English
Related papers

Related papers: Laplace-based strategies for Bayesian optimal expe…

200 papers

Computational models support high-stakes decisions across engineering and science, and practitioners increasingly seek probabilistic predictions to quantify uncertainty in such models. Existing approaches generate predictions either by…

Computational Engineering, Finance, and Science · Computer Science 2026-04-13 Rileigh Bandy , Enrico Camporeale , Andong Hu , Thomas Berger , Rebecca Morrison

The problem of Bayes minimax estimation for the mean of a multivariate normal distribution under quadratic loss has attracted significant attention recently. These estimators have the advantageous property of being admissible, similar to…

Statistics Theory · Mathematics 2025-05-13 Dominique Fourdrinier , William E. Strawderman , Martin T. Wells

This paper examines solutions to the Laplace equation using analytical techniques, including separation of variables and the Poisson integral formula, and probabilistic methods, such as Brownian motion. We address applications to imaging,…

Analysis of PDEs · Mathematics 2025-08-19 Arina Oberoi

In many instances, the application of approximate Bayesian methods is hampered by two practical features: 1) the requirement to project the data down to low-dimensional summary, including the choice of this projection, which ultimately…

Methodology · Statistics 2020-06-26 David T. Frazier

Approximate Bayesian inference for the class of latent Gaussian models can be achieved efficiently with integrated nested Laplace approximations (INLA). Based on recent reformulations in the INLA methodology, we propose a further extension…

Methodology · Statistics 2025-02-27 Shourya Dutta , Janet van Niekerk , Haavard Rue

Latent variable models for ordinal data represent a useful tool in different fields of research in which the constructs of interest are not directly observable. In such models, problems related to the integration of the likelihood function…

Methodology · Statistics 2012-06-26 Silvia Bianconcini , Silvia Cagnone

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…

Machine Learning · Statistics 2019-09-12 Tomasz Kuśmierczyk , Joseph Sakaya , Arto Klami

Laplace approximations are popular techniques for endowing deep networks with epistemic uncertainty estimates as they can be applied without altering the predictions of the trained network, and they scale to large models and datasets. While…

Machine Learning · Computer Science 2024-11-01 Tristan Cinquin , Marvin Pförtner , Vincent Fortuin , Philipp Hennig , Robert Bamler

The Bayesian decision-theoretic approach to design of experiments involves specifying a design (values of all controllable variables) to maximise the expected utility function (expectation with respect to the distribution of responses and…

Statistics Theory · Mathematics 2021-09-24 Antony M. Overstall

Bayesian Experimental Design (BED), which aims to find the optimal experimental conditions for Bayesian inference, is usually posed as to optimize the expected information gain (EIG). The gradient information is often needed for efficient…

Machine Learning · Statistics 2023-12-14 Ziqiao Ao , Jinglai Li

Symbolic regression with polynomial neural networks and polynomial neural ordinary differential equations (ODEs) are two recent and powerful approaches for equation recovery of many science and engineering problems. However, these methods…

Machine Learning · Computer Science 2023-08-28 Colby Fronk , Jaewoong Yun , Prashant Singh , Linda Petzold

Bayesian optimization is a popular and versatile approach that is well suited to solve challenging optimization problems. Their popularity comes from their effective minimization of expensive function evaluations, their capability to…

Optimization and Control · Mathematics 2026-05-14 André L. Marchildon , David W. Zingg

Our paper deals with inferring simulator-based statistical models given some observed data. A simulator-based model is a parametrized mechanism which specifies how data are generated. It is thus also referred to as generative model. We…

Machine Learning · Statistics 2016-01-01 Michael U. Gutmann , Jukka Corander

Background: We aimed to design a Bayesian adaption trial through extensive simulations to determine values for key design parameters, demonstrate error rates, and establish the expected sample size. The complexity of the proposed outcome…

The marginal likelihood is a well established model selection criterion in Bayesian statistics. It also allows to efficiently calculate the marginal posterior model probabilities that can be used for Bayesian model averaging of quantities…

Computation · Statistics 2016-11-07 Aliaksandr Hubin , Geir Storvik

The integrated nested Laplace approximation (INLA) method has become a popular approach for computationally efficient approximate Bayesian computation. In particular, by leveraging sparsity in random effect precision matrices, INLA is…

Methodology · Statistics 2024-07-02 Finn Lindgren , Fabian Bachl , Janine Illian , Man Ho Suen , Håvard Rue , Andrew E. Seaton

There is a growing demand for performing larger-scale Bayesian inference tasks, arising from greater data availability and higher-dimensional model parameter spaces. In this work we present parallelization strategies for the methodology of…

Computation · Statistics 2022-04-12 Lisa Gaedke-Merzhäuser , Janet van Niekerk , Olaf Schenk , Håvard Rue

Computing expected information gain (EIG) from prior to posterior (equivalently, mutual information between candidate observations and model parameters or other quantities of interest) is a fundamental challenge in Bayesian optimal…

Methodology · Statistics 2026-01-30 Fengyi Li , Ricardo Baptista , Youssef Marzouk

Bayesian optimal experimental design is a sub-field of statistics focused on developing methods to make efficient use of experimental resources. Any potential design is evaluated in terms of a utility function, such as the (theoretically…

Machine Learning · Computer Science 2022-10-21 Noble Kennamer , Steven Walton , Alexander Ihler

Implicit stochastic models, where the data-generation distribution is intractable but sampling is possible, are ubiquitous in the natural sciences. The models typically have free parameters that need to be inferred from data collected in…

Machine Learning · Statistics 2020-08-17 Steven Kleinegesse , Michael U. Gutmann