Related papers: Bayesian Multiscale Finite Element Methods. Modeli…
In this paper, we propose a Bayesian approach for multiscale problems with the availability of dynamic observational data. Our method selects important degrees of freedom probabilistically in a Generalized multiscale finite element method…
In this paper, we present a multiscale method for simulations of the multicontinua unsaturated flow problems in heterogeneous fractured porous media. The mathematical model is described by the system of Richards equations for each continuum…
We develop a new spatial semidiscrete multiscale method based upon the edge multiscale methods to solve semilinear parabolic problems with heterogeneous coefficients and smooth initial data. This method allows for a cheap spatial…
Gaussian graphical models are widely used to infer dependence structures. Bayesian methods are appealing to quantify uncertainty associated with structural learning, i.e., the plausibility of conditional independence statements given the…
The increased availability of observation data from engineering systems in operation poses the question of how to incorporate this data into finite element models. To this end, we propose a novel statistical construction of the finite…
In this paper, we discuss a general multiscale model reduction framework based on multiscale finite element methods. We give a brief overview of related multiscale methods. Due to page limitations, the overview focuses on a few related…
The problem of joint estimation of multiple graphical models from high dimensional data has been studied in the statistics and machine learning literature, due to its importance in diverse fields including molecular biology, neuroscience…
Numerical modeling of wave propagation in heterogeneous media is important in many applications. Due to the complex nature, direct numerical simulations on the fine grid are prohibitively expensive. It is therefore important to develop…
We study the convergence properties of the Gibbs Sampler in the context of posterior distributions arising from Bayesian analysis of conditionally Gaussian hierarchical models. We develop a multigrid approach to derive analytic expressions…
A fully Bayesian approach is proposed for ultrahigh-dimensional nonparametric additive models in which the number of additive components may be larger than the sample size, though ideally the true model is believed to include only a small…
In recent years, there has been a growing demand to discern clusters of subjects in datasets characterized by a large set of features. Often, these clusters may be highly variable in size and present partial hierarchical structures. In this…
This paper presents a novel mass-conservative mixed multiscale method for solving flow equations in heterogeneous porous media. The media properties (the permeability) contain multiple scales and high contrast. The proposed method solves…
We address multiscale elliptic problems with random coefficients that are a perturbation of multiscale deterministic problems. Our approach consists in taking benefit of the perturbative context to suitably modify the classical Finite…
Statistical inference with nonresponse is quite challenging, especially when the response mechanism is nonignorable. In this case, the validity of statistical inference depends on untestable correct specification of the response model. To…
In this paper, we propose a multiscale empirical interpolation method for solving nonlinear multiscale partial differential equations. The proposed method combines empirical interpolation techniques and local multiscale methods, such as the…
Finite mixture models are a useful statistical model class for clustering and density approximation. In the Bayesian framework finite mixture models require the specification of suitable priors in addition to the data model. These priors…
Finite mixtures are a flexible modeling tool for irregularly shaped densities and samples from heterogeneous populations. When modeling with mixtures using an exchangeable prior on the component features, the component labels are arbitrary…
Matrix completion and robust principal component analysis have been widely used for the recovery of data suffering from missing entries or outliers. In many real-world applications however, the data is also time-varying, and the naive…
In many inverse problems, model parameters cannot be precisely determined from observational data. Bayesian inference provides a mechanism for capturing the resulting parameter uncertainty, but typically at a high computational cost. This…
We tackle the problem of multiscale regression for predictors that are spatially or temporally indexed, or with a pre-specified multiscale structure, with a Bayesian modular approach. The regression function at the finest scale is expressed…