|
Variance Reduction
In mathematics, more specifically in the theory of Monte Carlo methods, variance reduction is a procedure used to increase the precision of the estimates obtained for a given simulation or computational effort. Every output random variable from the simulation is associated with a variance which limits the precision of the simulation results. In order to make a simulation statistically efficient, i.e., to obtain a greater precision and smaller confidence intervals for the output random variable of interest, variance reduction techniques can be used. The main variance reduction methods are * common random numbers * antithetic variates * control variates * importance sampling * stratified sampling * moment matching * conditional Monte Carlo * and quasi random variables (in Quasi-Monte Carlo method) For simulation with black-box models subset simulation and line sampling can also be used. Under these headings are a variety of specialized techniques; for example, parti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Line Sampling
Line sampling is a method used in reliability engineering to compute small (i.e., rare event) failure probabilities encountered in engineering systems. The method is particularly suitable for Curse of dimensionality, high-dimensional reliability problems, in which the performance function exhibits moderate non-linearity with respect to the uncertain parameters The method is suitable for analyzing black box systems, and unlike the importance sampling method of variance reduction, does not require detailed knowledge of the system. The basic idea behind line sampling is to refine estimates obtained from the first-order reliability method (FORM), which may be incorrect due to the non-linearity of the Limit_state_design, limit state function. Conceptually, this is achieved by averaging the result of different FORM simulations. In practice, this is made possible by identifying the importance direction \boldsymbol \alpha in the input parameter space, which points towards the region w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quasi Random Variables
''Quasi'' may refer to: * Quasi (band), American indie rock band * ''Quasi'' (film), 2023 American film *Quasi, a musical term meaning "almost" * ''Quasi'' (fly), a genus of insect * ''Quasi'' (sculpture), an artwork in Wellington, New Zealand *"Quasi", by Logic from '' Vinyl Days'' (2022) *Quasi-Sport like to Hobby horsinghttps://web.archive.org/web/20250519061928/https://quasisports.com/ See also * Graman Quassi (1692–1787), Surinamese healer and botanist References {{disambiguation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Journal Of The Operations Research Society Of America
''Operations Research'' is a bimonthly peer-reviewed academic journal covering operations research that is published by the Institute for Operations Research and the Management Sciences. It was established in 1952 as the ''Journal of the Operations Research Society of America'' and obtained its current name in 1955. The editor-in-chief is Amy Ward (University of Chicago). Abstracting and indexing The journal is abstracted and indexed by ''Mathematical Reviews'', MathSciNet, Science Citation Index Expanded, Scopus, Social Sciences Citation Index, and ''Zentralblatt MATH''. According to the ''Journal Citation Reports'', the journal has a 2018 impact factor The impact factor (IF) or journal impact factor (JIF) of an academic journal is a type of journal ranking. Journals with higher impact factor values are considered more prestigious or important within their field. The Impact Factor of a journa ... of 2.604. References External links * Operations research journals Academi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Regularization (mathematics)
In mathematics, statistics, Mathematical finance, finance, and computer science, particularly in machine learning and inverse problems, regularization is a process that converts the Problem solving, answer to a problem to a simpler one. It is often used in solving ill-posed problems or to prevent overfitting. Although regularization procedures can be divided in many ways, the following delineation is particularly helpful: * Explicit regularization is regularization whenever one explicitly adds a term to the optimization problem. These terms could be Prior probability, priors, penalties, or constraints. Explicit regularization is commonly employed with ill-posed optimization problems. The regularization term, or penalty, imposes a cost on the optimization function to make the optimal solution unique. * Implicit regularization is all other forms of regularization. This includes, for example, early stopping, using a robust loss function, and discarding outliers. Implicit regularizat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Explained Variance
In statistics, explained variation measures the proportion to which a mathematical model accounts for the variation ( dispersion) of a given data set. Often, variation is quantified as variance; then, the more specific term explained variance can be used. The complementary part of the total variation is called unexplained or residual variation; likewise, when discussing variance as such, this is referred to as unexplained or residual variance. Definition in terms of information gain Information gain by better modelling Following Kent (1983), we use the Fraser information (Fraser 1965) :F(\theta) = \int \textrmr\,g(r)\,\ln f(r;\theta) where g(r) is the probability density of a random variable R\,, and f(r;\theta)\, with \theta\in\Theta_i (i=0,1\,) are two families of parametric models. Model family 0 is the simpler one, with a restricted parameter space \Theta_0\subset\Theta_1. Parameters are determined by maximum likelihood estimation, :\theta_i = \operatorname_ F(\theta). ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Central Limit Theorem
In probability theory, the central limit theorem (CLT) states that, under appropriate conditions, the Probability distribution, distribution of a normalized version of the sample mean converges to a Normal distribution#Standard normal distribution, standard normal distribution. This holds even if the original variables themselves are not Normal distribution, normally distributed. There are several versions of the CLT, each applying in the context of different conditions. The theorem is a key concept in probability theory because it implies that probabilistic and statistical methods that work for normal distributions can be applicable to many problems involving other types of distributions. This theorem has seen many changes during the formal development of probability theory. Previous versions of the theorem date back to 1811, but in its modern form it was only precisely stated as late as 1920. In statistics, the CLT can be stated as: let X_1, X_2, \dots, X_n denote a Sampling ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Independent And Identically Distributed Random Variables
Independent or Independents may refer to: Arts, entertainment, and media Artist groups * Independents (artist group), a group of modernist painters based in Pennsylvania, United States * Independentes (English: Independents), a Portuguese artist group Music Groups, labels, and genres * Independent music, a number of genres associated with independent labels * Independent record label, a record label not associated with a major label * Independent Albums, American albums chart Albums * ''Independent'' (Ai album), 2012 * ''Independent'' (Faze album), 2006 * ''Independent'' (Sacred Reich album), 1993 Songs * "Independent" (song), a 2007 song by Webbie * "Independent", a 2002 song by Ayumi Hamasaki from '' H'' News media organizations * Independent Media Center (also known as Indymedia or IMC), an open publishing network of journalist collectives that report on political and social issues, e.g., in ''The Indypendent'' newspaper of NYC * ITV (TV network) (Independent Televi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Probability Space
In probability theory, a probability space or a probability triple (\Omega, \mathcal, P) is a mathematical construct that provides a formal model of a random process or "experiment". For example, one can define a probability space which models the throwing of a . A probability space consists of three elements:Stroock, D. W. (1999). Probability theory: an analytic view. Cambridge University Press. # A '' sample space'', \Omega, which is the set of all possible outcomes of a random process under consideration. # An event space, \mathcal, which is a set of events, where an event is a subset of outcomes in the sample space. # A '' probability function'', P, which assigns, to each event in the event space, a probability, which is a number between 0 and 1 (inclusive). In order to provide a model of probability, these elements must satisfy probability axioms. In the example of the throw of a standard die, # The sample space \Omega is typically the set \ where each element in the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Subset Simulation
Subset simulation is a method used in reliability engineering to compute small (i.e., rare event) failure probabilities encountered in engineering systems. The basic idea is to express a small failure probability as a product of larger conditional probabilities by introducing intermediate failure events. This conceptually converts the original rare-event problem into a series of frequent-event problems that are easier to solve. In the actual implementation, samples conditional on intermediate failure events are adaptively generated to gradually populate from the frequent to rare event region. These 'conditional samples' provide information for estimating the complementary cumulative distribution function (CCDF) of the quantity of interest (that governs failure), covering the high as well as the low probability regions. They can also be used for investigating the cause and consequence of failure events. The generation of conditional samples is not trivial but can be performed efficient ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Black-box
In science, computing, and engineering, a black box is a system which can be viewed in terms of its inputs and outputs (or transfer characteristics), without any knowledge of its internal workings. Its implementation is "opaque" (black). The term can be used to refer to many inner workings, such as those of a transistor, an engine, an algorithm, the human brain, or an institution or government. To analyze an open system with a typical "black box approach", only the behavior of the stimulus/response will be accounted for, to infer the (unknown) ''box''. The usual representation of this "black box system" is a data flow diagram centered in the box. The opposite of a black box is a system where the inner components or logic are available for inspection, which is most commonly referred to as a white box (sometimes also known as a "clear box" or a "glass box"). History The modern meaning of the term "black box" seems to have entered the English language around 1945. In electroni ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quasi-Monte Carlo Method
In numerical analysis, the quasi-Monte Carlo method is a method for numerical integration and solving some other problems using low-discrepancy sequences (also called quasi-random sequences or sub-random sequences) to achieve variance reduction. This is in contrast to the regular Monte Carlo method or Monte Carlo integration, which are based on sequences of pseudorandom numbers. Monte Carlo and quasi-Monte Carlo methods are stated in a similar way. The problem is to approximate the integral of a function ''f'' as the average of the function evaluated at a set of points ''x''1, ..., ''x''''N'': : \int_ f(u)\,u \approx \frac\,\sum_^N f(x_i). Since we are integrating over the ''s''-dimensional unit cube, each ''x''''i'' is a vector of ''s'' elements. The difference between quasi-Monte Carlo and Monte Carlo is the way the ''x''''i'' are chosen. Quasi-Monte Carlo uses a low-discrepancy sequence such as the Halton sequence, the Sobol sequence, or the Faure sequence, whereas Mont ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
