Related papers: Bayesian Error Estimation in Density Functional Th…
A method is described, which computes from an observed sample of events upper limits for production rates of particles, or, in case of appearance of a signal, the probability for an upwards fluctuation of the background. For any candidate,…
This paper applies the Bayesian Model Averaging (BMA) statistical ensemble technique to estimate small molecule solvation free energies. There is a wide range of methods available for predicting solvation free energies, ranging from…
Accurate charge densities are essential for reliable electronic structure calculations because they significantly impact predictions of various chemical properties and in particular, according to the Hellmann-Feynman theorem, atomic forces.…
We show how machine learning techniques based on Bayesian inference can be used to reach new levels of realism in the computer simulation of molecular materials, focusing here on water. We train our machine-learning algorithm using…
Recently, we proposed a method to estimate parameters of stochastic dynamics based on the linear response statistics. The method rests upon a nonlinear least-squares problem that takes into account the response properties that stem from the…
Recently, the progression toward more exact density functional theory has been questioned, implying a need for more formal ways to systematically measure progress, i.e. a path. Here I use the Hohenberg-Kohn theorems and the definition of…
A new density functional theory (DFT) exchange-correlation functional for the exploration of reaction mechanisms is proposed. This new functional, denoted BMK (Boese-Martin for Kinetics), has an accuracy in the 2 kcal/mol range for…
Modeling complex physical systems such as they arise in civil engineering applications requires finding a trade-off between physical fidelity and practicality. Consequently, deviations of simulation from measurements are ubiquitous even…
Given a sample $\{X_i\}_{i=1}^n$ from $f_X$, we construct kernel density estimators for $f_Y$, the convolution of $f_X$ with a known error density $f_{\epsilon}$. This problem is known as density estimation with Berkson error and has…
A general procedure for the optimization of atomic density-fitting basis functions is designed with the balance between accuracy and numerical stability in mind. Given one-electron wavefunctions and energies, weights are assigned to the…
The swift progression of machine learning (ML) has not gone unnoticed in the realm of statistical mechanics. ML techniques have attracted attention by the classical density-functional theory (DFT) community, as they enable discovery of…
Density functional theory is the workhorse of chemistry and materials science, and novel density functional approximations (DFAs) are published every year. To become available in program packages, the novel DFAs need to be (re)implemented.…
The problem of estimating trend and seasonal variation in time-series data has been studied over several decades, although mostly using single time series. This paper studies the problem of estimating these components from functional data,…
Use of an error correction code in a given transmission channel can be regarded as the statistical experiment. Therefore, powerful results from the theory of comparison of experiments can be applied to compare the performances of different…
In this paper we study the problem of density deconvolution under general assumptions on the measurement error distribution. Typically deconvolution estimators are constructed using Fourier transform techniques, and it is assumed that the…
We present procedures based on Bayesian statistics for estimating, from data, the parameters of effective field theories (EFTs). The extraction of low-energy constants (LECs) is guided by theoretical expectations in a quantifiable way…
In engineering, it is a common desire to couple existing simulation tools together into one big system by passing information from subsystems as parameters into the subsystems under influence. As executed at fixed time points, this data…
Dynamical system state estimation and parameter calibration problems are ubiquitous across science and engineering. Bayesian approaches to the problem are the gold standard as they allow for the quantification of uncertainties and enable…
Estimation of permutation entropy (PE) using Bayesian statistical methods is presented for systems where the ordinal pattern sampling follows an independent, multinomial distribution. It is demonstrated that the PE posterior distribution is…
In experiments to estimate parameters of a parametric model, Bayesian experiment design allows measurement settings to be chosen based on utility, which is the predicted improvement of parameter distributions due to modeled measurement…