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Linear mixed-effects models are a central analytical tool for modeling hierarchical and longitudinal data, as they allow simultaneous representation of fixed and random sources of variation. In practice, inference for such models is most…
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The performance of deep (reinforcement) learning systems crucially depends on the choice of hyperparameters. Their tuning is notoriously expensive, typically requiring an iterative training process to run for numerous steps to convergence.…
The Bayesian approach to data analysis provides a powerful way to handle uncertainty in all observations, model parameters, and model structure using probability theory. Probabilistic programming languages make it easier to specify and fit…
Calibration of computer models is a key step in making inferences, predictions, and decisions for complex science and engineering systems. We formulate and analyze a nonparametric Bayesian methodology for computer model calibration. This…
We address the problem of providing inference from a Bayesian perspective for parameters selected after viewing the data. We present a Bayesian framework for providing inference for selected parameters, based on the observation that…
Several fundamental problems in science and engineering consist of global optimization tasks involving unknown high-dimensional (black-box) functions that map a set of controllable variables to the outcomes of an expensive experiment.…
The particle filter is a powerful framework for estimating hidden states in dynamic systems where uncertainty, noise, and nonlinearity dominate. This mini-book offers a clear and structured introduction to the core ideas behind particle…
In this paper we introduce a novel particle filter scheme for a class of partially-observed multivariate diffusions. %continuous-time dynamic models where the %signal is given by a multivariate diffusion process. We consider a variety of…
Recursive estimation of nonlinear dynamical systems is an important problem that arises in several engineering applications. Consistent and accurate propagation of uncertainties is important to ensuring good estimation performance. It is…
The purpose of this review is to present a comprehensive overview of the theory of ensemble Kalman-Bucy filtering for continuous-time, linear-Gaussian signal and observation models. We present a system of equations that describe the flow of…
Non-Gaussian Bayesian filtering is a core problem in stochastic filtering. The difficulty of the problem lies in parameterizing the state estimates. However the existing methods are not able to treat it well. We propose to use power moments…
In computational inverse problems, it is common that a detailed and accurate forward model is approximated by a computationally less challenging substitute. The model reduction may be necessary to meet constraints in computing time when…
There is a rich literature proposing methods and establishing asymptotic properties of Bayesian variable selection methods for parametric models, with a particular focus on the normal linear regression model and an increasing emphasis on…
Bayesian Optimization aims at optimizing an unknown non-convex/concave function that is costly to evaluate. We are interested in application scenarios where concurrent function evaluations are possible. Under such a setting, BO could choose…
Bayesian optimization (BO) is a popular technique for sequential black-box function optimization, with applications including parameter tuning, robotics, environmental monitoring, and more. One of the most important challenges in BO is the…
We describe a novel procedure for deciding when a mass-action model is incompatible with observed steady-state data that does not require any parameter estimation. Thus, we avoid the difficulties of nonlinear optimization typically…
Bayesian estimation is a vital tool in robotics as it allows systems to update the robot state belief using incomplete information from noisy sensors. To render the state estimation problem tractable, many systems assume that the motion and…
We develop a new computational approach for "focused" optimal Bayesian experimental design with nonlinear models, with the goal of maximizing expected information gain in targeted subsets of model parameters. Our approach considers…