Related papers: Montecarlo Techniques as a tool for teaching stati…
Bootstrapping was designed to randomly resample data from a fixed sample using Monte Carlo techniques. However, the original sample itself defines a discrete distribution. Convolutional methods are well suited for discrete distributions,…
Models of stochastic processes are widely used in almost all fields of science. Theory validation, parameter estimation, and prediction all require model calibration and statistical inference using data. However, data are almost always…
As increasingly complex hypothesis-testing scenarios are considered in many scientific fields, analytic derivation of null distributions is often out of reach. To the rescue comes Monte Carlo testing, which may appear deceptively simple: as…
The detection of anisotropies with respect to a given direction in a vector field is a common problem in astronomy. Several methods have been proposed that rely on the distribution of the acute angles between the data and a reference…
We introduce an efficient numerical implementation of a Markov Chain Monte Carlo method to sample a probability distribution on a manifold (introduced theoretically in Zappa, Holmes-Cerfon, Goodman (2018)), where the manifold is defined by…
The EM algorithm is a powerful tool for maximum likelihood estimation with missing data. In practice, the calculations required for the EM algorithm are often intractable. We review numerous methods to circumvent this intractability, all of…
The multilevel Monte Carlo method is applied to an academic example in the field of electromagnetism. The method exhibits a reduced variance by assigning the samples to multiple models with a varying spatial resolution. For the given…
A scientometric analysis of Monte Carlo simulation and Monte Carlo codes has been performed over a set of representative scholarly journals related to radiation physics. The results of this study are reported and discussed. They document…
We introduce a new method, combination of random testing and abstract interpretation, for the analysis of programs featuring both probabilistic and non-probabilistic nondeterminism. After introducing "ordinary" testing, we show how to…
Notes for a Course on Probability and Statistics: L1: Elements of Probability; L2: Bayesian Inference; L3: Monte Carlo Methods
The assisted Schwinger effect, which is predicted to display non-perturbative quantum tunnelling, is expected to be produced in precision lab experiments with electron beams and intense lasers. Indeed, many novel effects predicted by a…
Monte Carlo techniques play a central role in statistical mechanics approaches for connecting macroscopic thermodynamic and kinetic properties to the electronic structure of a material. This paper describes the implementation of Monte Carlo…
Theories of new physics often involve a large number of unknown parameters which need to be scanned. Additionally, a putative signal in a particular channel may be due to a variety of distinct models of new physics. This makes experimental…
This is a comment on the article "Probabilistic Integration: A Role in Statistical Computation?" by F.-X. Briol, C. J. Oates, M. Girolami, M. A. Osborne and D. Sejdinovic to appear in Statistical Science. There is a role for statistical…
We present a preconditioned Monte Carlo method for computing high-dimensional multivariate normal and Student-$t$ probabilities arising in spatial statistics. The approach combines a tile-low-rank representation of covariance matrices with…
We describe Monte Carlo methods for estimating lower envelopes of expectations of real random variables. We prove that the estimation bias is negative and that its absolute value shrinks with increasing sample size. We discuss fairly…
We review the method of stochastic error correction which eliminates the truncation error associated with any subspace diagonalization. Monte Carlo sampling is used to compute the contribution of the remaining basis vectors not included in…
We briefly review the principles, mathematical bases, numerical shortcuts and applications of fast random walk (FRW) algorithms. This Monte Carlo technique allows one to simulate individual trajectories of diffusing particles in order to…
Tossing a coin is the most elementary Monte Carlo experiment. In a computer the coin is replaced by a pseudo random number generator. It can be shown analytically and by exact enumerations that popular random number generators are not…
Markov Chain Monte Carlo (MCMC) methods have become a cornerstone of many modern scientific analyses by providing a straightforward approach to numerically estimate uncertainties in the parameters of a model using a sequence of random…