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Data-driven risk analysis involves the inference of probability distributions from measured or simulated data. In the case of a highly reliable system, such as the electricity grid, the amount of relevant data is often exceedingly limited,…
The main contribution of this paper is to develop a hierarchical Bayesian formulation of PINNs for linear inverse problems, which is called BPINN-IP. The proposed methodology extends PINN to account for prior knowledge on the nature of the…
We present the first general purpose framework for marginal maximum a posteriori estimation of probabilistic program variables. By using a series of code transformations, the evidence of any probabilistic program, and therefore of any…
An important task of uncertainty quantification is to identify {the probability of} undesired events, in particular, system failures, caused by various sources of uncertainties. In this work we consider the construction of Gaussian…
Computer models, aiming at simulating a complex real system, are often calibrated in the light of data to improve performance. Standard calibration methods assume that the optimal values of calibration parameters are invariant to the model…
For a Bayesian, real-time forecasting with the posterior predictive distribution can be challenging for a variety of time series models. First, estimating the parameters of a time series model can be difficult with sample-based approaches…
Although linear regression models are fundamental tools in statistical science, the estimation results can be sensitive to outliers. While several robust methods have been proposed in frequentist frameworks, statistical inference is not…
Bayesian decision theory provides an elegant framework for acting optimally under uncertainty when tractable posterior distributions are available. Modern Bayesian models, however, typically involve intractable posteriors that are…
Stability selection is a versatile framework for structure estimation and variable selection in high-dimensional setting, primarily grounded in frequentist principles. In this paper, we propose an enhanced methodology that integrates…
Accurate simulation of complex physical systems enables the development, testing, and certification of control strategies before they are deployed into the real systems. As simulators become more advanced, the analytical tractability of the…
Understanding the uncertainty of a neural network's (NN) predictions is essential for many purposes. The Bayesian framework provides a principled approach to this, however applying it to NNs is challenging due to large numbers of parameters…
We consider the problem of estimating rare event probabilities, focusing on systems whose evolution is governed by differential equations with uncertain input parameters. If the system dynamics is expensive to compute, standard sampling…
Inferring the causal structure of a system typically requires interventional data, rather than just observational data. Since interventional experiments can be costly, it is preferable to select interventions that yield the maximum amount…
We consider the problem of computing reach-avoid probabilities for iterative predictions made with Bayesian neural network (BNN) models. Specifically, we leverage bound propagation techniques and backward recursion to compute lower bounds…
The determination of Parton Distribution Functions from a finite set of data is a typical example of an inverse problem. Inverse problems are notoriously difficult to solve, in particular when a robust determination of the uncertainty in…
Scenario programs have established themselves as efficient tools towards decision-making under uncertainty. To assess the quality of scenario-based solutions a posteriori, validation tests based on Bernoulli trials have been widely adopted…
Bayesian inference and uncertainty quantification in a general class of non-linear inverse regression models is considered. Analytic conditions on the regression model $\{\mathscr G(\theta): \theta \in \Theta\}$ and on Gaussian process…
Probabilistic programming is a rapidly developing programming paradigm which enables the formulation of Bayesian models as programs and the automation of posterior inference. It facilitates the development of models and conducting Bayesian…
We formulate, and present a numerical method for solving, an inverse problem for inferring parameters of a deterministic model from stochastic observational data (quantities of interest). The solution, given as a probability measure, is…
Traditionally, the MaxEnt workshops start by a tutorial day. This paper summarizes my talk during 2001'th workshop at John Hopkins University. The main idea in this talk is to show how the Bayesian inference can naturally give us all the…