相关论文: Discrepancy Bounds for a Class of Negatively Depen…
This paper presents an improved result on the negative-binomial Monte Carlo technique analyzed in a previous paper for the estimation of an unknown probability p. Specifically, the confidence level associated to a relative interval…
We study lithium systems over a range of number of atoms, e.g., atomic anion, dimer, metallic cluster, and body-centered cubic crystal by the diffusion Monte Carlo method. The calculations include both core and valence electrons in order to…
Let $f:[0,1]^d\to\mathbb{R}$ be a completely monotone integrand as defined by Aistleitner and Dick (2015) and let points $\boldsymbol{x}_0,\dots,\boldsymbol{x}_{n-1}\in[0,1]^d$ have a non-negative local discrepancy (NNLD) everywhere in…
Contrastive learning is a highly successful technique for learning representations of data from labeled tuples, specifying the distance relations within the tuple. We study the sample complexity of contrastive learning, i.e. the minimum…
We present a nonlinear (in the sense of McKean) generalization of Hamiltonian Monte Carlo (HMC) termed nonlinear HMC (nHMC) capable of sampling from nonlinear probability measures of mean-field type. When the underlying confinement…
We present an extensive study of the radiative transfer in dusty galaxies based on Monte Carlo simulations. The main output of these simulations are the attenuation curves ${\cal A}_\lambda$ (i.e. the ratio between the observed, dust…
A new (unadjusted) Langevin Monte Carlo (LMC) algorithm with improved rates in total variation and in Wasserstein distance is presented. All these are obtained in the context of sampling from a target distribution $\pi$ that has a density…
A statistical learning approach for parametric PDEs related to Uncertainty Quantification is derived. The method is based on the minimization of an empirical risk on a selected model class and it is shown to be applicable to a broad range…
Kernel discrepancies are a powerful tool for analyzing worst-case errors in quasi-Monte Carlo (QMC) methods. Building on recent advances in optimizing such discrepancy measures, we extend the subset selection problem to the setting of…
One of purposes for High Energy accelerator experiments is confrontation of theory and measurements in ever new realms. Any new agreement extends theory applicability domain, any discrepancy hints to unexplained. That calls for better…
We introduce a general Monte Carlo method based on Nested Sampling (NS), for sampling complex probability distributions and estimating the normalising constant. The method uses one or more particles, which explore a mixture of nested…
The propagation of uncertainties in reaction cross sections and rates of neutron-, proton-, and $\alpha$-induced reactions into the final isotopic abundances obtained in nucleosynthesis models is an important issue in studies of…
Consider a central problem in randomized approximation schemes that use a Monte Carlo approach. Given a sequence of independent, identically distributed random variables $X_1,X_2,\ldots$ with mean $\mu$ and standard deviation at most $c…
Simple Monte Carlo is a versatile computational method with a convergence rate of $O(n^{-1/2})$. It can be used to estimate the means of random variables whose distributions are unknown. Bernoulli random variables, $Y$, are widely used to…
We consider bond percolation on the square lattice with perfectly correlated random probabilities. According to scaling considerations, mapping to a random walk problem and the results of Monte Carlo simulations the critical behavior of the…
Intractable generative models are models for which the likelihood is unavailable but sampling is possible. Most approaches to parameter inference in this setting require the computation of some discrepancy between the data and the…
The rank envelope test (Myllym\"aki et al., Global envelope tests for spatial processes, arXiv:1307.0239 [stat.ME]) is proposed as a solution to multiple testing problem for Monte Carlo tests. Three different situations are recognized: 1) a…
An extended Hubbard model on a two-leg ladder is numerically studied by means of the quantum Monte Carlo techniques. The model we study has the nearest-neighbor interactions which are repulsive along chains and attractive for rungs. The…
We introduce bounded category forcing axioms for well-behaved classes $\Gamma$. These are strong forms of bounded forcing axioms which completely decide the theory of some initial segment of the universe $H_{\lambda_\Gamma^+}$ modulo…
A key limitation of sampling algorithms for approximate inference is that it is difficult to quantify their approximation error. Widely used sampling schemes, such as sequential importance sampling with resampling and Metropolis-Hastings,…