Related papers: A multiscale strategy for Bayesian inference using…
This study proposes the first Bayesian approach for learning high-dimensional linear Bayesian networks. The proposed approach iteratively estimates each element of the topological ordering from backward and its parent using the inverse of a…
We present a computational framework for estimating the uncertainty in the numerical solution of linearized infinite-dimensional statistical inverse problems. We adopt the Bayesian inference formulation: given observational data and their…
The Bayesian approach to inverse problems typically relies on posterior sampling approaches, such as Markov chain Monte Carlo, for which the generation of each sample requires one or more evaluations of the parameter-to-observable map or…
This article focuses on inference in logistic regression for high-dimensional binary outcomes. A popular approach induces dependence across the outcomes by including latent factors in the linear predictor. Bayesian approaches are useful for…
In this article, we study Bayesian inverse problems with multi-layered Gaussian priors. We first describe the conditionally Gaussian layers in terms of a system of stochastic partial differential equations. We build the computational…
Transporting causal information across populations is a critical challenge in clinical decision-making. Causal modeling provides criteria for identifiability and transportability, but these require knowledge of the causal graph, which…
Model inadequacy and measurement uncertainty are two of the most confounding aspects of inference and prediction in quantitative sciences. The process of scientific inference (the inverse problem) and prediction (the forward problem)…
Mathematical models in computational physics contain uncertain parameters that impact prediction accuracy. In turbulence modeling, this challenge is especially significant: Reynolds averaged Navier-Stokes (RANS) models, such as the…
In this article we consider Bayesian estimation of static parameters for a class of partially observed McKean-Vlasov diffusion processes with discrete-time observations over a fixed time interval. This problem features several obstacles to…
Bayesian statistical inverse problems are often solved with Markov chain Monte Carlo (MCMC)-type schemes. When the problems are governed by large-scale discrete nonlinear partial differential equations (PDEs), they are computationally…
This paper proposes a Bayesian framework for localization of multiple sources in the event of accidental hazardous contaminant release. The framework assimilates sensor measurements of the contaminant concentration with an integrated…
In Bayesian applications, there is a huge interest in rapid and accurate estimation of the posterior distribution, particularly for high dimensional or hierarchical models. In this article, we propose to use optimization to solve for a…
We consider the problem of estimating high-dimensional covariance matrices of a particular structure, which is a summation of low rank and sparse matrices. This covariance structure has a wide range of applications including factor analysis…
We propose a hybrid generative model for efficient sampling of high-dimensional, multimodal probability distributions for Bayesian inference. Traditional Monte Carlo methods, such as the Metropolis-Hastings and Langevin Monte Carlo sampling…
To accurately reproduce measurements from the real world, simulators need to have an adequate model of the physical system and require the parameters of the model be identified. We address the latter problem of estimating parameters through…
Tucker tensor decomposition offers a more effective representation for multiway data compared to the widely used PARAFAC model. However, its flexibility brings the challenge of selecting the appropriate latent multi-rank. To overcome the…
In this paper, we present a theoretical and computational workflow for the non-parametric Bayesian inference of drift and diffusion functions of autonomous diffusion processes. We base the inference on the partial differential equations…
Bayesian filtering deals with computing the posterior distribution of the state of a stochastic dynamic system given noisy observations. In this paper, motivated by applications in counter-adversarial systems, we consider the following…
Multi-scale problems, where variables of interest evolve in different time-scales and live in different state-spaces, can be found in many fields of science. Here, we introduce a new recursive methodology for Bayesian inference that aims at…
Due to the importance of uncertainty quantification (UQ), Bayesian approach to inverse problems has recently gained popularity in applied mathematics, physics, and engineering. However, traditional Bayesian inference methods based on Markov…