Related papers: Appropriate basis selection based on Bayesian infe…
The lasso and elastic net linear regression models impose a double-exponential prior distribution on the model parameters to achieve regression shrinkage and variable selection, allowing the inference of robust models from large data sets.…
The Bayes factor, the data-based updating factor of the prior to posterior odds of two hypotheses, is a natural measure of statistical evidence for one hypothesis over the other. We show how Bayes factors can also be used for parameter…
The ill-posed problem of phase retrieval in optics, using one or more intensity measurements, has a multitude of applications using electromagnetic or matter waves. Many phase retrieval algorithms are computed on pixel arrays using discrete…
Diffusion models have impressive image generation capability, but low-quality generations still exist, and their identification remains challenging due to the lack of a proper sample-wise metric. To address this, we propose BayesDiff, a…
In-situ EXAFS experiments were performed at the Ag $K$-edge after adsorbing NO on the hydrogen reduced silver cluster. The coordination parameters, i.e. inter-atomic distance, coordination number and Debye-Waller factor were derived from a…
In this paper, we propose a Bayesian spectral deconvolution considering the properties of peaks in different energy domains. Bayesian spectral deconvolution regresses spectral data into the sum of multiple basis functions. Conventional…
Non-negative tensor factorization models enable predictive analysis on count data. Among them, Bayesian Poisson-Gamma models can derive full posterior distributions of latent factors and are less sensitive to sparse count data. However,…
Expected-posterior priors (EPP) have been proved to be extremely useful for testing hypothesis on the regression coefficients of normal linear models. One of the advantages of using EPPs is that impropriety of baseline priors causes no…
In this note we introduce linear regression with basis functions in order to apply Bayesian model selection. The goal is to incorporate Occam's razor as provided by Bayes analysis in order to automatically pick the model optimally able to…
Boolean matrix has been used to represent digital information in many fields, including bank transaction, crime records, natural language processing, protein-protein interaction, etc. Boolean matrix factorization (BMF) aims to find an…
We implement an efficient method of computation of two dimensional Fourier-type integrals based on approximation of the integrand by Gaussian radial basis functions, which constitute a standard tool in approximation theory. As a result, we…
The Finite Element Method (FEM) is a widely used technique for simulating crash scenarios with high accuracy and reliability. To reduce the significant computational costs associated with FEM, the Finite Element Method Integrated Networks…
Diffraction Anomalous Fine Structure (DAFS) spectroscopy uses resonant elastic x-rays scattering as an atomic, shell and site selective probe that gives information on the electronic structure and the local atomic environment as well as on…
Bayesian inference affords scientists with powerful tools for testing hypotheses. One of these tools is the Bayes factor, which indexes the extent to which support for one hypothesis over another is updated after seeing the data. Part of…
Dark-field x-ray microscopy utilizes Bragg diffraction to collect full-field x-ray images of "mesoscale" structure of ordered materials. Information regarding the structural heterogeneities and their physical implications is gleaned through…
To estimate accurately the parameters of a regression model, the sample size must be large enough relative to the number of possible predictors for the model. In practice, sufficient data is often lacking, which can lead to overfitting of…
Advanced experimental measurements are crucial for driving theoretical developments and unveiling novel phenomena in condensed matter and material physics, which often suffer from the scarcity of facility resources and increasing…
As a new type of series expansion, the so-called one-dimensional adaptive Fourier decomposition (AFD) and its variations (1D-AFDs) have effective applications in signal analysis and system identification. The 1D-AFDs have considerable…
We use semi-automated data acquisition and processing to produce digital large angle CBED (D-LACBED) patterns. We demonstrate refinements of atomic coordinates and isotropic Debye-Waller factors for well-known materials using simulations…
In the bayesian analysis of Inverse Problems most relevant cases the forward maps (FM, or regressor function) are defined in terms of a system of (O, P)DE's with intractable solutions. These necessarily involve a numerical method to find…