Related papers: Bold Diagrammatic Monte Carlo: When Sign Problem i…
The primary focus of Monte Carlo simulation is to identify and quantify risk related to uncertainty and variability in spreadsheet model inputs. The stress of Monte Carlo simulation often reveals logical errors in the underlying spreadsheet…
Random sampling of graph partitions under constraints has become a popular tool for evaluating legislative redistricting plans. Analysts detect partisan gerrymandering by comparing a proposed redistricting plan with an ensemble of sampled…
We present a guiding principle for designing fermionic Hamiltonians and quantum Monte Carlo (QMC) methods that are free from the infamous sign problem by exploiting the Lie groups and Lie algebras that appear naturally in the Monte Carlo…
Monte Carlo method is a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results. They are often used in physical and mathematical problems and are most useful when it is difficult or…
Strongly-coupled fermionic systems can support a variety of low-energy phenomena, giving rise to collective condensation, symmetry breaking and a rich phase structure. We explore the potential of worldline Monte Carlo methods for analyzing…
Monte Carlo methods play important part in modern statistical physics. The application of these methods suffer from two main difficulties.The first is caused by the relatively small number of particles that can participate in any numerical…
Adaptive Monte Carlo schemes developed over the last years usually seek to ensure ergodicity of the sampling process in line with MCMC tradition. This poses constraints on what is possible in terms of adaptation. In the general case…
The Green's function Monte Carlo (GFMC) method provides accurate solutions to the nuclear many-body problem and predicts properties of light nuclei starting from realistic two- and three-body interactions. Controlling the GFMC fermion-sign…
We present the first practical Monte Carlo calculations of the recently proposed Lefschetz thimble formulation of quantum field theories. Our results provide strong evidence that the numerical sign problem that afflicts Monte Carlo…
Quantum Monte Carlo (QMC) is a family of powerful tools for addressing quantum many-body problems. However, its applications are often plagued by the fermionic sign problem. A promising strategy is to simulate an interaction without sign…
Sequential Monte Carlo (SMC) is a methodology for sampling approximately from a sequence of probability distributions of increasing dimension and estimating their normalizing constants. We propose here an alternative methodology named…
We design and implement a novel algorithm for computing a multilevel Monte Carlo (MLMC) estimator of the cumulative distribution function of a quantity of interest in problems with random input parameters or initial conditions. Our approach…
We consider the problem of estimating the probability of a large loss from a financial portfolio, where the future loss is expressed as a conditional expectation. Since the conditional expectation is intractable in most cases, one may…
We analyze the accuracy and sample complexity of variational Monte Carlo approaches to simulate the dynamics of many-body quantum systems classically. By systematically studying the relevant stochastic estimators, we are able to: (i) prove…
Bayesian Neural Networks (BNNs) provide a promising framework for modeling predictive uncertainty and enhancing out-of-distribution robustness (OOD) by estimating the posterior distribution of network parameters. Stochastic Gradient Markov…
Probabilistic programming is an approach to reasoning under uncertainty by encoding inference problems as programs. In order to solve these inference problems, probabilistic programming languages (PPLs) employ different inference…
Sequential Monte Carlo methods, also known as particle methods, are a popular set of techniques for approximating high-dimensional probability distributions and their normalizing constants. These methods have found numerous applications in…
The identification of parameters in mathematical models using noisy observations is a common task in uncertainty quantification. We employ the framework of Bayesian inversion: we combine monitoring and observational data with prior…
We provide a pedagogical introduction to the two main variants of real-space quantum Monte Carlo methods for electronic-structure calculations: variational Monte Carlo (VMC) and diffusion Monte Carlo (DMC). Assuming no prior knowledge on…
Bayesian reasoning in linear mixed-effects models (LMMs) is challenging and often requires advanced sampling techniques like Markov chain Monte Carlo (MCMC). A common approach is to write the model in a probabilistic programming language…