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{ "type" : "literal", "value" : "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 ones are common random numbers, antithetic variates, control variates, importance sampling, stratified sampling, , and . For simulation with black-box models subset simulation and line sampling can also be used. Under these headings ar" , "lang" : "en" } ,
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{ "type" : "literal", "value" : "La r\u00E9duction de la variance regroupe l'ensemble des techniques, plus ou moins simples, qui permettent de r\u00E9duire la variance des estimateurs de Monte-Carlo. En voici une courte liste : \n* Variable antith\u00E9tique : on introduit une seconde variable al\u00E9atoire tr\u00E8s fortement n\u00E9gativement corr\u00E9l\u00E9e avec la premi\u00E8re, permettant de r\u00E9duire la variance. L'\u00E9l\u00E9ment clef est la formule suivante, valable pour deux variables : \n* Variable de contr\u00F4le : on introduit une variable tierce, dite variable de contr\u00F4le, et on construit une nouvelle classe d'estimateurs, d\u00E9pendant d'un param\u00E8tre c. On cherche la valeur du param\u00E8tre c permettant de r\u00E9aliser une r\u00E9duction de variance, par rapport \u00E0 l'estimation Monte-Carlo de base ; \n* L'\u00E9chantillonnage pr\u00E9f\u00E9rentiel (ou importance sampling en anglais) : lors du tirage de donn\u00E9es al\u00E9atoires, certaines valeurs ont plus d'importance que d'autres dans l'\u00E9valuation de l'esp\u00E9rance/int\u00E9grale. L'id\u00E9e est donc d'abandonner l'\u00E9chantillonnage uniforme (selon la loi uniforme continue) pour un \u00E9chantillonnage selon une autre loi, plus appropri\u00E9e. \n* Le conditionnement statistique : \n* La stratification : \n* Portail des probabilit\u00E9s et de la statistique \n* Portail de la physique" , "lang" : "fr" } ,
{ "type" : "literal", "value" : "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 ones are common random numbers, antithetic variates, control variates, importance sampling, stratified sampling, , and . 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, particle transport simulations make extensive use of \"weight windows\" and \"splitting/Russian roulette\" techniques, which are a form of importance sampling." , "lang" : "en" } ,
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