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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 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.

蒙特卡罗模拟通常需要拥有属性许多未知参数，其中许多参数很难通过实验获得。蒙特卡罗模拟方法并不总是要求真正的随机数是有用的(尽管，对于素数测试等一些应用，不可预测性是至关重要的)。许多最有用的技术使用确定性，伪随机序列，使它很容易测试和重新运行模拟。伪随机序列在某种意义上表现出足够的“足够随机” ，这是进行良好模拟所必需的唯一品质。

蒙特卡罗模拟的典型特征是有许多未知参数，其中许多参数很难通过实验获得。蒙特卡罗模拟方法并不总是要求真正的随机数是有用的(尽管对于一些应用程序，如质数测试，不可预测性是至关重要的)。许多最有用的技术使用确定性的伪随机序列，使测试和重新运行模拟变得很容易。伪随机序列在某种意义上表现地“足够随机”，这是进行良好模拟所必需的唯一品质。

From 1950 to 1996, all the publications on Sequential Monte Carlo methodologies, including the pruning and resample Monte Carlo methods introduced in computational physics and molecular chemistry, present natural and heuristic-like algorithms applied to different situations without a single proof of their consistency, nor a discussion on the bias of the estimates and on genealogical and ancestral tree based algorithms. The mathematical foundations and the first rigorous analysis of these particle algorithms were written by Pierre Del Moral in 1996.<ref name="dm9622"/><ref name=":22">{{cite journal|last1 = Del Moral|first1 = Pierre|title = Measure Valued Processes and Interacting Particle Systems. Application to Non Linear Filtering Problems|journal = Annals of Applied Probability|date = 1998|edition = Publications du Laboratoire de Statistique et Probabilités, 96-15 (1996)|volume = 8|issue = 2|pages = 438–495|url = http://projecteuclid.org/download/pdf_1/euclid.aoap/1028903535|doi = 10.1214/aoap/1028903535|citeseerx = 10.1.1.55.5257}}</ref>

From 1950 to 1996, all the publications on Sequential Monte Carlo methodologies, including the pruning and resample Monte Carlo methods introduced in computational physics and molecular chemistry, present natural and heuristic-like algorithms applied to different situations without a single proof of their consistency, nor a discussion on the bias of the estimates and on genealogical and ancestral tree based algorithms. The mathematical foundations and the first rigorous analysis of these particle algorithms were written by Pierre Del Moral in 1996.<ref name="dm9622"/><ref name=":22">{{cite journal|last1 = Del Moral|first1 = Pierre|title = Measure Valued Processes and Interacting Particle Systems. Application to Non Linear Filtering Problems|journal = Annals of Applied Probability|date = 1998|edition = Publications du Laboratoire de Statistique et Probabilités, 96-15 (1996)|volume = 8|issue = 2|pages = 438–495|url = http://projecteuclid.org/download/pdf_1/euclid.aoap/1028903535|doi = 10.1214/aoap/1028903535|citeseerx = 10.1.1.55.5257}}</ref>

 

What this means depends on the application, but typically they should pass a series of statistical tests. Testing that the numbers are uniformly distributed or follow another desired distribution when a large enough number of elements of the sequence are considered is one of the simplest and most common ones. Weak correlations between successive samples are also often desirable/necessary.

What this means depends on the application, but typically they should pass a series of statistical tests. Testing that the numbers are uniformly distributed or follow another desired distribution when a large enough number of elements of the sequence are considered is one of the simplest and most common ones. Weak correlations between successive samples are also often desirable/necessary.

Branching type particle methodologies with varying population sizes were also developed in the end of the 1990s by Dan Crisan, Jessica Gaines and Terry Lyons,<ref name=":42">{{cite journal|last1 = Crisan|first1 = Dan|last2 = Gaines|first2 = Jessica|last3 = Lyons|first3 = Terry|title = Convergence of a branching particle method to the solution of the Zakai|journal = SIAM Journal on Applied Mathematics|date = 1998|volume = 58|issue = 5|pages = 1568–1590|doi = 10.1137/s0036139996307371|s2cid = 39982562|url = https://semanticscholar.org/paper/99e8759a243cd0568b0f32cbace2ad0525b16bb6}}</ref><ref>{{cite journal|last1 = Crisan|first1 = Dan|last2 = Lyons|first2 = Terry|title = Nonlinear filtering and measure-valued processes|journal = Probability Theory and Related Fields|date = 1997|volume = 109|issue = 2|pages = 217–244|doi = 10.1007/s004400050131|s2cid = 119809371}}</ref><ref>{{cite journal|last1 = Crisan|first1 = Dan|last2 = Lyons|first2 = Terry|title = A particle approximation of the solution of the Kushner–Stratonovitch equation|journal = Probability Theory and Related Fields|date = 1999|volume = 115|issue = 4|pages = 549–578|doi = 10.1007/s004400050249|s2cid = 117725141}}</ref> and by Dan Crisan, Pierre Del Moral and Terry Lyons.<ref name=":52">{{cite journal|last1 = Crisan|first1 = Dan|last2 = Del Moral|first2 = Pierre|last3 = Lyons|first3 = Terry|title = Discrete filtering using branching and interacting particle systems|journal = Markov Processes and Related Fields|date = 1999|volume = 5|issue = 3|pages = 293–318|url = http://web.maths.unsw.edu.au/~peterdel-moral/crisan98discrete.pdf}}</ref> Further developments in this field were developed in 2000 by P. Del Moral, A. Guionnet and L. Miclo.<ref name="dmm002"/><ref name="dg99">{{cite journal|last1 = Del Moral|first1 = Pierre|last2 = Guionnet|first2 = Alice|title = On the stability of Measure Valued Processes with Applications to filtering|journal = C. R. Acad. Sci. Paris|date = 1999|volume = 39|issue = 1|pages = 429–434}}</ref><ref name="dg01">{{cite journal|last1 = Del Moral|first1 = Pierre|last2 = Guionnet|first2 = Alice|title = On the stability of interacting processes with applications to filtering and genetic algorithms|journal = Annales de l'Institut Henri Poincaré|date = 2001|volume = 37|issue = 2|pages = 155–194|url = http://web.maths.unsw.edu.au/~peterdel-moral/ihp.ps|doi = 10.1016/s0246-0203(00)01064-5|bibcode=2001AnIHP..37..155D}}</ref>

Branching type particle methodologies with varying population sizes were also developed in the end of the 1990s by Dan Crisan, Jessica Gaines and Terry Lyons,<ref name=":42">{{cite journal|last1 = Crisan|first1 = Dan|last2 = Gaines|first2 = Jessica|last3 = Lyons|first3 = Terry|title = Convergence of a branching particle method to the solution of the Zakai|journal = SIAM Journal on Applied Mathematics|date = 1998|volume = 58|issue = 5|pages = 1568–1590|doi = 10.1137/s0036139996307371|s2cid = 39982562|url = https://semanticscholar.org/paper/99e8759a243cd0568b0f32cbace2ad0525b16bb6}}</ref><ref>{{cite journal|last1 = Crisan|first1 = Dan|last2 = Lyons|first2 = Terry|title = Nonlinear filtering and measure-valued processes|journal = Probability Theory and Related Fields|date = 1997|volume = 109|issue = 2|pages = 217–244|doi = 10.1007/s004400050131|s2cid = 119809371}}</ref><ref>{{cite journal|last1 = Crisan|first1 = Dan|last2 = Lyons|first2 = Terry|title = A particle approximation of the solution of the Kushner–Stratonovitch equation|journal = Probability Theory and Related Fields|date = 1999|volume = 115|issue = 4|pages = 549–578|doi = 10.1007/s004400050249|s2cid = 117725141}}</ref> and by Dan Crisan, Pierre Del Moral and Terry Lyons.<ref name=":52">{{cite journal|last1 = Crisan|first1 = Dan|last2 = Del Moral|first2 = Pierre|last3 = Lyons|first3 = Terry|title = Discrete filtering using branching and interacting particle systems|journal = Markov Processes and Related Fields|date = 1999|volume = 5|issue = 3|pages = 293–318|url = http://web.maths.unsw.edu.au/~peterdel-moral/crisan98discrete.pdf}}</ref> Further developments in this field were developed in 2000 by P. Del Moral, A. Guionnet and L. Miclo.<ref name="dmm002"/><ref name="dg99">{{cite journal|last1 = Del Moral|first1 = Pierre|last2 = Guionnet|first2 = Alice|title = On the stability of Measure Valued Processes with Applications to filtering|journal = C. R. Acad. Sci. Paris|date = 1999|volume = 39|issue = 1|pages = 429–434}}</ref><ref name="dg01">{{cite journal|last1 = Del Moral|first1 = Pierre|last2 = Guionnet|first2 = Alice|title = On the stability of interacting processes with applications to filtering and genetic algorithms|journal = Annales de l'Institut Henri Poincaré|date = 2001|volume = 37|issue = 2|pages = 155–194|url = http://web.maths.unsw.edu.au/~peterdel-moral/ihp.ps|doi = 10.1016/s0246-0203(00)01064-5|bibcode=2001AnIHP..37..155D}}</ref>

萨维罗斯基列出了高质量蒙特卡罗模拟的特点:

萨维罗斯基列出了高质量蒙特卡罗模拟的特点:

==Definitions==

==Definitions==