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第457行： − 蒙特卡罗方法在计算物理学、物理化学和相关应用领域中非常重要，并且有各种各样的应用，从复杂的量子色动力学计算到设计热屏和空气动力学形式，以及辐射剂量计算的辐射传输模型。在统计物理学中，蒙特卡罗分子模拟是计算分子动力学的一种替代方法，而蒙特卡罗方法被用来计算简单粒子和聚合物体系的统计场理论。量子蒙特卡罗法方法解决了量子系统的多体问题。在实验粒子物理学中，蒙特卡罗方法被用来设计探测器，了解它们的行为，并将实验数据与理论进行比较。在天体物理学中，它们以各种不同的方式被用来模拟星系演化和微波辐射通过粗糙行星表面的传输。蒙特卡罗方法也用于构成现代天气预报基础的集合模型中。+ − + 第462行：
第467行： + + + − + + + + + + + + − + − − {{Quote|text=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.<ref>{{cite book|title=Climate Change 2013 The Physical Science Basis|date=2013|publisher=Cambridge University Press|isbn=978-1-107-66182-0|page=697|url=http://www.climatechange2013.org/images/report/WG1AR5_ALL_FINAL.pdf|accessdate=2 March 2016}}</ref>}}
无编辑摘要
20世纪90年代末，'''丹·克里桑 Dan Crisan'''、'''杰西卡·盖恩斯 Jessica Gaines'''和'''特里·利昂斯 Terry Lyons'''，以及丹·克里桑、皮埃尔·德尔·莫勒尔和特里·利昂斯也发展了具有不同种群大小的分支型粒子方法。2000年，皮埃尔·德尔·莫勒尔、'''爱丽丝·吉奥内 A. Guionnet'''和'''洛朗·米克洛 L. Miclo'''进一步发展了这一领域。
20世纪90年代末，'''丹·克里桑 Dan Crisan'''、'''杰西卡·盖恩斯 Jessica Gaines'''和'''特里·利昂斯 Terry Lyons'''，以及丹·克里桑、皮埃尔·德尔·莫勒尔和特里·利昂斯也发展了具有不同种群大小的分支型粒子方法。2000年，皮埃尔·德尔·莫勒尔、'''爱丽丝·吉奥内 A. Guionnet'''和'''洛朗·米克洛 L. Miclo'''进一步发展了这一领域。
==Definitions==
==Definitions 定义==
There is no consensus on how ''Monte Carlo'' should be defined. For example, Ripley<ref name=Ripley>{{harvnb|Ripley|1987}}</ref> defines most probabilistic modeling as ''[[stochastic simulation]]'', with ''Monte Carlo'' being reserved for [[Monte Carlo integration]] and Monte Carlo statistical tests. [[Shlomo Sawilowsky|Sawilowsky]]<ref name=Sawilowsky>{{harvnb|Sawilowsky|2003}}</ref> distinguishes between a [[simulation]], a Monte Carlo method, and a Monte Carlo simulation: a simulation is a fictitious representation of reality, a Monte Carlo method is a technique that can be used to solve a mathematical or statistical problem, and a Monte Carlo simulation uses repeated sampling to obtain the statistical properties of some phenomenon (or behavior). Examples:
There is no consensus on how ''Monte Carlo'' should be defined. For example, Ripley<ref name=Ripley>{{harvnb|Ripley|1987}}</ref> defines most probabilistic modeling as ''[[stochastic simulation]]'', with ''Monte Carlo'' being reserved for [[Monte Carlo integration]] and Monte Carlo statistical tests. [[Shlomo Sawilowsky|Sawilowsky]]<ref name=Sawilowsky>{{harvnb|Sawilowsky|2003}}</ref> distinguishes between a [[simulation]], a Monte Carlo method, and a Monte Carlo simulation: a simulation is a fictitious representation of reality, a Monte Carlo method is a technique that can be used to solve a mathematical or statistical problem, and a Monte Carlo simulation uses repeated sampling to obtain the statistical properties of some phenomenon (or behavior). Examples:
'''Monte Carlo and random numbers'''
'''Monte Carlo and random numbers'''
蒙特卡罗和随机数
The main idea behind this method is that the results are computed based on repeated random sampling and statistical analysis. The Monte Carlo simulation is, in fact, random experimentations, in the case that, the results of these experiments are not well known. Monte Carlo simulations are typically characterized by many unknown parameters, many of which are difficult to obtain experimentally. Monte Carlo simulation methods do not always require truly random numbers to be useful (although, for some applications such as primality testing, unpredictability is vital). Many of the most useful techniques use deterministic, pseudorandom sequences, making it easy to test and re-run simulations. The only quality usually necessary to make good simulations is for the pseudo-random sequence to appear "random enough" in a certain sense.
The main idea behind this method is that the results are computed based on repeated random sampling and statistical analysis. The Monte Carlo simulation is, in fact, random experimentations, in the case that, the results of these experiments are not well known. Monte Carlo simulations are typically characterized by many unknown parameters, many of which are difficult to obtain experimentally. Monte Carlo simulation methods do not always require truly random numbers to be useful (although, for some applications such as primality testing, unpredictability is vital). Many of the most useful techniques use deterministic, pseudorandom sequences, making it easy to test and re-run simulations. The only quality usually necessary to make good simulations is for the pseudo-random sequence to appear "random enough" in a certain sense.
'''Monte Carlo simulation versus "what if" scenarios'''
'''Monte Carlo simulation versus "what if" scenarios'''
蒙特卡罗模拟与“假如”情景
There are ways of using probabilities that are definitely not Monte Carlo simulations – for example, deterministic modeling using single-point estimates. Each uncertain variable within a model is assigned a "best guess" estimate. Scenarios (such as best, worst, or most likely case) for each input variable are chosen and the results recorded.
There are ways of using probabilities that are definitely not Monte Carlo simulations – for example, deterministic modeling using single-point estimates. Each uncertain variable within a model is assigned a "best guess" estimate. Scenarios (such as best, worst, or most likely case) for each input variable are chosen and the results recorded.
====Mersenne_twister (MT19937) in Python (a Monte Carlo method simulation)====
====Mersenne_twister (MT19937) in Python (a Monte Carlo method simulation)====
'''Mersenne_twister (MT19937)在Python中的应用(一种蒙特卡罗方法仿真)'''
A ''Monte Carlo method'' simulation is defined as any method that utilizes sequences of random numbers to perform the simulation. Monte Carlo simulations are applied to many topics including [[quantum chromodynamics]], cancer radiation therapy, traffic flow, [[stellar evolution]] and VLSI design. All these simulations require the use of random numbers and therefore [[pseudorandom number generator]]s, which makes creating random-like numbers very important.
A ''Monte Carlo method'' simulation is defined as any method that utilizes sequences of random numbers to perform the simulation. Monte Carlo simulations are applied to many topics including [[quantum chromodynamics]], cancer radiation therapy, traffic flow, [[stellar evolution]] and VLSI design. All these simulations require the use of random numbers and therefore [[pseudorandom number generator]]s, which makes creating random-like numbers very important.
</syntaxhighlight>
</syntaxhighlight>
==Applications==
==Applications 应用==
Monte Carlo methods are especially useful for simulating phenomena with significant [[uncertainty]] in inputs and systems with many [[coupling (physics)|coupled]] degrees of freedom. Areas of application include:
Monte Carlo methods are especially useful for simulating phenomena with significant [[uncertainty]] in inputs and systems with many [[coupling (physics)|coupled]] degrees of freedom. Areas of application include:
蒙特卡罗方法尤其适用于模拟输入和多自由度耦合系统中具有明显不确定性的现象。申请范围包括:
蒙特卡罗方法尤其适用于模拟输入和多自由度耦合系统中具有明显不确定性的现象。申请范围包括:
===Physical sciences===
===Physical sciences 物理科学===
{{Computational physics}}
{{Computational physics}}
Monte Carlo methods are very important in computational physics, physical chemistry, and related applied fields, and have diverse applications from complicated quantum chromodynamics calculations to designing heat shields and aerodynamic forms as well as in modeling radiation transport for radiation dosimetry calculations. In statistical physics Monte Carlo molecular modeling is an alternative to computational molecular dynamics, and Monte Carlo methods are used to compute statistical field theories of simple particle and polymer systems. Quantum Monte Carlo methods solve the many-body problem for quantum systems. In experimental particle physics, Monte Carlo methods are used for designing detectors, understanding their behavior and comparing experimental data to theory. In astrophysics, they are used in such diverse manners as to model both galaxy evolution and microwave radiation transmission through a rough planetary surface. Monte Carlo methods are also used in the ensemble models that form the basis of modern weather forecasting.
Monte Carlo methods are very important in computational physics, physical chemistry, and related applied fields, and have diverse applications from complicated quantum chromodynamics calculations to designing heat shields and aerodynamic forms as well as in modeling radiation transport for radiation dosimetry calculations. In statistical physics Monte Carlo molecular modeling is an alternative to computational molecular dynamics, and Monte Carlo methods are used to compute statistical field theories of simple particle and polymer systems. Quantum Monte Carlo methods solve the many-body problem for quantum systems. In experimental particle physics, Monte Carlo methods are used for designing detectors, understanding their behavior and comparing experimental data to theory. In astrophysics, they are used in such diverse manners as to model both galaxy evolution and microwave radiation transmission through a rough planetary surface. Monte Carlo methods are also used in the ensemble models that form the basis of modern weather forecasting.
蒙特卡罗方法在计算物理、物理化学及相关应用领域中非常重要，从复杂的量子色动力学计算到设计热屏蔽和空气动力学形式，以及在辐射剂量计算中模拟辐射传输等方面都有不同的应用。在统计物理中，蒙特卡罗分子建模是计算分子动力学的替代方法，蒙特卡罗方法用于计算简单粒子和聚合物体系的统计场理论。量子蒙特卡罗方法解决了量子系统的多体问题。在实验粒子物理学中，蒙特卡罗方法用于设计探测器，了解它们的行为，并将实验数据与理论进行比较。在天体物理学中，它们被以不同的方式用于模拟星系演化和微波辐射通过粗糙行星表面的传输。蒙特卡罗方法也用于构成现代天气预报基础的集合模型。
===Engineering===
===Engineering 工程学===
Monte Carlo methods are widely used in engineering for [[sensitivity analysis]] and quantitative [[probabilistic]] analysis in [[Process design (chemical engineering)|process design]]. The need arises from the interactive, co-linear and non-linear behavior of typical process simulations. For example,
Monte Carlo methods are widely used in engineering for [[sensitivity analysis]] and quantitative [[probabilistic]] analysis in [[Process design (chemical engineering)|process design]]. The need arises from the interactive, co-linear and non-linear behavior of typical process simulations. For example,
* In [[microelectronics|microelectronics engineering]], Monte Carlo methods are applied to analyze correlated and uncorrelated variations in [[Analog signal|analog]] and [[Digital data|digital]] [[integrated circuits]].
* In [[microelectronics|microelectronics engineering]], Monte Carlo methods are applied to analyze correlated and uncorrelated variations in [[Analog signal|analog]] and [[Digital data|digital]] [[integrated circuits]].
* 在微电子工程中，蒙特卡罗方法被用于分析模拟和数字集成电路中相关和不相关的变化。
* In [[geostatistics]] and [[geometallurgy]], Monte Carlo methods underpin the design of [[mineral processing]] [[process flow diagram|flowsheets]] and contribute to [[quantitative risk analysis]].<ref name="mbv01">{{Cite book | last1 =Mazhdrakov | first1 =Metodi | last2 =Benov | first2 =Dobriyan |last3=Valkanov|first3=Nikolai | year =2018 | title =The Monte Carlo Method. Engineering Applications | publisher =ACMO Academic Press | volume = | pages = 250| isbn =978-619-90684-3-4 | doi = |url=https://books.google.com/books?id=t0BqDwAAQBAJ&q=the+monte+carlo+method+engineering+applications+mazhdrakov}}</ref>
* In [[geostatistics]] and [[geometallurgy]], Monte Carlo methods underpin the design of [[mineral processing]] [[process flow diagram|flowsheets]] and contribute to [[quantitative risk analysis]].<ref name="mbv01">{{Cite book | last1 =Mazhdrakov | first1 =Metodi | last2 =Benov | first2 =Dobriyan |last3=Valkanov|first3=Nikolai | year =2018 | title =The Monte Carlo Method. Engineering Applications | publisher =ACMO Academic Press | volume = | pages = 250| isbn =978-619-90684-3-4 | doi = |url=https://books.google.com/books?id=t0BqDwAAQBAJ&q=the+monte+carlo+method+engineering+applications+mazhdrakov}}</ref>
* 在地质统计学和地质冶金学中，蒙特卡罗方法是矿物处理流程设计的基础，并有助于定量风险分析。
* In [[wind energy]] yield analysis, the predicted energy output of a wind farm during its lifetime is calculated giving different levels of uncertainty ([[Percentile|P90]], P50, etc.)
* In [[wind energy]] yield analysis, the predicted energy output of a wind farm during its lifetime is calculated giving different levels of uncertainty ([[Percentile|P90]], P50, etc.)
* 在风能产量分析中，考虑不同的不确定性(P90、P50等)，计算风电场在其生命周期内的预测发电量。
* impacts of pollution are simulated<ref name="IntPanis1">{{harvnb|Int Panis|De Nocker|De Vlieger|Torfs|2001}}</ref> and diesel compared with petrol.<ref name="IntPanis2">{{harvnb|Int Panis|Rabl|De Nocker|Torfs|2002}}</ref>
* Impacts of pollution are simulated<ref name="IntPanis1">{{harvnb|Int Panis|De Nocker|De Vlieger|Torfs|2001}}</ref> and diesel compared with petrol.<ref name="IntPanis2">{{harvnb|Int Panis|Rabl|De Nocker|Torfs|2002}}</ref>
* 模拟了污染产生的影响，并将柴油和汽油进行了比较。
* In [[fluid dynamics]], in particular [[gas dynamics|rarefied gas dynamics]], where the Boltzmann equation is solved for finite [[Knudsen number]] fluid flows using the [[direct simulation Monte Carlo]]<ref>G. A. Bird, Molecular Gas Dynamics, Clarendon, Oxford (1976)</ref> method in combination with highly efficient computational algorithms.<ref>{{cite journal | last1 = Dietrich | first1 = S. | last2 = Boyd | first2 = I. | year = 1996 | title = A Scalar optimized parallel implementation of the DSMC technique | url = | journal = Journal of Computational Physics | volume = 126 | issue = 2| pages = 328–42 | doi=10.1006/jcph.1996.0141|bibcode = 1996JCoPh.126..328D }}</ref>
* In [[fluid dynamics]], in particular [[gas dynamics|rarefied gas dynamics]], where the Boltzmann equation is solved for finite [[Knudsen number]] fluid flows using the [[direct simulation Monte Carlo]]<ref>G. A. Bird, Molecular Gas Dynamics, Clarendon, Oxford (1976)</ref> method in combination with highly efficient computational algorithms.<ref>{{cite journal | last1 = Dietrich | first1 = S. | last2 = Boyd | first2 = I. | year = 1996 | title = A Scalar optimized parallel implementation of the DSMC technique | url = | journal = Journal of Computational Physics | volume = 126 | issue = 2| pages = 328–42 | doi=10.1006/jcph.1996.0141|bibcode = 1996JCoPh.126..328D }}</ref>
* 在流体动力学，特别是稀薄气体动力学中，采用直接模拟蒙特卡罗方法结合高效计算算法求解有限克努森数流体的玻尔兹曼方程。
* In [[autonomous robotics]], [[Monte Carlo localization]] can determine the position of a robot. It is often applied to stochastic filters such as the [[Kalman filter]] or [[particle filter]] that forms the heart of the [[Simultaneous localization and mapping|SLAM]] (simultaneous localization and mapping) algorithm.
* In [[autonomous robotics]], [[Monte Carlo localization]] can determine the position of a robot. It is often applied to stochastic filters such as the [[Kalman filter]] or [[particle filter]] that forms the heart of the [[Simultaneous localization and mapping|SLAM]] (simultaneous localization and mapping) algorithm.
* 在自主机器人中，蒙特卡洛定位可以确定机器人的位置。它通常应用于随机滤波器，如卡尔曼滤波器或粒子滤波器，构成同步定位和映射算法的核心。
* In [[telecommunications]], when planning a wireless network, design must be proved to work for a wide variety of scenarios that depend mainly on the number of users, their locations and the services they want to use. Monte Carlo methods are typically used to generate these users and their states. The network performance is then evaluated and, if results are not satisfactory, the network design goes through an optimization process.
* In [[telecommunications]], when planning a wireless network, design must be proved to work for a wide variety of scenarios that depend mainly on the number of users, their locations and the services they want to use. Monte Carlo methods are typically used to generate these users and their states. The network performance is then evaluated and, if results are not satisfactory, the network design goes through an optimization process.
* 在电信行业，在规划无线网络时，必须证明设计适用于各种主要取决于用户数量、他们的位置和他们想使用的服务的场景。蒙特卡罗方法通常用于生成这些用户及其状态。然后对网络性能进行评估，如果结果不令人满意，则进行网络设计优化。
* In [[reliability engineering]], Monte Carlo simulation is used to compute system-level response given the component-level response. For example, for a transportation network subject to an earthquake event, Monte Carlo simulation can be used to assess the ''k''-terminal reliability of the network given the failure probability of its components, e.g. bridges, roadways, etc.<ref>{{cite journal|last1=Nabian|first1=Mohammad Amin|last2=Meidani|first2=Hadi|date=2017-08-28|title=Deep Learning for Accelerated Reliability Analysis of Infrastructure Networks|journal=Computer-Aided Civil and Infrastructure Engineering|volume=33|issue=6|pages=443–458|arxiv=1708.08551|doi=10.1111/mice.12359|bibcode=2017arXiv170808551N|s2cid=36661983}}</ref><ref>{{Cite journal|last1=Nabian|first1=Mohammad Amin|last2=Meidani|first2=Hadi|date=2018|title=Accelerating Stochastic Assessment of Post-Earthquake Transportation Network Connectivity via Machine-Learning-Based Surrogates|url=https://trid.trb.org/view/1496617|journal=Transportation Research Board 97th Annual Meeting|volume=|pages=|via=}}</ref><ref>{{Cite journal|last1=Nabian|first1=Mohammad Amin|last2=Meidani|first2=Hadi|date=2017|title=Uncertainty Quantification and PCA-Based Model Reduction for Parallel Monte Carlo Analysis of Infrastructure System Reliability|url=https://trid.trb.org/view/1439614|journal=Transportation Research Board 96th Annual Meeting|volume=|pages=|via=}}</ref>
* In [[reliability engineering]], Monte Carlo simulation is used to compute system-level response given the component-level response. For example, for a transportation network subject to an earthquake event, Monte Carlo simulation can be used to assess the ''k''-terminal reliability of the network given the failure probability of its components, e.g. bridges, roadways, etc.<ref>{{cite journal|last1=Nabian|first1=Mohammad Amin|last2=Meidani|first2=Hadi|date=2017-08-28|title=Deep Learning for Accelerated Reliability Analysis of Infrastructure Networks|journal=Computer-Aided Civil and Infrastructure Engineering|volume=33|issue=6|pages=443–458|arxiv=1708.08551|doi=10.1111/mice.12359|bibcode=2017arXiv170808551N|s2cid=36661983}}</ref><ref>{{Cite journal|last1=Nabian|first1=Mohammad Amin|last2=Meidani|first2=Hadi|date=2018|title=Accelerating Stochastic Assessment of Post-Earthquake Transportation Network Connectivity via Machine-Learning-Based Surrogates|url=https://trid.trb.org/view/1496617|journal=Transportation Research Board 97th Annual Meeting|volume=|pages=|via=}}</ref><ref>{{Cite journal|last1=Nabian|first1=Mohammad Amin|last2=Meidani|first2=Hadi|date=2017|title=Uncertainty Quantification and PCA-Based Model Reduction for Parallel Monte Carlo Analysis of Infrastructure System Reliability|url=https://trid.trb.org/view/1439614|journal=Transportation Research Board 96th Annual Meeting|volume=|pages=|via=}}</ref>
* 在可靠性工程中，蒙特卡罗仿真被用来计算系统级响应给定的部件级响应。例如，对于一个受地震事件影响的交通网络，蒙特卡洛模拟可以用来评估网络的k终端可靠性，给定其组件，如桥梁、道路等的失效概率。
* In [[signal processing]] and [[Bayesian inference]], [[particle filter]]s and [[Sequential Monte Carlo method|sequential Monte Carlo techniques]] are a class of [[mean field particle methods]] for sampling and computing the posterior distribution of a signal process given some noisy and partial observations using interacting [[empirical measure]]s.
* In [[signal processing]] and [[Bayesian inference]], [[particle filter]]s and [[Sequential Monte Carlo method|sequential Monte Carlo techniques]] are a class of [[mean field particle methods]] for sampling and computing the posterior distribution of a signal process given some noisy and partial observations using interacting [[empirical measure]]s.
* 在信号处理和贝叶斯推断中，粒子滤波器和序列蒙特卡罗技术是一类平均场粒子方法，用于对给定噪声和局部观测的信号过程进行采样和计算后验分布，使用相互作用的经验测度。
* In groundwater modeling, Monte Carlo methods are utilized to generate a large number of realizations of heterogeneous parameter field for model uncertainty quantification or parameter inversion.
* In groundwater modeling, Monte Carlo methods are utilized to generate a large number of realizations of heterogeneous parameter field for model uncertainty quantification or parameter inversion.
* 在地下水模拟中，利用蒙特卡罗方法产生了大量的非均质参数场实现，用于模型不确定性量化或参数反演。
===Climate change and radiative forcing ===
===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===