Related papers: The application of Monte Carlo methods for learnin…
We explain in detail how to estimate mean values and assess statistical errors for arbitrary functions of elementary observables in Monte Carlo simulations. The method is to estimate and sum the relevant autocorrelation functions, which is…
The hybrid Monte Carlo (HMC) algorithm is used for Bayesian analysis of the generalized autoregressive conditional heteroscedasticity (GARCH) model. The HMC algorithm is one of Markov chain Monte Carlo (MCMC) algorithms and it updates all…
This work presents an efficient approach for accelerating multilevel Markov Chain Monte Carlo (MCMC) sampling for large-scale problems using low-fidelity machine learning models. While conventional techniques for large-scale Bayesian…
The advances in materials and biological sciences have necessitated the use of molecular simulations to study polymers. The Markov chain Monte Carlo simulations enable the sampling of relevant microstates of polymeric systems by traversing…
Monte Carlo methods use random sampling to estimate numerical quantities which are hard to compute deterministically. One important example is the use in statistical physics of rapidly mixing Markov chains to approximately compute partition…
By analogy with Monte Carlo algorithms, we propose new strategies for design and redesign of small molecule libraries in high-throughput experimentation, or combinatorial chemistry. Several Monte Carlo methods are examined, including…
We consider a wide range of matrix models and study them using the Monte Carlo technique in the large $N$ limit. The results we obtain agree with exact analytic expressions and recent numerical bootstrap methods for models with one and two…
Stochastic gradient Markov Chain Monte Carlo algorithms are popular samplers for approximate inference, but they are generally biased. We show that many recent versions of these methods (e.g. Chen et al. (2014)) cannot be corrected using…
Based on the principles of importance sampling and resampling, sequential Monte Carlo (SMC) encompasses a large set of powerful techniques dealing with complex stochastic dynamic systems. Many of these systems possess strong memory, with…
Stochastic Differential Equations (SDEs) are used as statistical models in many disciplines. However, intractable likelihood functions for SDEs make inference challenging, and we need to resort to simulation-based techniques to estimate and…
Stochastic processes are a flexible and widely used family of models for statistical modeling. While stochastic processes offer attractive properties such as inclusion of uncertainty properties, their inference is typically intractable,…
We develop the idea of using Monte Carlo sampling of random portfolios to solve portfolio investment problems. In this first paper we explore the need for more general optimization tools, and consider the means by which constrained random…
Adaptive Monte Carlo methods are very efficient techniques designed to tune simulation estimators on-line. In this work, we present an alternative to stochastic approximation to tune the optimal change of measure in the context of…
This article considers the sequential Monte Carlo (SMC) approximation of ratios of normalizing constants associated to posterior distributions which in principle rely on continuum models. Therefore, the Monte Carlo estimation error and the…
We analyse a multilevel Monte Carlo method for the approximation of distribution functions of univariate random variables. Since, by assumption, the target distribution is not known explicitly, approximations have to be used. We provide an…
We present Generative Monte Carlo (GMC), a novel paradigm for particle transport simulation that integrates generative artificial intelligence directly into the stochastic solution of the linear Boltzmann equation. By reformulating the…
Langevin Monte Carlo (LMC) is a popular Bayesian sampling method. For the log-concave distribution function, the method converges exponentially fast, up to a controllable discretization error. However, the method requires the evaluation of…
This article considers stochastic algorithms for efficiently solving a class of large scale non-linear least squares (NLS) problems which frequently arise in applications. We propose eight variants of a practical randomized algorithm where…
Gaussian processes are a natural way of defining prior distributions over functions of one or more input variables. In a simple nonparametric regression problem, where such a function gives the mean of a Gaussian distribution for an…
The Hamiltonian Monte Carlo (HMC) method has been recognized as a powerful sampling tool in computational statistics. We show that performance of HMC can be significantly improved by incorporating importance sampling and an irreversible…