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Uncertainty of decisions in safety-critical engineering applications can be estimated on the basis of the Bayesian Markov Chain Monte Carlo (MCMC) technique of averaging over decision models. The use of decision tree (DT) models assists…

Failure probabilities for grid components are often estimated using parametric models which can capitalize on operational grid data. This work formulates a Bayesian hierarchical framework designed to integrate data and domain expertise to…

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…

We construct a probabilistic coherence measure for information sets which determines a partial coherence ordering. This measure is applied in constructing a criterion for expanding our beliefs in the face of new information. A number of…

We propose a fully Bayesian approach for causal inference with multivariate categorical data based on staged tree models, a class of probabilistic graphical models capable of representing asymmetric and context-specific dependencies. To…

Comparing competing mathematical models of complex natural processes is a shared goal among many branches of science. The Bayesian probabilistic framework offers a principled way to perform model comparison and extract useful metrics for…

A learning procedure takes as input a dataset and performs inference for the parameters $\theta$ of a model that is assumed to have given rise to the dataset. Here we consider learning procedures whose output is a probability distribution,…

This paper integrates Fault Tree Analysis (FTA) and Bayesian Networks (BN) to assess collision risk and establish Automotive Safety Integrity Level (ASIL) B failure rate targets for critical autonomous vehicle (AV) components. The FTA-BN…

We describe a method for Bayesian optimization by which one may incorporate data from multiple systems whose quantitative interrelationships are unknown a priori. All general (nonreal-valued) features of the systems are associated with…

The most fundamental problem in statistical causality is determining causal relationships from limited data. Probability trees, which combine prior causal structures with Bayesian updates, have been suggested as a possible solution. In this…

To date, most probabilistic reasoning systems have relied on a fixed belief network constructed at design time. The network is used by an application program as a representation of (in)dependencies in the domain. Probabilistic inference…

We propose a Bayesian approach for recursively estimating the classifier weights in online learning of a classifier ensemble. In contrast with past methods, such as stochastic gradient descent or online boosting, our approach estimates the…

A stream of algorithmic advances has steadily increased the popularity of the Bayesian approach as an inference paradigm, both from the theoretical and applied perspective. Even with apparent successes in numerous application fields, a…

Class imbalance is a pervasive problem in predictive toxicology, where the number of non-toxic compounds often exceeds the number of toxic ones. Models trained on such data often perform well on the majority class but poorly on the minority…

Discovery of an accurate causal Bayesian network structure from observational data can be useful in many areas of science. Often the discoveries are made under uncertainty, which can be expressed as probabilities. To guide the use of such…

As observations and student models become complex, educational assessments that exploit advances in technology and cognitive psychology can outstrip familiar testing models and analytic methods. Within the Portal conceptual framework for…

Count outcomes in longitudinal studies are frequent in clinical and engineering studies. In frequentist and Bayesian statistical analysis, methods such as Mixed linear models allow the variability or correlation within individuals to be…

Cybersecurity threats are increasingly marked by interdependence, uncertainty, and evolving complexity challenges that traditional assessment methods such as CVSS, STRIDE, and attack trees fail to adequately capture. This paper reviews the…

Safety-critical infrastructures must operate in a safe and reliable way. Fault tree analysis is a widespread method used for risk assessment of these systems: fault trees (FTs) are required by, e.g., the Federal Aviation Administration and…

This paper proposes a novel methodology for probabilistic dynamic security assessment and enhancement of power systems that considers load and generation variability, N-2 contingencies, and uncertain cascade propagation caused by uncertain…