Metode Monte Carlo: Perbedaan antara revisi
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[[File:Pi 30K.gif|thumb|right| Perhitungan nilai {{pi}} dengan menggunakan metode Monte Carlo.]]
'''Metode Monte Carlo''' adalah [[
<!--They are distinguished from other simulation methods (such as [[molecular dynamics]]) by being [[stochastic]], that is [[nondeterministic]] in some manner - usually by using [[random number]]s (or more often [[pseudo-random number]]s) - as opposed to [[deterministic algorithm]]s. -->
Metode Monte Carlo sangat penting dalam [[fisika komputasi]] dan bidang terapan lainnya, dan memiliki aplikasi yang beragam mulai dari perhitungan [[kromodinamika kuantum]] esoterik hingga perancangan aerodinamika. Metode ini terbukti efisien dalam memecahkan persamaan diferensial integral medan radians, sehingga metode ini digunakan dalam perhitungan [[iluminasi global]] yang menghasilkan gambar-gambar fotorealistik model tiga dimensi, dimana diterapkan dalam [[video games]], [[arsitektur]], [[perancangan]], [[film]] yang dihasilkan oleh komputer, efek-efek khusus dalam film, bisnis, ekonomi, dan bidang lainnya.
<!--Interestingly, the Monte Carlo method does not require truly random numbers to be useful. Much of the most useful techniques use deterministic, pseudo-random sequences, making it easy to test and re-run simulations. The only quality usually necessary to make good [[simulation]]s is for the pseudo-random sequence to appear "random enough" in a certain sense. That is that they must either be [[uniform distribution|uniformly distributed]] or follow another desired distribution when a large enough number of elements of the sequence are considered.-->
Karena
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== Sejarah ==
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Penggunaannya yang cukup dikenal adalah oleh [[Enrico Fermi]] pada tahun [[1930]], ketika ia menggunakan metode acak untuk menghitung sifat-sifat [[neutron]] yang waktu itu baru saja ditemukan. Metode Monte Carlo merupakan simulasi inti yang digunakan dalam [[Manhattan Project]], meski waktu itu masih menggunakan oleh peralatan komputasi yang sangat sederhana. Sejak digunakannya komputer elektronik pada tahun [[1945]], Monte Carlo mulai dipelajari secara mendalam. Pada tahun 1950-an, metode ini digunakan di Laboratorium Nasional [[Los Alamos National Laboratory|Los Alamos]] untuk penelitian awal pengembangan [[bom hidrogen]], dan kemudian sangat populer dalam bidang [[fisika]] dan [[riset operasi]]. ''Rand Corporation]]''an [[Angkatan Udara AS]] merupakan dua institusi utama yang bertanggung jawab dalam pendanaan dan penyebaran informasi mengenai Monte Carlo waktu itu, dan mereka mulai menemukan aplikasinya dalam berbagai bidang.
Penggunaan metode Monte Carlo memerlukan sejumlah besar [[bilangan acak]], dan hal tersebut semakin mudah dengan perkembangan [[pembangkit bilangan pseudoacak]], yang jauh lebih cepat dan praktis dibandingkan dengan metode sebelumnya yang
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== Perhitungan integral ==
Deterministic methods of [[numerical integration]] operate by taking a number of evenly spaced samples from a function. In general, this works very well for functions of one variable. However, for functions of [[vector space|vector]]s, deterministic quadrature methods can be very inefficient. To numerically integrate a function of a two-dimensional vector, equally spaced grid points over a two-dimensional surface are required. For instance a 10x10 grid requires 100 points. If the vector has 100 dimensions, the same spacing on the grid would require 10<sup>100</sup> points – that's far too many to be computed. 100 [[dimension]]s is by no means unreasonable, since in many physical problems, a "dimension" is equivalent to a [[degrees of freedom (physics and chemistry)|degree of freedom]].
Monte Carlo methods provide a way out of this exponential time-increase. As long as the function in question is reasonably [[well-behaved]], it can be estimated by randomly selecting points in 100-dimensional space, and taking some kind of average of the function values at these points. By the [[central limit theorem]], this method will display <math>1/\sqrt{N}</math> convergence – i.e. quadrupling the number of sampled points will halve the error, regardless of the number of dimensions.
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== Inverse Problems and Monte Carlo methods ==
Probabilistic formulation of inverse problems leads to the definition of a probability distribution in the model space. This probability distribution combines a priori information with new information obtained by measuring some observable parameters (data). As, in the general case, the theory linking data with model parameters is nonlinear, the a posteriori probability in the model space may not be easy to describe (it may be multimodal, some moments may not be defined, etc.). 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 a large number of 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. The most well 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. For details, see Mosegaard and Tarantola (1995) [http://www.ipgp.jussieu.fr/~tarantola/Files/Professional/Papers_PDF/MonteCarlo_latex.pdf]
== Other methods ==
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=== Aplikasi metode Monte Carlo ===
* Grafis, terutama untuk ''[[ray tracing]]''
*
* [[Metode Monte Carlo dalam bidang finansial]]
* Simulasi prediksi struktur protein
* Dalam riset peralatan semikonduktor, untuk memodelkan transportasi pembawa arus
* [[Peta genetik|Pemetaan genetik]] yang melibatkan ratusan [[penanda genetik]] dan analisis [[lokus sifat kuantitatif|QTL]]
* Distribusi potensial listrik.<ref>Analisis distribusi potensial listrik dalam koordinat kartesian tiga dimensi dengan metode Monte Carlo, Suyoso & [[Hary Gunarto]], [https://repository.ugm.ac.id/55424/ Thesis S2, Univ. Gadjah Mada,] 1994.</ref>
== Referensi ==
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* Harvey Gould & Jan Tobochnik, ''An Introduction to Computer Simulation Methods, Part 2, Applications to Physical Systems'', [[1988]], ISBN 0-201-16504-X
* C.P. Robert and G. Casella. "Monte Carlo Statistical Methods" (second edition). New York: Springer-Verlag, [[2004]], ISBN 0-387-21239-6
* Pembuat paket komersial yang mengimplementasikan
* Mosegaard, Klaus., and Tarantola, Albert, 1995. Monte Carlo sampling of solutions to inverse problems. J. Geophys. Res., 100, B7, 12431-12447.
* Tarantola, Albert, ''Inverse Problem Theory'' ([http://www.ipgp.jussieu.fr/~tarantola/Files/Professional/SIAM/index.html versi PDF bebas]), Society for Industrial and Applied Mathematics, 2005. ISBN 0-89871-572-5
== Rujukan ==
{{reflist}}
[[Kategori:Analisis numerik]]
[[Kategori:Statistika]]
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