Random variableVariable representing a random phenomenonA random variable (also called random quantity, aleatory variable, or stochastic variable) is a mathematical formalization of a quantity or object which depends on random events.
Monte Carlo methodProbabilistic problem-solving algorithmThe approximation of a normal distribution with a Monte Carlo methodMonte Carlo methods, also called the Monte Carlo experiments or Monte Carlo simulations, are a broad class of computational algorithms based on repeatedrandom sampling for obtaining numerical results, conceptualized by Polish mathematician Stanisław Ulam. The underlying concept is to use randomness to solve deterministic problems.Probability distributionMathematical function for the probability a given outcome occurs in an experimentIn probability theory and statistics, a probability distribution describes how probabilities are assigned to the possible results of a random phenomenon—more precisely, to events, which are sets of possible outcomes of a probabilistic experiment. Informally, a probability distribution tells us how likely different results are.
Umbrella samplingUmbrella sampling is a technique in computational physics and chemistry, used to improve sampling of a system (or different systems) where ergodicity is hindered by the form of the system's energy landscape. It was first suggested by Torrie and Valleau in 1977. It is a particular physical application of the more general importance sampling in statistics. Systems in which an energy barrier separates two regions of configuration space may suffer from poor sampling.
Monte Carlo method in statistical mechanicsMonte Carlo in statistical physics refers to the application of the Monte Carlo method to problems in statistical physics, or statistical mechanics. OverviewThe general motivation to use the Monte Carlo method in statistical physics is to evaluate a multivariable integral. The typical problem begins with a system for which the Hamiltonian is known, it is at a given temperature and it follows the Boltzmann statistics.
Probability spaceIn probability theory, a probability space or a probability triple(Ω,F,P){\displaystyle (\Omega ,{\mathcal {F}},P)} is a mathematical construct that provides a formal model of a random process or experiment.
Expected valueAverage value of a random variableIn probability theory, the expected value (also called expectation, mean, or first moment) is a generalization of the weighted average. Provided that it is finite, the expected value can be interpreted as the long-run average of results from independent repetitions of the same random experiment, as formalized by the law of large numbers.EstimatorIn statistics, an estimator is a rule for calculating an estimate of a given quantity based on observed data: thus the rule (the estimator), the quantity of interest (the estimand) and its result (the estimate) are distinguished. For example, the sample mean is a commonly used estimator of the population mean. There are point and interval estimators. The point estimators yield single-valued results.
Almost everywhereIn measure theory (a branch of mathematical analysis), a property holds almost everywhere (sometimes abbreviated as a.e.) if the set for which the property does not hold is negligible in a technical sense. The notion of "almost everywhere" is a companion notion to the concept of measure zero, and is analogous to the notion of almost surely in probability theory.
Teun KloekTeunis (Teun) Kloek (born 1934) is a Dutch economist and emeritus Professor of Econometrics at the Erasmus Universiteit Rotterdam. His research interests centered on econometric methods and their applications, especially nonparametric and robust methods in econometrics.
Computational physicsComputational physics is the study and implementation of numerical analysis to solve problems in physics. Historically, computational physics was the first application of modern computers in science, and is now a subset of computational science.Herman K. van DijkHerman Koene van Dijk (1946 – 24 January 2025) was a Dutch economist who was a consultant at the Research Department of Norges Bank and Professor Emeritus at the Econometric Institute of the Erasmus University Rotterdam, known for his contributions in the field of Bayesian analysis.*As an Amazon Associate I earn from qualifying purchases.