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Simulation-based Bayesian inference (SBI) can be used to estimate the parameters of complex mechanistic models given observed model outputs without requiring access to explicit likelihood evaluations. A prime example for the application of…
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.…
Bayesian optimization is a coherent, ubiquitous approach to decision-making under uncertainty, with applications including multi-arm bandits, active learning, and black-box optimization. Bayesian optimization selects decisions (i.e.…
Bayesian model selection provides a powerful framework for objectively comparing models directly from observed data, without reference to ground truth data. However, Bayesian model selection requires the computation of the marginal…
The PC algorithm is a popular method for learning the structure of Gaussian Bayesian networks. It carries out statistical tests to determine absent edges in the network. It is hence governed by two parameters: (i) The type of test, and (ii)…
Bayesian optimization has been successfully applied throughout Chemical Engineering for the optimization of functions that are expensive-to-evaluate, or where gradients are not easily obtainable. However, domain experts often possess…
Computer experiments are becoming increasingly important in scientific investigations. In the presence of uncertainty, analysts employ probabilistic sensitivity methods to identify the key-drivers of change in the quantities of interest.…
Bayesian methods lie at the heart of modern data science and provide a powerful scaffolding for estimation in data-constrained settings and principled quantification and propagation of uncertainty. Yet in many real-world use cases where…
Bayesian inference in deep neural networks is challenging due to the high-dimensional, strongly multi-modal parameter posterior density landscape. Markov chain Monte Carlo approaches asymptotically recover the true posterior but are…
In Bayesian inference for the Cox proportional hazards model, modeling the baseline hazard function is challenging. Recently, direct Bayesian inference using the partial likelihood is considered in the framework of general Bayesian…
Causal discovery is crucial for understanding complex systems and informing decisions. While observational data can uncover causal relationships under certain assumptions, it often falls short, making active interventions necessary. Current…
While Robert and Rousseau (2010) addressed the foundational aspects of Bayesian analysis, the current chapter details its practical aspects through a review of the computational methods available for approximating Bayesian procedures.…
Bayesian models are a powerful tool for studying complex data, allowing the analyst to encode rich hierarchical dependencies and leverage prior information. Most importantly, they facilitate a complete characterization of uncertainty…
We propose practical extensions to Bayesian optimization for solving dynamic problems. We model dynamic objective functions using spatiotemporal Gaussian process priors which capture all the instances of the functions over time. Our…
Bayesian optimization offers a flexible framework to optimize an objective function that is expensive to be evaluated. A Bayesian optimizer iteratively queries the function values on its carefully selected points. Subsequently, it makes a…
We consider the problem of estimating a probability of failure $\alpha$, defined as the volume of the excursion set of a function $f:\mathbb{X} \subseteq \mathbb{R}^{d} \to \mathbb{R}$ above a given threshold, under a given probability…
Gaussian process (GP) based Bayesian optimization (BO) is a powerful method for optimizing black-box functions efficiently. The practical performance and theoretical guarantees of this approach depend on having the correct GP hyperparameter…
Bayesian variable selection methods are powerful techniques for fitting and inferring on sparse high-dimensional linear regression models. However, many are computationally intensive or require restrictive prior distributions on model…
Bayesian analysis is increasingly popular for use in social science and other application areas where the data are observations from an informative sample. An informative sampling design leads to inclusion probabilities that are correlated…
Bayesian optimization is a sample-efficient method for solving expensive, black-box optimization problems. Stochastic programming concerns optimization under uncertainty where, typically, average performance is the quantity of interest. In…