R->R, the distribution of X may easily be computed from the distribution of A.

Information generating functions have been used for generating various entropy and divergence measures. In the present work, we introduce quantile based relative information generating function and study its properties. The proposed…

We consider statistical models where functional data are artificially contaminated by independent Wiener processes in order to satisfy privacy constraints. We show that the corrupted observations have a Wiener density which determines the…

Functional depth is the functional data analysis technique that orders a functional data set. Unlike the case of data on the real line, defining this order is non-trivial, and particularly, with functional data, there are a number of…

We propose an alternative to $k$-nearest neighbors for functional data whereby the approximating neighboring curves are piecewise functions built from a functional sample. Using a locally defined distance function that satisfies…

This article develops an analytical framework for studying information divergences and likelihood ratios associated with Poisson processes and point patterns on general measurable spaces. The main results include explicit analytical…

A fast nonparametric procedure for classifying functional data is introduced. It consists of a two-step transformation of the original data plus a classifier operating on a low-dimensional hypercube. The functional data are first mapped…

Accurate approximation of a real-valued function depends on two aspects of the available data: the density of inputs within the domain of interest and the variation of the outputs over that domain. There are few methods for assessing…

$f$-divergences, which quantify discrepancy between probability distributions, are ubiquitous in information theory, machine learning, and statistics. While there are numerous methods for estimating $f$-divergences from data, a limit…

Histograms are convenient non-parametric density estimators, which continue to be used ubiquitously. Summary quantities estimated from histogram-based probability density models depend on the choice of the number of bins. We introduce a…

Most saliency estimation methods aim to explicitly model low-level conspicuity cues such as edges or blobs and may additionally incorporate top-down cues using face or text detection. Data-driven methods for training saliency models using…

Optimality results for two outstanding Bayesian estimation problems are given in this paper: the estimation of the sampling distribution for the squared total variation function and the estimation of the density for the $L^1$-squared loss…

In supervised learning, the output variable to be predicted is often represented as a function, such as a spectrum or probability distribution. Despite its importance, functional output regression remains relatively unexplored. In this…