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Fossil-based palaeoclimate reconstruction is an important area of ecological science that has gained momentum in the backdrop of the global climate change debate. The hierarchical Bayesian paradigm provides an interesting platform for…
In this paper we give a profound insight into the computation capability of delay-based reservoir computing via an eigenvalue analysis. We concentrate on the task-independent memory capacity to quantify the reservoir performance and compare…
Bayesian approach, as a useful tool for quantifying uncertainties, has been widely used for solving inverse problems of partial differential equations (PDEs). One of the key difficulties for employing Bayesian approach for the issue is how…
The signal demixing problem seeks to separate a superposition of multiple signals into its constituent components. This paper studies a two-stage approach that first decompresses and subsequently deconvolves the noisy and undersampled…
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…
We propose the application of iterative regularization for the development of ensemble methods for solving Bayesian inverse problems. In concrete, we construct (i) a variational iterative regularizing ensemble Levenberg-Marquardt method…
We solve the inverse problem of deblurring a pixelized image of Jupiter using regularized deconvolution and by sample-based Bayesian inference. By efficiently sampling the marginal posterior distribution for hyperparameters, then the full…
A physics-informed neural network is presented for poroelastic problems with coupled flow and deformation processes. The governing equilibrium and mass balance equations are discussed and specific derivations for two-dimensional cases are…
We propose a method for optimal Bayesian filtering with deterministic particles. In order to avoid particle degeneration, the filter step is not performed at once. Instead, the particles progressively flow from prior to posterior. This is…
This paper considers convolution equations that arise from problems such as measurement error and non-parametric regression with errors in variables with independence conditions. The equations are examined in spaces of generalized functions…
Physical parameterizations are used as representations of unresolved subgrid processes within weather and global climate models or coarse-scale turbulent models, whose resolutions are too coarse to resolve small-scale processes. These…
This study presents a Bayesian framework for (inverse) uncertainty quantification and parameter estimation in a two-step Chemical Vapor Deposition coating process using production data. We develop an XGBoost surrogate model that maps…
A Bayesian approach to nonlinear inverse problems is considered where the unknown quantity (input) is a random spatial field. The forward model is complex and non-linear, therefore computationally expensive. An emulator-based methodology is…
We study a blind deconvolution problem on graphs, which arises in the context of localizing a few sources that diffuse over networks. While the observations are bilinear functions of the unknown graph filter coefficients and sparse input…
We harness the power of Bayesian emulation techniques, designed to aid the analysis of complex computer models, to examine the structure of complex Bayesian analyses themselves. These techniques facilitate robust Bayesian analyses and/or…
In this paper the Bayesian analysis is applied to assign a probability density to the value of a quantity having a definite sign. This analysis is logically consistent with the results, positive or negative, of repeated measurements.…
Understanding dynamics of hydrological responses is essential in producing skillful runoff forecast. This can be quantitatively done by tracking changes in hydrology model parameters that represent physical characteristics. In this study,…
A series of experiments in stationary and moving passenger rail cars were conducted to measure removal rates of particles in the size ranges of SARS-CoV-2 viral aerosols, and the air changes per hour provided by existing and modified air…
The proposal and study of dependent prior processes has been a major research focus in the recent Bayesian nonparametric literature. In this paper, we introduce a flexible class of dependent nonparametric priors, investigate their…
The means to obtain the rate constants of a chemical reaction is a fundamental open problem in both science and the industry. Traditional techniques for finding rate constants require either chemical modifications of the reactants or…