Related papers: Optimal properties of the canonical tight probabil…
Given a metric space with a Borel probability measure, for each integer $N$ we obtain a probability distribution on $N\times N$ distance matrices by considering the distances between pairs of points in a sample consisting of $N$ points…
We formulate, and present a numerical method for solving, an inverse problem for inferring parameters of a deterministic model from stochastic observational data (quantities of interest). The solution, given as a probability measure, is…
The Wasserstein distance is an attractive tool for data analysis but statistical inference is hindered by the lack of distributional limits. To overcome this obstacle, for probability measures supported on finitely many points, we derive…
Estimating a $d$-dimensional distribution $\mu$ by the empirical measure $\hat{\mu}_n$ of its samples is an important task in probability theory, statistics and machine learning. It is well known that $\mathbb{E}[\mathcal{W}_p(\hat{\mu}_n,…
Given two measurable spaces $H$ and $D$ with countably generated $\sigma$-algebras, a perfect prior probability measure $P_H$ on $H$ and a sampling distribution $S: H \rightarrow D$, there is a corresponding inference map $I: D \rightarrow…
In this paper, we explore a static setting for the assessment of risk in the context of mathematical finance and actuarial science that takes into account model uncertainty in the distribution of a possibly infinite-dimensional risk factor.…
I propose a semiparametric Bayesian inference framework for conditional moment equalities. The core idea is that these models deterministically map a conditional distribution of data to a structural parameter via the restriction that a…
The topic of this paper is the typical behavior of the spectral measures of large random matrices drawn from several ensembles of interest, including in particular matrices drawn from Haar measure on the classical Lie groups, random…
We propose a new abstract formalism for probabilistic timed systems, Parametric Interval Probabilistic Timed Automata, based on an extension of Parametric Timed Automata and Interval Markov Chains. In this context, we consider the…
We study what is arguably the most experimentally appealing Boson Sampling architecture: Gaussian states sampled with threshold detectors. We show that in this setting, the probability of observing a given outcome is related to a matrix…
We investigate the minimal error in approximating a general probability measure $\mu$ on $\mathbb{R}^d$ by the uniform measure on a finite set with prescribed cardinality $n$. The error is measured in the $p$-Wasserstein distance. In…
Probabilistic programming methods have revolutionised Bayesian inference, making it easier than ever for practitioners to perform Markov-chain-Monte-Carlo sampling from non-conjugate posterior distributions. Here we focus on Stan, arguably…
This paper presents a detailed theoretical analysis of the three stochastic approximation proximal gradient algorithms proposed in our companion paper [49] to set regularization parameters by marginal maximum likelihood estimation. We prove…
In this paper we introduce randomized branching as a tool for parameterized approximation and develop the mathematical machinery for its analysis. Our algorithms improve the best known running times of parameterized approximation algorithms…
We introduce a novel optimal transport framework for probabilistic circuits (PCs). While it has been shown recently that divergences between distributions represented as certain classes of PCs can be computed tractably, to the best of our…
The Chisholm rational approximant is a natural generalization to two variables of the well-known single variable Pad\'e approximant, and has the advantage of reducing to the latter when one of the variables is set equals to 0. We present,…
Let $H$ be an infinite-dimensional separable Hilbert space and let $(X,d,\mu)$ be a metric measure space satisfying the doubling and upper Alhfors regularity conditions at small scale. We prove that every bounded continuous tight frame…
The inferential model (IM) framework offers alternatives to the familiar probabilistic (e.g., Bayesian and fiducial) uncertainty quantification in statistical inference. Allowing this uncertainty quantification to be imprecise makes it…
We examine Fourier frames and, more generally, frame measures for different probability measures. We prove that if a measure has an associated frame measure, then it must have a certain uniformity in the sense that the weight is distributed…
Stochastic filtering refers to estimating the probability distribution of the latent stochastic process conditioned on the observed measurements in time. In this paper, we introduce a new class of convergent filters that represent the…