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Bayesian optimal experimental design (OED) seeks experiments that maximize the expected information gain (EIG) in model parameters. Directly estimating the EIG using nested Monte Carlo is computationally expensive and requires an explicit…

We propose a variance-penalized formulation of Bayesian optimal experimental design for nonlinear models that augments the classical expected utility criterion with a penalty on utility variability, yielding a mean--variance objective that…

Bayesian inference typically relies on specifying a parametric model that approximates the data-generating process. However, misspecified models can yield poor convergence rates and unreliable posterior calibration. Bayesian empirical…

High-fidelity simulations and physical experiments are essential for engineering analysis and design, yet their high cost often makes two critical tasks--global sensitivity analysis (GSA) and optimization--prohibitively expensive. This…

Genetic Gaussian network of multiple phenotypes constructed through the genetic correlation matrix is informative for understanding their biological dependencies. However, its interpretation may be challenging because the estimated genetic…

Gaussian process regression is a popular Bayesian framework for surrogate modeling of expensive data sources. As part of a broader effort in scientific machine learning, many recent works have incorporated physical constraints or other a…

Statistical models are central to machine learning with broad applicability across a range of downstream tasks. The models are controlled by free parameters that are typically estimated from data by maximum-likelihood estimation or…

Estimating information-theoretic quantities such as entropy and mutual information is central to many problems in statistics and machine learning, but challenging in high dimensions. This paper presents estimators of entropy via inference…

A new methodology for model determination in decomposable graphical Gaussian models is developed. The Bayesian paradigm is used and, for each given graph, a hyper inverse Wishart prior distribution on the covariance matrix is considered.…

Generalized variational inference (GVI) provides an optimization-theoretic framework for statistical estimation that encapsulates many traditional estimation procedures. The typical GVI problem is to compute a distribution of parameters…

Probabilistic state estimation is essential for robots navigating uncertain environments. Accurately and efficiently managing uncertainty in estimated states is key to robust robotic operation. However, nonlinearities in robotic platforms…

Many real-life decision-making situations allow further relevant information to be acquired at a specific cost, for example, in assessing the health status of a patient we may decide to take additional measurements such as diagnostic tests…

Solving Bayesian inference problems approximately with variational approaches can provide fast and accurate results. Capturing correlation within the approximation requires an explicit parametrization. This intrinsically limits this…

We propose a practical Bayesian optimization method using Gaussian process regression, of which the marginal likelihood is maximized where the number of model selection steps is guided by a pre-defined threshold. Since Bayesian optimization…

We study model evaluation and model selection from the perspective of generalization ability (GA): the ability of a model to predict outcomes in new samples from the same population. We believe that GA is one way formally to address…

Intrinsically motivated artificial agents learn advantageous behavior without externally-provided rewards. Previously, it was shown that maximizing mutual information between agent actuators and future states, known as the empowerment…

In this work we review the application of the theory of Gaussian processes to the modeling of noise in pulsar-timing data analysis, and we derive various useful and optimized representations for the likelihood expressions that are needed in…

This paper addresses the issue of estimating the expectation of a real-valued random variable of the form $X = g(\mathbf{U})$ where $g$ is a deterministic function and $\mathbf{U}$ can be a random finite- or infinite-dimensional vector.…

We propose a new method for simplification of Gaussian process (GP) models by projecting the information contained in the full encompassing model and selecting a reduced number of variables based on their predictive relevance. Our results…

Experimental design is crucial for inference where limitations in the data collection procedure are present due to cost or other restrictions. Optimal experimental designs determine parameters that in some appropriate sense make the data…