Related papers: Prior- and likelihood-free probabilistic inference…

In this paper we consider the estimation of unknown parameters in Bayesian inverse problems. In most cases of practical interest, there are several barriers to performing such estimation, This includes a numerical approximation of a…

When the sample path of a Hawkes process is observed discretely, such that only the total event counts in disjoint time intervals are known, the likelihood function becomes intractable. To overcome the challenge of likelihood-based…

We present a multi-fidelity method for uncertainty quantification of parameter estimates in complex systems, leveraging generative models trained to sample the target conditional distribution. In the Bayesian inference setting, traditional…

Quantifying and reducing uncertainty in Earth system model parameterizations is essential to improving their reliability in decision-making. Forward uncertainty propagation is used to derive parameter sensitivity but requires physically…

Using observation data to estimate unknown parameters in computational models is broadly important. This task is often challenging because solutions are non-unique due to the complexity of the model and limited observation data. However,…

Rigorous statistical methods, including parameter estimation with accompanying uncertainties, underpin the validity of scientific discovery, especially in the natural sciences. With increasingly complex data models such as deep learning…

In this article the issues are discussed with the Bayesian approach, least-square fits, and most-likely fits. Trying to counter these issues, a method, based on weighted confidence, is proposed for estimating probabilities and other…

This paper explores generalised probabilistic modelling and uncertainty estimation in comparative LLM-as-a-judge frameworks. We show that existing Product-of-Experts methods are specific cases of a broader framework, enabling diverse…

This paper addresses the problem of quantification and propagation of uncertainties associated with dependence modeling when data for characterizing probability models are limited. Practically, the system inputs are often assumed to be…

A maximum likelihood methodology for the parameters of models with an intractable likelihood is introduced. We produce a likelihood-free version of the stochastic approximation expectation-maximization (SAEM) algorithm to maximize the…

Modern applications routinely collect high-dimensional data, leading to statistical models having more parameters than there are samples available. A common solution is to impose sparsity in parameter estimation, often using penalized…

We present a computational framework for estimating the uncertainty in the numerical solution of linearized infinite-dimensional statistical inverse problems. We adopt the Bayesian inference formulation: given observational data and their…

Constructing tests or confidence regions that control over the error rates in the long-run is probably one of the most important problem in statistics. Yet, the theoretical justification for most methods in statistics is asymptotic. The…

Empirical Bayes methods are widely used for large-scale estimation and inference in the Poisson means problem. Existing results establish theoretical properties of the nonparametric maximum likelihood estimator (NPMLE) for optimal posterior…

We extend the model-free Data-Driven computing paradigm to solids and structures that are stochastic due to intrinsic randomness in the material behavior. The behavior of such materials is characterized by a likelihood measure instead of a…

Given i.i.d. data from an unknown distribution, we consider the problem of predicting future items. An adaptive way to estimate the probability density is to recursively subdivide the domain to an appropriate data-dependent granularity. A…

We present a universal framework for constructing confidence sets based on sequential likelihood mixing. Building upon classical results from sequential analysis, we provide a unifying perspective on several recent lines of work, and…

Conformal prediction (CP) was developed to provide finite-sample probabilistic prediction guarantees. While CP algorithms are a relatively general-purpose approach to uncertainty quantification, with finite-sample guarantees, they lack…

Divide-and-conquer methods use large-sample approximations to provide frequentist guarantees when each block of data is both small enough to facilitate efficient computation and large enough to support approximately valid inferences. When…

Likelihood-free inference provides a rigorous approach to preform Bayesian analysis using forward simulations only. The main advantage of likelihood-free methods is its ability to account for complex physical processes and observational…