Related papers: Convergence of Probability Densities using Approxi…

We provide finite-sample distribution approximations, that are uniform in the parameter, for inference in linear mixed models. Focus is on variances and covariances of random effects in cases where existing theory fails because their…

This paper concerns a spectral estimation problem in which we want to find a spectral density function that is consistent with estimated second-order statistics. It is an inverse problem admitting multiple solutions, and selection of a…

Accurate approximation of probability measures is essential in numerical applications. This paper explores the quantization of probability measures using the maximum mean discrepancy (MMD) distance as a guiding metric. We first investigate…

Probabilistic programs are typically normal-looking programs describing posterior probability distributions. They intrinsically code up randomized algorithms and have long been at the heart of modern machine learning and approximate…

Diffusion models have emerged as powerful tools for solving inverse problems, yet prior work has primarily focused on observations with Gaussian measurement noise, restricting their use in real-world scenarios. This limitation persists due…

Bayesian models quantify uncertainty and facilitate optimal decision-making in downstream applications. For most models, however, practitioners are forced to use approximate inference techniques that lead to sub-optimal decisions due to…

A common problem in natural sciences is the comparison of competing models in the light of observed data. Bayesian model comparison provides a statistically sound framework for this comparison based on the evidence each model provides for…

The inverse potential problem consists in determining the density of the volume potential from measurements outside the sources. Its ill-posedness is due both to the non-uniqueness of the solution and to the instability of the solution with…

Inverse Kohn-Sham (iKS) problems are needed to fully understand the one-to-one mapping between densities and potentials on which Density Functional Theory is based. They are also important to advance computational schemes that rely on…

We compute approximate solutions to inverse problems for determining parameters in differential equation models with stochastic data on output quantities. The formulation of the problem and modeling framework define a solution as a…

Finite mixture models provide a flexible framework for approximating and estimating multivariate probability densities. We study mixtures formed from translated and rescaled copies of a fixed density kernel and obtain explicit results for…

Probabilistic databases (PDBs) are used to model uncertainty in data in a quantitative way. In the standard formal framework, PDBs are finite probability spaces over relational database instances. It has been argued convincingly that this…

We report the application of implicit likelihood inference to the prediction of the macro-parameters of strong lensing systems with neural networks. This allows us to perform deep learning analysis of lensing systems within a well-defined…

In quantum mechanics, a norm squared wave function can be interpreted as the probability density that describes the likelihood of a particle to be measured in a given position or momentum. This statistical property is at the core of the…

The probability density quantile (pdQ) carries essential information regarding shape and tail behavior of a location-scale family. Convergence of repeated applications of the pdQ mapping to the uniform distribution is investigated and new…

We present a critical survey on the consistency of uncertainty quantification used in deep learning and highlight partial uncertainty coverage and many inconsistencies. We then provide a comprehensive and statistically consistent framework…

We consider statistical inference in the density estimation model using a tree-based Bayesian approach, with Optional P\'olya trees as prior distribution. We derive near-optimal convergence rates for corresponding posterior distributions…

An often-cited fact regarding mixing or mixture distributions is that their density functions are able to approximate the density function of any unknown distribution to arbitrary degrees of accuracy, provided that the mixing or mixture…

Kernel density estimation is a widely used nonparametric approach to estimate an unknown distribution. Recent work in Bayesian predictive inference has considered stochastic processes formed by specifying the predictive distribution for the…

In ill-posed inverse problems, it is commonly desirable to obtain insight into the full spectrum of plausible solutions, rather than extracting only a single reconstruction. Information about the plausible solutions and their likelihoods is…