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第517行： − − − {{anchor|Monte Carlo tree search}} − − A Monte Carlo approach was used for evaluating the potential value of a proposed program to help female petitioners in Wisconsin be successful in their applications for harassment and domestic abuse restraining orders. It was proposed to help women succeed in their petitions by providing them with greater advocacy thereby potentially reducing the risk of rape and physical assault. However, there were many variables in play that could not be estimated perfectly, including the effectiveness of restraining orders, the success rate of petitioners both with and without advocacy, and many others. The study ran trials that varied these variables to come up with an overall estimate of the success level of the proposed program as a whole. − − 蒙特卡洛方法被用来评估一个拟议的方案的潜在价值，以帮助威斯康星州的女性请愿者成功地申请骚扰和家庭虐待限制令。提议帮助妇女成功地提出请愿，向她们提供更多的宣传，从而有可能减少强奸和人身攻击的风险。然而，还有许多变量无法完全估计，包括限制令的有效性，上访者的成功率，无论有没有主张，以及许多其他因素。这项研究通过改变这些变量进行了试验，得出了对整个计划成功程度的总体评估。 第574行：
第567行： − − A similar approach, the quasi-Monte Carlo method, uses low-discrepancy sequences. These sequences "fill" the area better and sample the most important points more frequently, so quasi-Monte Carlo methods can often converge on the integral more quickly. − − 一个类似的方法，拟蒙特卡罗方法，使用低差异序列。这些序列能更好地“填充”区域，更频繁地采样最重要的点，因此拟蒙特卡罗方法往往能更快地收敛于积分。 − − Another class of methods for sampling points in a volume is to simulate random walks over it (Markov chain Monte Carlo). Such methods include the Metropolis–Hastings algorithm, Gibbs sampling, Wang and Landau algorithm, and interacting type MCMC methodologies such as the sequential Monte Carlo samplers. − − 另一类方法是模拟体积上的随机游动(马尔科夫蒙特卡洛)。这些方法包括 Metropolis-Hastings 算法、 Gibbs 抽样、 Wang 和 Landau 算法以及交互式 MCMC 方法，如序贯蒙特卡罗抽样。 第604行：
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第605行： − − [[Monte Carlo methods in finance]] are often used to [[Corporate finance#Quantifying uncertainty|evaluate investments in projects]] at a business unit or corporate level, or other financial valuations. They can be used to model [[project management|project schedules]], where simulations aggregate estimates for worst-case, best-case, and most likely durations for each task to determine outcomes for the overall project.[https://risk.octigo.pl/] Monte Carlo methods are also used in option pricing, default risk analysis.<ref>{{Cite book|title = An Introduction to Particle Methods with Financial Applications|publisher = Springer Berlin Heidelberg|journal = Numerical Methods in Finance|date = 2012|isbn = 978-3-642-25745-2|pages = 3–49|series = Springer Proceedings in Mathematics|volume = 12|first1 = René|last1 = Carmona|first2 = Pierre|last2 = Del Moral|first3 = Peng|last3 = Hu|first4 = Nadia|last4 = Oudjane|editor-first = René A.|editor-last = Carmona|editor2-first = Pierre Del|editor2-last = Moral|editor3-first = Peng|editor3-last = Hu|editor4-first = Nadia|display-editors = 3 |editor4-last = Oudjane|doi=10.1007/978-3-642-25746-9_1|citeseerx = 10.1.1.359.7957}}</ref><ref>{{Cite book |volume = 12|doi=10.1007/978-3-642-25746-9|series = Springer Proceedings in Mathematics|year = 2012|isbn = 978-3-642-25745-2|url = https://basepub.dauphine.fr/handle/123456789/11498|title=Numerical Methods in Finance|last1=Carmona|first1=René|last2=Del Moral|first2=Pierre|last3=Hu|first3=Peng|last4=Oudjane|first4=Nadia}}</ref><ref name="kr11">{{cite book|last1 = Kroese|first1 = D. P.|last2 = Taimre|first2 = T.|last3 = Botev|first3 = Z. I. |title = Handbook of Monte Carlo Methods|year = 2011|publisher = John Wiley & Sons}}</ref> Additionally, they can be used to estimate the financial impact of medical interventions.<ref>{{Cite journal |doi = 10.1371/journal.pone.0189718|pmid = 29284026|pmc = 5746244|title = A Monte Carlo simulation approach for estimating the health and economic impact of interventions provided at a student-run clinic|journal = PLOS ONE|volume = 12|issue = 12|pages = e0189718|year = 2017|last1 = Arenas|first1 = Daniel J.|last2 = Lett|first2 = Lanair A.|last3 = Klusaritz|first3 = Heather|last4 = Teitelman|first4 = Anne M.|bibcode = 2017PLoSO..1289718A}}</ref> 第625行：
第610行： + + + + + + − − A Monte Carlo approach was used for evaluating the potential value of a proposed program to help female petitioners in Wisconsin be successful in their applications for [[Harassment Restraining Order|harassment]] and [[Domestic Abuse Restraining Order|domestic abuse restraining orders]]. It was proposed to help women succeed in their petitions by providing them with greater advocacy thereby potentially reducing the risk of [[rape]] and [[physical assault]]. However, there were many variables in play that could not be estimated perfectly, including the effectiveness of restraining orders, the success rate of petitioners both with and without advocacy, and many others. The study ran trials that varied these variables to come up with an overall estimate of the success level of the proposed program as a whole.<ref name="montecarloanalysis">{{cite web|url=http://legalaidresearch.org/wp-content/uploads/Research-Increasing-Access-to-REstraining-Order-for-Low-Income-Victims-of-DV-A-Cost-Benefit-Analysis-of-the-Proposed-Domestic-Abuse-Grant-Program.pdf| title=Increasing Access to Restraining Orders for Low Income Victims of Domestic Violence: A Cost-Benefit Analysis of the Proposed Domestic Abuse Grant Program |publisher=[[State Bar of Wisconsin]] |date=December 2006 |accessdate=2016-12-12|last1=Elwart|first1=Liz|last2=Emerson|first2=Nina|last3=Enders|first3=Christina|last4=Fumia|first4=Dani|last5=Murphy|first5=Kevin|url-status=dead|archive-url=https://web.archive.org/web/20181106220526/https://legalaidresearch.org/wp-content/uploads/Research-Increasing-Access-to-REstraining-Order-for-Low-Income-Victims-of-DV-A-Cost-Benefit-Analysis-of-the-Proposed-Domestic-Abuse-Grant-Program.pdf|archive-date=6 November 2018}}</ref> 第669行：
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→Definitions
蒙特卡罗方法也是近似随机化和置换检验的折衷。近似随机化测试是基于所有排列的特定子集(这需要潜在的庞大的内务管理，其中排列已被考虑)。蒙特卡罗方法是基于一定数量的随机排列(如果排列被抽取两次或更频繁，精度会有轻微的损失，因为不必追踪哪些排列已经被选择)。
蒙特卡罗方法也是近似随机化和置换检验的折衷。近似随机化测试是基于所有排列的特定子集(这需要潜在的庞大的内务管理，其中排列已被考虑)。蒙特卡罗方法是基于一定数量的随机排列(如果排列被抽取两次或更频繁，精度会有轻微的损失，因为不必追踪哪些排列已经被选择)。
===Artificial intelligence for games===
===Artificial intelligence for games===
{{See also|Computer Go}}
{{See also|Computer Go}}
===Design and visuals===
===Design and visuals===
Monte Carlo methods are also efficient in solving coupled integral differential equations of radiation fields and energy transport, and thus these methods have been used in [[global illumination]] computations that produce photo-realistic images of virtual 3D models, with applications in [[video game]]s, [[architecture]], [[design]], computer generated [[film]]s, and cinematic special effects.<ref>{{harvnb|Szirmay–Kalos|2008}}</ref>
Monte Carlo methods are also efficient in solving coupled integral differential equations of radiation fields and energy transport, and thus these methods have been used in [[global illumination]] computations that produce photo-realistic images of virtual 3D models, with applications in [[video game]]s, [[architecture]], [[design]], computer generated [[film]]s, and cinematic special effects.<ref>{{harvnb|Szirmay–Kalos|2008}}</ref>
蒙特卡罗模拟通常用于评估影响不同决策方案结果的风险和不确定性。蒙特卡洛模拟允许商业风险分析师在销售量、商品和劳动力价格、利率和汇率等变量中考虑不确定性的总体影响，以及不同风险事件的影响，如合同的取消或税法的改变。
蒙特卡罗模拟通常用于评估影响不同决策方案结果的风险和不确定性。蒙特卡洛模拟允许商业风险分析师在销售量、商品和劳动力价格、利率和汇率等变量中考虑不确定性的总体影响，以及不同风险事件的影响，如合同的取消或税法的改变。
[[Monte Carlo methods in finance]] are often used to [[Corporate finance#Quantifying uncertainty|evaluate investments in projects]] at a business unit or corporate level, or other financial valuations. They can be used to model [[project management|project schedules]], where simulations aggregate estimates for worst-case, best-case, and most likely durations for each task to determine outcomes for the overall project.[https://risk.octigo.pl/] Monte Carlo methods are also used in option pricing, default risk analysis.<ref>{{Cite book|title = An Introduction to Particle Methods with Financial Applications|publisher = Springer Berlin Heidelberg|journal = Numerical Methods in Finance|date = 2012|isbn = 978-3-642-25745-2|pages = 3–49|series = Springer Proceedings in Mathematics|volume = 12|first1 = René|last1 = Carmona|first2 = Pierre|last2 = Del Moral|first3 = Peng|last3 = Hu|first4 = Nadia|last4 = Oudjane|editor-first = René A.|editor-last = Carmona|editor2-first = Pierre Del|editor2-last = Moral|editor3-first = Peng|editor3-last = Hu|editor4-first = Nadia|display-editors = 3 |editor4-last = Oudjane|doi=10.1007/978-3-642-25746-9_1|citeseerx = 10.1.1.359.7957}}</ref><ref>{{Cite book |volume = 12|doi=10.1007/978-3-642-25746-9|series = Springer Proceedings in Mathematics|year = 2012|isbn = 978-3-642-25745-2|url = https://basepub.dauphine.fr/handle/123456789/11498|title=Numerical Methods in Finance|last1=Carmona|first1=René|last2=Del Moral|first2=Pierre|last3=Hu|first3=Peng|last4=Oudjane|first4=Nadia}}</ref><ref name="kr11">{{cite book|last1 = Kroese|first1 = D. P.|last2 = Taimre|first2 = T.|last3 = Botev|first3 = Z. I. |title = Handbook of Monte Carlo Methods|year = 2011|publisher = John Wiley & Sons}}</ref> Additionally, they can be used to estimate the financial impact of medical interventions.<ref>{{Cite journal |doi = 10.1371/journal.pone.0189718|pmid = 29284026|pmc = 5746244|title = A Monte Carlo simulation approach for estimating the health and economic impact of interventions provided at a student-run clinic|journal = PLOS ONE|volume = 12|issue = 12|pages = e0189718|year = 2017|last1 = Arenas|first1 = Daniel J.|last2 = Lett|first2 = Lanair A.|last3 = Klusaritz|first3 = Heather|last4 = Teitelman|first4 = Anne M.|bibcode = 2017PLoSO..1289718A}}</ref>
Monte Carlo methods in finance are often used to evaluate investments in projects at a business unit or corporate level, or other financial valuations. They can be used to model project schedules, where simulations aggregate estimates for worst-case, best-case, and most likely durations for each task to determine outcomes for the overall project.[https://risk.octigo.pl/] Monte Carlo methods are also used in option pricing, default risk analysis. Additionally, they can be used to estimate the financial impact of medical interventions.
Monte Carlo methods in finance are often used to evaluate investments in projects at a business unit or corporate level, or other financial valuations. They can be used to model project schedules, where simulations aggregate estimates for worst-case, best-case, and most likely durations for each task to determine outcomes for the overall project.[https://risk.octigo.pl/] Monte Carlo methods are also used in option pricing, default risk analysis. Additionally, they can be used to estimate the financial impact of medical interventions.
反问题的概率公式导致了模型空间中概率分布的定义。该概率分布将先前的信息与通过测量一些可观测的参数(数据)获得的新信息结合起来。
反问题的概率公式导致了模型空间中概率分布的定义。该概率分布将先前的信息与通过测量一些可观测的参数(数据)获得的新信息结合起来。
As, in the general case, the theory linking data with model parameters is nonlinear, the posterior probability in the model space may not be easy to describe (it may be multimodal, some moments may not be defined, etc.).
As, in the general case, the theory linking data with model parameters is nonlinear, the posterior probability in the model space may not be easy to describe (it may be multimodal, some moments may not be defined, etc.).
因为，在一般情况下，连接数据和模型参数的理论是非线性的，模型空间中的后验概率可能不容易描述(它可能是多模态的，一些矩可能没有定义，等等。).
因为，在一般情况下，连接数据和模型参数的理论是非线性的，模型空间中的后验概率可能不容易描述(它可能是多模态的，一些矩可能没有定义，等等。).
===Law===
===Law===
A Monte Carlo approach was used for evaluating the potential value of a proposed program to help female petitioners in Wisconsin be successful in their applications for [[Harassment Restraining Order|harassment]] and [[Domestic Abuse Restraining Order|domestic abuse restraining orders]]. It was proposed to help women succeed in their petitions by providing them with greater advocacy thereby potentially reducing the risk of [[rape]] and [[physical assault]]. However, there were many variables in play that could not be estimated perfectly, including the effectiveness of restraining orders, the success rate of petitioners both with and without advocacy, and many others. The study ran trials that varied these variables to come up with an overall estimate of the success level of the proposed program as a whole.<ref name="montecarloanalysis">{{cite web|url=http://legalaidresearch.org/wp-content/uploads/Research-Increasing-Access-to-REstraining-Order-for-Low-Income-Victims-of-DV-A-Cost-Benefit-Analysis-of-the-Proposed-Domestic-Abuse-Grant-Program.pdf| title=Increasing Access to Restraining Orders for Low Income Victims of Domestic Violence: A Cost-Benefit Analysis of the Proposed Domestic Abuse Grant Program |publisher=[[State Bar of Wisconsin]] |date=December 2006 |accessdate=2016-12-12|last1=Elwart|first1=Liz|last2=Emerson|first2=Nina|last3=Enders|first3=Christina|last4=Fumia|first4=Dani|last5=Murphy|first5=Kevin|url-status=dead|archive-url=https://web.archive.org/web/20181106220526/https://legalaidresearch.org/wp-content/uploads/Research-Increasing-Access-to-REstraining-Order-for-Low-Income-Victims-of-DV-A-Cost-Benefit-Analysis-of-the-Proposed-Domestic-Abuse-Grant-Program.pdf|archive-date=6 November 2018}}</ref>
A Monte Carlo approach was used for evaluating the potential value of a proposed program to help female petitioners in Wisconsin be successful in their applications for harassment and domestic abuse restraining orders. It was proposed to help women succeed in their petitions by providing them with greater advocacy thereby potentially reducing the risk of rape and physical assault. However, there were many variables in play that could not be estimated perfectly, including the effectiveness of restraining orders, the success rate of petitioners both with and without advocacy, and many others. The study ran trials that varied these variables to come up with an overall estimate of the success level of the proposed program as a whole.
蒙特卡洛方法被用来评估一个拟议的方案的潜在价值，以帮助威斯康星州的女性请愿者成功地申请骚扰和家庭虐待限制令。提议帮助妇女成功地提出请愿，向她们提供更多的宣传，从而有可能减少强奸和人身攻击的风险。然而，还有许多变量无法完全估计，包括限制令的有效性，上访者的成功率，无论有没有主张，以及许多其他因素。这项研究通过改变这些变量进行了试验，得出了对整个计划成功程度的总体评估。
When analyzing an inverse problem, obtaining a maximum likelihood model is usually not sufficient, as we normally also wish to have information on the resolution power of the data. In the general case we may have many model parameters, and an inspection of the marginal probability densities of interest may be impractical, or even useless. But it is possible to pseudorandomly generate a large collection of models according to the posterior probability distribution and to analyze and display the models in such a way that information on the relative likelihoods of model properties is conveyed to the spectator. This can be accomplished by means of an efficient Monte Carlo method, even in cases where no explicit formula for the a priori distribution is available.
When analyzing an inverse problem, obtaining a maximum likelihood model is usually not sufficient, as we normally also wish to have information on the resolution power of the data. In the general case we may have many model parameters, and an inspection of the marginal probability densities of interest may be impractical, or even useless. But it is possible to pseudorandomly generate a large collection of models according to the posterior probability distribution and to analyze and display the models in such a way that information on the relative likelihoods of model properties is conveyed to the spectator. This can be accomplished by means of an efficient Monte Carlo method, even in cases where no explicit formula for the a priori distribution is available.
当分析一个反问题时，获得一个最大似然模型通常是不够的，因为我们通常也希望有关于数据的分辨率的信息。在一般情况下，我们可能有许多模型参数，检查的边际概率密度的兴趣可能是不切实际的，甚至无用的。但是，根据《后验概率可以伪随机生成大量的模型集合，并以这样一种方式分析和显示模型，模型属性的相对可能性信息被传达给观众，这是可能的。这可以通过一个有效的蒙特卡罗方法安全管理系统来实现，即使在没有黎曼显式公式安全管理先验概率的情况下。
当分析一个反问题时，获得一个最大似然模型通常是不够的，因为我们通常也希望有关于数据的分辨率的信息。在一般情况下，我们可能有许多模型参数，检查的边际概率密度的兴趣可能是不切实际的，甚至无用的。但是，根据《后验概率可以伪随机生成大量的模型集合，并以这样一种方式分析和显示模型，模型属性的相对可能性信息被传达给观众，这是可能的。这可以通过一个有效的蒙特卡罗方法安全管理系统来实现，即使在没有黎曼显式公式安全管理先验概率的情况下。
The best-known importance sampling method, the Metropolis algorithm, can be generalized, and this gives a method that allows analysis of (possibly highly nonlinear) inverse problems with complex a priori information and data with an arbitrary noise distribution.
The best-known importance sampling method, the Metropolis algorithm, can be generalized, and this gives a method that allows analysis of (possibly highly nonlinear) inverse problems with complex a priori information and data with an arbitrary noise distribution.
A similar approach, the [[quasi-Monte Carlo method]], uses [[low-discrepancy sequence]]s. These sequences "fill" the area better and sample the most important points more frequently, so quasi-Monte Carlo methods can often converge on the integral more quickly.
A similar approach, the [[quasi-Monte Carlo method]], uses [[low-discrepancy sequence]]s. These sequences "fill" the area better and sample the most important points more frequently, so quasi-Monte Carlo methods can often converge on the integral more quickly.
A similar approach, the quasi-Monte Carlo method, uses low-discrepancy sequences. These sequences "fill" the area better and sample the most important points more frequently, so quasi-Monte Carlo methods can often converge on the integral more quickly.
一个类似的方法，拟蒙特卡罗方法，使用低差异序列。这些序列能更好地“填充”区域，更频繁地采样最重要的点，因此拟蒙特卡罗方法往往能更快地收敛于积分。
Another class of methods for sampling points in a volume is to simulate random walks over it ([[Markov chain Monte Carlo]]). Such methods include the [[Metropolis–Hastings algorithm]], [[Gibbs sampling]], [[Wang and Landau algorithm]], and interacting type MCMC methodologies such as the [[Particle filter|sequential Monte Carlo]] samplers.<ref>{{Cite journal|title = Sequential Monte Carlo samplers|journal = Journal of the Royal Statistical Society, Series B|doi=10.1111/j.1467-9868.2006.00553.x|volume=68|issue = 3|pages=411–436|year = 2006|last1 = Del Moral|first1 = Pierre|last2 = Doucet|first2 = Arnaud|last3 = Jasra|first3 = Ajay|arxiv = cond-mat/0212648|s2cid = 12074789}}</ref>
Another class of methods for sampling points in a volume is to simulate random walks over it ([[Markov chain Monte Carlo]]). Such methods include the [[Metropolis–Hastings algorithm]], [[Gibbs sampling]], [[Wang and Landau algorithm]], and interacting type MCMC methodologies such as the [[Particle filter|sequential Monte Carlo]] samplers.<ref>{{Cite journal|title = Sequential Monte Carlo samplers|journal = Journal of the Royal Statistical Society, Series B|doi=10.1111/j.1467-9868.2006.00553.x|volume=68|issue = 3|pages=411–436|year = 2006|last1 = Del Moral|first1 = Pierre|last2 = Doucet|first2 = Arnaud|last3 = Jasra|first3 = Ajay|arxiv = cond-mat/0212648|s2cid = 12074789}}</ref>
Another class of methods for sampling points in a volume is to simulate random walks over it (Markov chain Monte Carlo). Such methods include the Metropolis–Hastings algorithm, Gibbs sampling, Wang and Landau algorithm, and interacting type MCMC methodologies such as the sequential Monte Carlo samplers.
另一类方法是模拟体积上的随机游动(马尔科夫蒙特卡洛)。这些方法包括 Metropolis-Hastings 算法、 Gibbs 抽样、 Wang 和 Landau 算法以及交互式 MCMC 方法，如序贯蒙特卡罗抽样。
=== Simulation and optimization ===
=== Simulation and optimization ===