Related papers: Causality and Bayesian network PDEs for multiscale…
Double generalized linear models provide a flexible framework for modeling data by allowing the mean and the dispersion to vary across observations. Common members of the exponential dispersion family including the Gaussian, Poisson,…
Multivariate functional data arise in a wide range of applications. One fundamental task is to understand the causal relationships among these functional objects of interest, which has not yet been fully explored. In this article, we…
In this work we consider time series with a finite number of discrete point changes. We assume that the data in each segment follows a different probability density functions (pdf). We focus on the case where the data in all segments are…
High-dimensional data can be useful for causal inference by providing many confounders that may bolster the plausibility of the ignorability assumption. Propensity score methods are powerful tools for causal inference, are popular in health…
Analysts often use data-driven approaches to supplement their substantive knowledge when selecting covariates for causal effect estimation. Multiple variable selection procedures tailored for causal effect estimation have been devised in…
Inference in deep Bayesian neural networks is only fully understood in the infinite-width limit, where the posterior flexibility afforded by increased depth washes out and the posterior predictive collapses to a shallow Gaussian process.…
In scientific applications, predictive modeling is often of limited use without accurate uncertainty quantification (UQ) to indicate when a model may be extrapolating or when more data needs to be collected. Bayesian Neural Networks (BNNs)…
We consider identifiability of partially linear additive structural equation models with Gaussian noise (PLSEMs) and estimation of distributionally equivalent models to a given PLSEM. Thereby, we also include robustness results for errors…
Causal Bayesian Networks provide an important tool for reasoning under uncertainty with potential application to many complex causal systems. Structure learning algorithms that can tell us something about the causal structure of these…
Convection-driven porous media flows are common in industrial processes and in nature. The multiscale and multiphase character of these systems and the inherent non-linear flow dynamics make convection in porous media a complex phenomenon.…
In this study, we propose a novel microstructure-sensitive Bayesian optimization (BO) framework designed to enhance the efficiency of materials discovery by explicitly incorporating microstructural information. Traditional materials design…
In image reconstruction, an accurate quantification of uncertainty is of great importance for informed decision making. Here, the Bayesian approach to inverse problems can be used: the image is represented through a random function that…
The predictability of a certain effect or phenomenon is often equated with the knowledge of relevant physical laws, typically understood as a functional or numerically derived relationship between the observations and known states of the…
The paper provides a macro-microscopic coupled constitutive model for fluid-saturated porous media with respect to the compressibility of the solid skeleton, the real solid material and the fluid phase. The derivation of the model is…
Sensitivity forecasts inform the design of experiments and the direction of theoretical efforts. To arrive at representative results, Bayesian forecasts should marginalize their conclusions over uncertain parameters and noise realizations…
While probabilistic models describe the dependence structure between observed variables, causal models go one step further: they predict, for example, how cognitive functions are affected by external interventions that perturb neuronal…
In statistical applications, it is common to encounter parameters supported on a varying or unknown dimensional space. Examples include the fused lasso regression, the matrix recovery under an unknown low rank, etc. Despite the ease of…
We describe algorithms for learning Bayesian networks from a combination of user knowledge and statistical data. The algorithms have two components: a scoring metric and a search procedure. The scoring metric takes a network structure,…
Recent research has shown the potential utility of Deep Gaussian Processes. These deep structures are probability distributions, designed through hierarchical construction, which are conditionally Gaussian. In this paper, the current…
We investigate the chemical dissolution of porous media using a network model in which the system is represented as a series of interconnected pipes with the diameter of each segment increasing in proportion to the local reactant…