Related papers: Building effective models from sparse but precise …

Finite Gaussian mixture models are widely used for model-based clustering of continuous data. Nevertheless, since the number of model parameters scales quadratically with the number of variables, these models can be easily…

The process of calibrating computer models of natural phenomena is essential for applications in the physical sciences, where plenty of domain knowledge can be embedded into simulations and then calibrated against real observations. Current…

In this work, we review the theory involved in the Bayesian calibration of complex computer models, with particular emphasis on their use for applications involving computationally expensive simulations and scarce experimental data. In the…

Many conventional statistical procedures are extremely sensitive to seemingly minor deviations from modeling assumptions. This problem is exacerbated in modern high-dimensional settings, where the problem dimension can grow with and…

In all areas of human knowledge, datasets are increasing in both size and complexity, creating the need for richer statistical models. This trend is also true for economic data, where high-dimensional and nonlinear/nonparametric inference…

Statistical sufficiency formalizes the notion of data reduction. In the decision theoretic interpretation, once a model is chosen all inferences should be based on a sufficient statistic. However, suppose we start with a set of procedures…

Spatial fields in the Earth and environmental sciences are often available at multiple scales or resolutions. While coarse-scale data (e.g., from global circulation models) are often abundant, they lack the local detail provided by…

Statistical modeling is a key component in the extraction of physical results from lattice field theory calculations. Although the general models used are often strongly motivated by physics, many model variations can frequently be…

We introduce a general framework that extends Bayesian inference by allowing the researcher to explicitly encode confidence in each source of uncertainty within the model. This mechanism provides a new handle for model design and…

In high-dimensional Bayesian statistics, various methods have been developed, including prior distributions that induce parameter sparsity to handle many parameters. Yet, these approaches often overlook the rich spectral structure of the…

Hierarchical probabilistic models, such as mixture models, are used for cluster analysis. These models have two types of variables: observable and latent. In cluster analysis, the latent variable is estimated, and it is expected that…

The construction of computer models (mathematical models implemented in computer codes), with respect to observed phenomena, is usually undertaken by building different variants depending on modeller sensibility, and choosing the one…

This paper proposes a novel uncertainty quantification framework for computationally demanding systems characterized by a large vector of non-Gaussian uncertainties. It combines state-of-the-art techniques in advanced Monte Carlo sampling…

Gaussian graphical models are widely used to infer dependence structures. Bayesian methods are appealing to quantify uncertainty associated with structural learning, i.e., the plausibility of conditional independence statements given the…

Probability forecasting is common in the geosciences, the finance sector, and elsewhere. It is sometimes the case that one has multiple probability-forecasts for the same target. How is the information in these multiple forecast systems…

Bayesian methods have been very successful in quantifying uncertainty in physics-based problems in parameter estimation and prediction. In these cases, physical measurements y are modeled as the best fit of a physics-based model…

Current analysis of astronomical data are confronted with the daunting task of modeling the awkward features of astronomical data, among which heteroscedastic (point-dependent) errors, intrinsic scatter, non-ignorable data collection…

Scientific knowledge expands by observing the world, hypothesizing some theories about it, and testing them against collected data. When those theories take the form of statistical models, statistical analyses are involved in the process of…

Bayesian calibration of computer models tunes unknown input parameters by comparing outputs with observations. For model outputs that are distributed over space, this becomes computationally expensive because of the output size. To overcome…

The use of mathematical models to make predictions about tumor growth and response to treatment has become increasingly more prevalent in the clinical setting. The level of complexity within these models ranges broadly, and the calibration…