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The theory of more sophisticated mean-field type particle Monte Carlo methods had certainly started by the mid-1960s, with the work of [[Henry McKean|Henry P. McKean Jr.]] on Markov interpretations of a class of nonlinear parabolic partial differential equations arising in fluid mechanics.<ref name="mck67">{{cite journal |author-last=McKean |author-first=Henry P. |title=Propagation of chaos for a class of non-linear parabolic equations |journal=Lecture Series in Differential Equations, Catholic Univ. |year=1967 |volume=7 |pages=41–57 }}</ref><ref>{{cite journal |author-last1=McKean |author-first1=Henry P. |title=A class of Markov processes associated with nonlinear parabolic equations |journal = Proc. Natl. Acad. Sci. USA |year=1966 |volume=56 |issue=6 |pages=1907–1911 |doi=10.1073/pnas.56.6.1907 |pmid=16591437 |pmc=220210 |bibcode=1966PNAS...56.1907M |doi-access=free }}</ref> We also quote an earlier pioneering article by [[Ted Harris (mathematician)|Theodore E. Harris]] and Herman Kahn, published in 1951, using mean-field [[genetic algorithm|genetic]]-type Monte Carlo methods for estimating particle transmission energies.<ref>{{cite journal |author-last1=Herman |author-first1=Kahn |author-last2=Theodore |author-first2=Harris E. |title=Estimation of particle transmission by random sampling |journal=Natl. Bur. Stand. Appl. Math. Ser. |year=1951 |volume=12 |pages=27–30 |url=https://dornsifecms.usc.edu/assets/sites/520/docs/kahnharris.pdf }}</ref> Mean-field genetic type Monte Carlo methodologies are also used as heuristic natural search algorithms (a.k.a. [[metaheuristic]]) in evolutionary computing. The origins of these mean-field computational techniques can be traced to 1950 and 1954 with the work of [[Alan Turing]] on genetic type mutation-selection learning machines<ref>{{cite journal |author-last=Turing |author-first=Alan M. |title=Computing machinery and intelligence |journal=Mind |volume=LIX |issue=238 |pages=433–460 |doi=10.1093/mind/LIX.236.433 |year=1950 }}</ref> and the articles by [[Nils Aall Barricelli]] at the [[Institute for Advanced Study]] in [[Princeton, New Jersey]].<ref>{{cite journal |author-last=Barricelli |author-first=Nils Aall |year=1954 |author-link=Nils Aall Barricelli |title=Esempi numerici di processi di evoluzione |journal=Methodos |pages=45–68 }}</ref><ref>{{cite journal |author-last=Barricelli |author-first=Nils Aall |year=1957 |author-link=Nils Aall Barricelli |title=Symbiogenetic evolution processes realized by artificial methods |journal=Methodos |pages=143–182 }}</ref>
[[Quantum Monte Carlo]], and more specifically [[Diffusion Monte Carlo|diffusion Monte Carlo methods]] can also be interpreted as a mean-field particle Monte Carlo approximation of [[Richard Feynman|Feynman]]–[[Mark Kac|Kac]] path integrals.<ref name="dp04">{{cite book |author-last=Del Moral |author-first=Pierre |title=Feynman–Kac formulae. Genealogical and interacting particle approximations |year=2004 |publisher=Springer |quote=Series: Probability and Applications |url=https://www.springer.com/mathematics/probability/book/978-0-387-20268-6 |page=575 |isbn=9780387202686 |series=Probability and Its Applications}}</ref><ref name="dmm002">{{cite book |author-last1=Del Moral |author-first1=P. |author-last2=Miclo |author-first2=L. |contribution=Branching and interacting particle systems approximations of Feynman–Kac formulae with applications to non-linear filtering |contribution-url=http://archive.numdam.org/item/SPS_2000__34__1_0 |doi=10.1007/BFb0103798 |mr=1768060 |pages=1–145 |publisher=Springer |location=Berlin |series=Lecture Notes in Mathematics |title=Séminaire de Probabilités, XXXIV |volume=1729 |year=2000 |isbn=978-3-540-67314-9 |url=http://www.numdam.org/item/SPS_2000__34__1_0/}}</ref><ref name="dmm00m">{{cite journal|author-last1=Del Moral |author-first1=Pierre |author-last2=Miclo |author-first2=Laurent |title=A Moran particle system approximation of Feynman–Kac formulae. |journal=Stochastic Processes and Their Applications |year=2000 |volume=86 |issue=2 |pages=193–216 |doi=10.1016/S0304-4149(99)00094-0 |doi-access=free}}</ref><ref name="dm-esaim03">{{cite journal|author-last1=Del Moral |author-first1=Pierre |title=Particle approximations of Lyapunov exponents connected to Schrödinger operators and Feynman–Kac semigroups |journal=ESAIM Probability & Statistics |date=2003 |volume=7 |pages=171–208 |url=http://journals.cambridge.org/download.php?file=%2FPSS%2FPSS7%2FS1292810003000016a.pdf&code=a0dbaa7ffca871126dc05fe2f918880a |doi=10.1051/ps:2003001 |doi-access=free}}</ref><ref name="caffarel1">{{cite journal|author-last1=Assaraf |author-first1=Roland |author-last2=Caffarel |author-first2=Michel |author-last3=Khelif |author-first3=Anatole |title=Diffusion Monte Carlo Methods with a fixed number of walkers |journal=Phys. Rev. E |url=http://qmcchem.ups-tlse.fr/files/caffarel/31.pdf |date=2000 |volume=61 |issue=4 |pages=4566–4575 |doi=10.1103/physreve.61.4566 |pmid=11088257 |bibcode=2000PhRvE..61.4566A |url-status=dead |archive-url=https://web.archive.org/web/20141107015724/http://qmcchem.ups-tlse.fr/files/caffarel/31.pdf |archive-date=7 November 2014 }}</ref><ref name="caffarel2">{{cite journal|author-last1=Caffarel |author-first1=Michel |author-last2=Ceperley |author-first2=David |author-last3=Kalos |author-first3=Malvin |title=Comment on Feynman–Kac Path-Integral Calculation of the Ground-State Energies of Atoms |journal=Phys. Rev. Lett. |date=1993 |volume=71 |issue=13 |doi=10.1103/physrevlett.71.2159 |bibcode=1993PhRvL..71.2159C |pages=2159 |pmid=10054598}}</ref><ref name="h84">{{cite journal |author-last=Hetherington |author-first=Jack H. |title=Observations on the statistical iteration of matrices |journal=Phys. Rev. A |date=1984 |volume=30 |issue=2713 |doi=10.1103/PhysRevA.30.2713 |pages=2713–2719 |bibcode=1984PhRvA..30.2713H}}</ref> The origins of Quantum Monte Carlo methods are often attributed to Enrico Fermi and [[Robert D. Richtmyer|Robert Richtmyer]] who developed in 1948 a mean-field particle interpretation of neutron-chain reactions,<ref>{{cite journal|author-last1=Fermi |author-first1=Enrique |author-last2=Richtmyer |author-first2=Robert D. |title = Note on census-taking in Monte Carlo calculations |journal=LAM |date=1948 |volume=805 |issue=A |url=http://scienze-como.uninsubria.it/bressanini/montecarlo-history/fermi-1948.pdf |quote=Declassified report Los Alamos Archive}}</ref> but the first heuristic-like and genetic type particle algorithm (a.k.a. Resampled or Reconfiguration Monte Carlo methods) for estimating ground state energies of quantum systems (in reduced matrix models) is due to Jack H. Hetherington in 1984<ref name="h84" /> In molecular chemistry, the use of genetic heuristic-like particle methodologies (a.k.a. pruning and enrichment strategies) can be traced back to 1955 with the seminal work of [[Marshall Rosenbluth|Marshall N. Rosenbluth]] and [[Arianna W. Rosenbluth]].<ref name=":0">{{cite journal |author-last1 = Rosenbluth|author-first1=Marshall N. |author-last2=Rosenbluth |author-first2=Arianna W. |title=Monte-Carlo calculations of the average extension of macromolecular chains |journal=J. Chem. Phys. |date=1955 |volume=23 |issue=2 |pages=356–359 |bibcode=1955JChPh..23..356R |doi=10.1063/1.1741967 |s2cid=89611599 |url=https://semanticscholar.org/paper/1570c85ba9aca1cb413ada31e215e0917c3ccba7|doi-access=free }}</ref>
The use of [[Sequential Monte Carlo method|Sequential Monte Carlo]] in advanced [[signal processing]] and [[Bayesian inference]] is more recent. It was in 1993, that Gordon et al., published in their seminal work<ref>{{cite journal|title=Novel approach to nonlinear/non-Gaussian Bayesian state estimation |journal=IEE Proceedings F - Radar and Signal Processing |date=April 1993 |issn=0956-375X |pages=107–113 |volume=140 |issue=2 |author-first1=N.J. |author-last1=Gordon |author-first2=D.J. |author-last2=Salmond |author-first3 = A.F.M. |author-last3=Smith |doi=10.1049/ip-f-2.1993.0015 |s2cid=12644877 |url=https://semanticscholar.org/paper/65484334a5cd4cabf6e5f7a17f606f07e2acf625}}</ref> the first application of a Monte Carlo [[Resampling (statistics)|resampling]] algorithm in Bayesian statistical inference. The authors named their algorithm 'the bootstrap filter', and demonstrated that compared to other filtering methods, their bootstrap algorithm does not require any assumption about that state-space or the noise of the system. We also quote another pioneering article in this field of Genshiro Kitagawa on a related "Monte Carlo filter",<ref>{{cite journal
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