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===Climate change and radiative forcing 气候变化与辐射强迫 ===

===Climate change and radiative forcing 气候变化与辐射强迫 ===

The [[IPCC|Intergovernmental Panel on Climate Change]] relies on Monte Carlo methods in [[probability density function]] analysis of [[radiative forcing]].

The [[IPCC|Intergovernmental Panel on Climate Change]] relies on Monte Carlo methods in [[probability density function]] analysis of [[radiative forcing]].

Probability density function (PDF) of ERF due to total GHG, aerosol forcing and total anthropogenic forcing. The GHG consists of WMGHG, ozone and stratospheric water vapour. The PDFs are generated based on uncertainties provided in Table 8.6. The combination of the individual RF agents to derive total forcing over the Industrial Era are done by Monte Carlo simulations and based on the method in Boucher and Haywood (2001). PDF of the ERF from surface albedo changes and combined contrails and contrail-induced cirrus are included in the total anthropogenic forcing, but not shown as a separate PDF. We currently do not have ERF estimates for some forcing mechanisms: ozone, land use, solar, etc.

Probability density function (PDF) of ERF due to total GHG, aerosol forcing and total anthropogenic forcing. The GHG consists of WMGHG, ozone and stratospheric water vapour. The PDFs are generated based on uncertainties provided in Table 8.6. The combination of the individual RF agents to derive total forcing over the Industrial Era are done by Monte Carlo simulations and based on the method in Boucher and Haywood (2001). PDF of the ERF from surface albedo changes and combined contrails and contrail-induced cirrus are included in the total anthropogenic forcing, but not shown as a separate PDF. We currently do not have ERF estimates for some forcing mechanisms: ozone, land use, solar, etc.

===Computational biology===

 

===Computational biology 计算生物学===

Monte Carlo methods are used in various fields of [[computational biology]], for example for [[Bayesian inference in phylogeny]], or for studying biological systems such as genomes, proteins,<ref>{{harvnb|Ojeda|et al.|2009}},</ref> or membranes.<ref>{{harvnb|Milik|Skolnick|1993}}</ref>The systems can be studied in the coarse-grained or ''ab initio'' frameworks depending on the desired accuracy. Computer simulations allow us to monitor the local environment of a particular [[biomolecule|molecule]] to see if some [[chemical reaction]] is happening for instance. In cases where it is not feasible to conduct a physical experiment, [[thought experiment]]s can be conducted (for instance: breaking bonds, introducing impurities at specific sites, changing the local/global structure, or introducing external fields).  

Monte Carlo methods are used in various fields of [[computational biology]], for example for [[Bayesian inference in phylogeny]], or for studying biological systems such as genomes, proteins,<ref>{{harvnb|Ojeda|et al.|2009}},</ref> or membranes.<ref>{{harvnb|Milik|Skolnick|1993}}</ref>The systems can be studied in the coarse-grained or ''ab initio'' frameworks depending on the desired accuracy. Computer simulations allow us to monitor the local environment of a particular [[biomolecule|molecule]] to see if some [[chemical reaction]] is happening for instance. In cases where it is not feasible to conduct a physical experiment, [[thought experiment]]s can be conducted (for instance: breaking bonds, introducing impurities at specific sites, changing the local/global structure, or introducing external fields).  

蒙特卡罗方法被用于计算生物学的各个领域，例如在系统发育学中的贝叶斯推断，或者用于研究生物系统，例如基因组、蛋白质或膜。该系统可以在粗粒度或从头开始框架中研究，这取决于所需的准确性。计算机模拟使我们能够监测特定分子的局部环境，看看是否正在发生某种化学反应，例如。在无法进行物理实验的情况下，可以进行思维实验(例如: 打破键，在特定位置引入杂质，改变局部/全球结构，或引入外部场)。

蒙特卡罗方法被用于计算生物学的各个领域，例如在系统发育学中的贝叶斯推断，或者用于研究生物系统，例如基因组、蛋白质或膜。该系统可以在粗粒度或从头开始框架中研究，这取决于所需的准确性。计算机模拟使我们能够监测特定分子的局部环境，看看是否正在发生某种化学反应，例如。在无法进行物理实验的情况下，可以进行思维实验(例如: 打破键，在特定位置引入杂质，改变局部/全球结构，或引入外部场)。

===Computer graphics===

===Computer graphics 计算机图形学===

[[Path tracing]], occasionally referred to as Monte Carlo ray tracing, renders a 3D scene by randomly tracing samples of possible light paths. Repeated sampling of any given pixel will eventually cause the average of the samples to converge on the correct solution of the [[rendering equation]], making it one of the most physically accurate 3D graphics rendering methods in existence.

[[Path tracing]], occasionally referred to as Monte Carlo ray tracing, renders a 3D scene by randomly tracing samples of possible light paths. Repeated sampling of any given pixel will eventually cause the average of the samples to converge on the correct solution of the [[rendering equation]], making it one of the most physically accurate 3D graphics rendering methods in existence.

路径追踪，偶尔被称为蒙特卡罗光线追踪，通过随机追踪可能光路的样本来呈现一个三维场景。对任何给定像素的重复采样最终将导致样本的平均值收敛到渲染方程的正确解，使其成为现存物理上最精确的3 d 图形渲染方法之一。

路径追踪，偶尔被称为蒙特卡罗光线追踪，通过随机追踪可能光路的样本来呈现一个三维场景。对任何给定像素的重复采样最终将导致样本的平均值收敛到渲染方程的正确解，使其成为现存物理上最精确的3 d 图形渲染方法之一。

===Applied statistics===

===Applied statistics 应用统计学===

The standards for Monte Carlo experiments in statistics were set by Sawilowsky.<ref>{{cite journal | last1 = Cassey | last2 = Smith | year = 2014 | title = Simulating confidence for the Ellison-Glaeser Index | url = | journal = Journal of Urban Economics | volume = 81 | issue = | page = 93 | doi =  10.1016/j.jue.2014.02.005}}</ref> In applied statistics, Monte Carlo methods may be used for at least four purposes:

The standards for Monte Carlo experiments in statistics were set by Sawilowsky.<ref>{{cite journal | last1 = Cassey | last2 = Smith | year = 2014 | title = Simulating confidence for the Ellison-Glaeser Index | url = | journal = Journal of Urban Economics | volume = 81 | issue = | page = 93 | doi =  10.1016/j.jue.2014.02.005}}</ref> In applied statistics, Monte Carlo methods may be used for at least four purposes:

{{anchor|Monte Carlo tree search}}

{{anchor|Monte Carlo tree search}}

===Artificial intelligence for games===

===Artificial intelligence for games 人工智能在游戏中的应用===

{{Main|Monte Carlo tree search}}

{{Main|Monte Carlo tree search}}

{{See also|Computer Go}}

{{See also|Computer Go}}

===Design and visuals===

===Design and visuals 设计与视觉效果===

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>

蒙特卡罗方法在解决辐射场和能量传输的耦合积分微分方程方面也很有效，因此这些方法已经被用于全局光源计算，产生虚拟3 d 模型的照片般逼真的图像，应用于视频游戏、建筑、设计、计算机生成的电影和电影特效。

蒙特卡罗方法在解决辐射场和能量传输的耦合积分微分方程方面也很有效，因此这些方法已经被用于全局光源计算，产生虚拟3 d 模型的照片般逼真的图像，应用于视频游戏、建筑、设计、计算机生成的电影和电影特效。

===Search and rescue===

===Search and rescue 搜寻与救援===

The [[US Coast Guard]] utilizes Monte Carlo methods within its computer modeling software [[SAROPS]] in order to calculate the probable locations of vessels during [[search and rescue]] operations. Each simulation can generate as many as ten thousand data points that are randomly distributed based upon provided variables.<ref>{{cite web|url=http://insights.dice.com/2014/01/03/how-the-coast-guard-uses-analytics-to-search-for-those-lost-at-sea|title=How the Coast Guard Uses Analytics to Search for Those Lost at Sea|work=Dice Insights|date=2014-01-03}}</ref> Search patterns are then generated based upon extrapolations of these data in order to optimize the probability of containment (POC) and the probability of detection (POD), which together will equal an overall probability of success (POS). Ultimately this serves as a practical application of [[probability distribution]] in order to provide the swiftest and most expedient method of rescue, saving both lives and resources.<ref>{{cite web|url=http://www.ifremer.fr/web-com/sar2011/Presentations/SARWS2011_STONE_L.pdf|title=Search Modeling and Optimization in USCG's Search and Rescue Optimal Planning System (SAROPS)|author1=Lawrence D. Stone|author2=Thomas M. Kratzke|author3=John R. Frost|website=Ifremer.fr|accessdate=28 October 2017}}</ref>

The [[US Coast Guard]] utilizes Monte Carlo methods within its computer modeling software [[SAROPS]] in order to calculate the probable locations of vessels during [[search and rescue]] operations. Each simulation can generate as many as ten thousand data points that are randomly distributed based upon provided variables.<ref>{{cite web|url=http://insights.dice.com/2014/01/03/how-the-coast-guard-uses-analytics-to-search-for-those-lost-at-sea|title=How the Coast Guard Uses Analytics to Search for Those Lost at Sea|work=Dice Insights|date=2014-01-03}}</ref> Search patterns are then generated based upon extrapolations of these data in order to optimize the probability of containment (POC) and the probability of detection (POD), which together will equal an overall probability of success (POS). Ultimately this serves as a practical application of [[probability distribution]] in order to provide the swiftest and most expedient method of rescue, saving both lives and resources.<ref>{{cite web|url=http://www.ifremer.fr/web-com/sar2011/Presentations/SARWS2011_STONE_L.pdf|title=Search Modeling and Optimization in USCG's Search and Rescue Optimal Planning System (SAROPS)|author1=Lawrence D. Stone|author2=Thomas M. Kratzke|author3=John R. Frost|website=Ifremer.fr|accessdate=28 October 2017}}</ref>

美国海岸警卫队在其计算机建模软件 SAROPS 中使用蒙特卡罗方法，以便在搜索和救援行动中计算可能的船只位置。每个模拟可以生成多达一万个数据点，这些数据点是根据提供的变量随机分布的。然后根据这些数据的推断生成搜索模式，以优化包容概率(POC)和检测概率(POD) ，这两者合起来等于总体成功概率(POS)。最终，这作为概率分布的一个实际应用，以提供最迅速和最便捷的救援方法，拯救生命和资源。

美国海岸警卫队在其计算机建模软件 SAROPS 中使用蒙特卡罗方法，以便在搜索和救援行动中计算可能的船只位置。每个模拟可以生成多达一万个数据点，这些数据点是根据提供的变量随机分布的。然后根据这些数据的推断生成搜索模式，以优化包容概率(POC)和检测概率(POD) ，这两者合起来等于总体成功概率(POS)。最终，这作为概率分布的一个实际应用，以提供最迅速和最便捷的救援方法，拯救生命和资源。

===Finance and business===

===Finance and business 金融与商业===

Monte Carlo simulation is commonly used to evaluate the risk and uncertainty that would affect the outcome of different decision options. Monte Carlo simulation allows the business risk analyst to incorporate the total effects of uncertainty in variables like sales volume, commodity and labour prices, interest and exchange rates, as well as the effect of distinct risk events like the cancellation of a contract or the change of a tax law.

Monte Carlo simulation is commonly used to evaluate the risk and uncertainty that would affect the outcome of different decision options. Monte Carlo simulation allows the business risk analyst to incorporate the total effects of uncertainty in variables like sales volume, commodity and labour prices, interest and exchange rates, as well as the effect of distinct risk events like the cancellation of a contract or the change of a tax law.

[[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 [[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>

===Law===

===Law===