Related papers: Statistical error estimates in dynamical mean-fiel…
Standard statistical analysis is unable to provide reliable confidence intervals on expectation values of probability distributions that do not satisfy the conditions of the central limit theorem. We present a regression-based estimator of…
The standard Kernel Quadrature method for numerical integration with random point sets (also called Bayesian Monte Carlo) is known to converge in root mean square error at a rate determined by the ratio $s/d$, where $s$ and $d$ encode the…
We propose the so-called jackknife empirical likelihood approach for the survey data of general unequal probability sampling designs, and analyze parameters defined according to U-statistics. We prove theoretically that jackknife…
The dual-fermion approach provides a formally exact prescription for calculating properties of a correlated electron system in terms of a diagrammatic expansion around dynamical mean-field theory (DMFT). Most practical implementations,…
Fault detection is crucial to ensure the reliability of navigation systems. However, mainstream fault detection methods are developed based on Gaussian assumptions on nominal errors, while current attempts at non-Gaussian fault detection…
Importance sampling with data-driven proposal distributions is widely used in practice. A common workflow first generates an auxiliary sample of size $N$ from an approximation of the target distribution, constructs a density estimate $\hat…
In this paper we propose a flexible nested error regression small area model with high dimensional parameter that incorporates heterogeneity in regression coefficients and variance components. We develop a new robust small area specific…
Using trial wavefunctions prepared on quantum devices to reduce the bias of auxiliary-field quantum Monte Carlo (QC-AFQMC) has established itself as a promising hybrid approach to the simulation of strongly correlated many body systems.…
Recent high resolution Compton scattering experiments in lithium have shown significant discrepancies with conventional band theoretical results. We present a pseudopotential quantum Monte Carlo study of electron-electron and electron-ion…
For real symmetric matrices that are accessible only through matrix vector products, we present Monte Carlo estimators for computing the diagonal elements. Our probabilistic bounds for normwise absolute and relative errors apply to Monte…
Several quantum and classical Monte Carlo algorithms for Betti Number Estimation (BNE) on clique complexes have recently been proposed, though it is unclear how their performances compare. We review these algorithms, emphasising their…
A method is developed that allows analysis of quantum Monte Carlo simulations to identify errors in trial wave functions. The purpose of this method is to allow for the systematic improvement of variational wave functions by identifying…
In modern statistics, interests shift from pursuing the uniformly minimum variance unbiased estimator to reducing mean squared error (MSE) or residual squared error. Shrinkage based estimation and regression methods offer better prediction…
Many methods have been proposed to quantify the predictive uncertainty associated with the outputs of deep neural networks. Among them, ensemble methods often lead to state-of-the-art results, though they require modifications to the…
We develop a statistical theory of the mean field. It is based on the proposition that the mean field can be obtained as an energy average. Moreover, it is assumed that the matrix elements of the residual interaction are random with the…
Mean-Field is an efficient way to approximate a posterior distribution in complex graphical models and constitutes the most popular class of Bayesian variational approximation methods. In most applications, the mean field distribution…
A common problem in analysis of experiments or in lattice QCD simulations is fitting a parameterized model to the average over a number of samples of correlated data values. If the number of samples is not infinite, estimates of the…
A Monte-Carlo algorithm for discrete statistical models that combines the full power of the Belief Propagation algorithm with the advantages of a detailed-balanced heat bath approach is presented. A sub-tree inside the factor graph is first…
The fixed node diffusion Monte Carlo (DMC) method has attracted interest in recent years as a way to calculate properties of solid materials with high accuracy. However, the framework for the calculation of properties such as total…
Simulations of extended quantum systems are typically performed by extrapolating results of a sequence of finite-system-size simulations to the thermodynamic limit. In the quantum Monte Carlo community, twist-averaging was pioneered as an…