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Topic · Statistics and Probability

Markov Chains and Monte Carlo Methods

Markov Chains and Monte Carlo Methods is a research topic within Statistics and Probability. Science Explorer counts 12k research works in it since 1950. 20.7% of them reached the world's top 10% most cited for their field and year.

This cluster of papers focuses on the application of Bayesian Monte Carlo methods, such as Markov Chain Monte Carlo (MCMC), Approximate Bayesian Computation, and Hamiltonian Monte Carlo, in scientific inference for inverse problems, model selection, and statistical estimation. It also explores adaptive MCMC algorithms and stochastic gradient Langevin dynamics for efficient parameter inference and approximation algorithms.

  • Bayesian Monte Carlo
  • Markov Chain
  • Approximate Bayesian Computation
  • Adaptive MCMC
  • Hamiltonian Monte Carlo
  • Stochastic Gradient Langevin Dynamics
  • Inverse Problems
  • Model Selection
  • Statistical Inference
  • Approximation Algorithms
Research works
12k
fractional, since 1950
In the world top 10%
2.4k
per year above
Top-10% rate
20.7%
share of its works in the world top 10%
Growth, 2013–17 → 2018–22
+1%
the tick is no change

Which countries lead Markov Chains and Monte Carlo Methods research?

By volume, the United States and France publish the most (462 and 200 works in 2022–2025).

By volume, 2022–2025

  1. 1 United States 462 works
  2. 2 France 200 works
  3. 3 China 149 works
  4. 4 United Kingdom 145 works
  5. 5 Germany 117 works
  6. 6 Italy 65 works
  7. 7 Japan 58 works
  8. 8 Canada 53 works
  9. 9 Russia 39 works
  10. 10 India 37 works

How concentrated that is

The same countries as shares of everything the list above accounts for. A node where two countries do two thirds of the work and one spread evenly across twelve read alike as a ranking and not at all alike here.

United States: 34.9%France: 15.1%China: 11.2%United Kingdom: 10.9%6 others listed: 27.8%35%largest
United States462 · 34.9%France200 · 15.1%China149 · 11.2%United Kingdom145 · 10.9%6 others listed368 · 27.8%

Shares of the rows listed above, not of the whole node.

Which institutions lead Markov Chains and Monte Carlo Methods research?

By volume in 2022–2025, Centre National de la Recherche Scientifique publishes the most Markov Chains and Monte Carlo Methods research, followed by University of Warwick and Stanford University.

By volume, 2022–2025

  1. 1 Centre National de la Recherche ScientifiqueFrance 26 works
  2. 2 University of WarwickUnited Kingdom 17 works
  3. 3 Stanford UniversityUnited States 16 works
  4. 4 University of CambridgeUnited Kingdom 14 works
  5. 5 Columbia UniversityUnited States 13 works
  6. 6 Georgia Institute of TechnologyUnited States 13 works
  7. 7 University of California, BerkeleyUnited States 12 works
  8. 8 Massachusetts Institute of TechnologyUnited States 11 works
  9. 9 University of Wisconsin–MadisonUnited States 11 works
  10. 10 University of OxfordUnited Kingdom 11 works

Who are the leading researchers in Markov Chains and Monte Carlo Methods?

The most-cited researchers publishing on Markov Chains and Monte Carlo Methods include Stanley Osher and Sayan Mukherjee.

  1. 1 Stanley Osher United States 8k citations
  2. 2 Sayan Mukherjee United States 5.7k citations

Ranked by citations received across their whole record, among researchers with at least three works on this topic.

Where is Markov Chains and Monte Carlo Methods research done?

The largest centres of Markov Chains and Monte Carlo Methods research in 2022–2025 are Paris (France), Beijing (China), New York (United States) and London (United Kingdom).

Largest cities, 2022–2025

  1. 1 Paris France 80 works
  2. 2 Beijing China 41 works
  3. 3 New York United States 34 works
  4. 4 London United Kingdom 32 works
  5. 5 Tokyo Japan 30 works
  6. 6 Moscow Russia 22 works
  7. 7 Cambridge United States 19 works
  8. 8 Rome Italy 18 works
  9. 9 Shanghai China 18 works
  10. 10 Coventry United Kingdom 18 works
See Markov Chains and Monte Carlo Methods on the map

Where is the best place to study Markov Chains and Monte Carlo Methods?

Among universities, judged by research, Massachusetts Institute of Technology, ETH Zurich and University of Warwick score highest, combining excellence, specialisation, size, growth and international reach. Research strength is one signal when choosing where to study; it does not measure teaching.

0%20%40%mean 26.05%fractional works in this node (log) →share in the world top 10% →Massachusetts Institute of Technology: 11, 39.2%ETH Zurich: 10, 34.5%University of Warwick: 17, 18.3%Columbia University: 13, 27.7%Stanford University: 16, 25.0%Sorbonne Université: 10, 18.7%Georgia Institute of Technology: 13, 24.5%University of Cambridge: 14, 21.1%University of Edinburgh: 9, 21.6%Imperial College London: 9, 29.9%Massachusetts Instit…ETH ZurichColumbia UniversityUniversity of Warwick
above the meannear itbelow it

One dot per university in the table below. The upper left is the interesting corner: small places doing unusually strong work.

#UniversityScoreTop 10%SpecialisationWorksGrowth
1 Massachusetts Institute of TechnologyUnited States 70.039.2%11.1×11 +25.3%
2 ETH ZurichSwitzerland 66.034.5%9.1×10 +40.8%
3 University of WarwickUnited Kingdom 57.218.3%23.1×17 +3.8%
4 Columbia UniversityUnited States 56.227.7%9.8×13 -11.7%
5 Stanford UniversityUnited States 55.725.0%8.4×16 +25.4%
6 Sorbonne UniversitéFrance 54.918.7%12.9×10 +41.5%
7 Georgia Institute of TechnologyUnited States 50.424.5%12.4×13 -32.4%
8 University of CambridgeUnited Kingdom 50.021.1%7.9×14 +11.8%
9 University of EdinburghUnited Kingdom 49.721.6%7.3×9 +115.6%
10 Imperial College LondonUnited Kingdom 46.529.9%6.4×9 +16.1%

Universities only. Score blends excellence (30%), specialisation (25%), size (20%), growth (15%) and international reach (10%), 2015–2022; growth compares 2010–14 with 2015–19.

Is Markov Chains and Monte Carlo Methods research growing?

Output in 2018–2022 was 1% higher than in 2013–2017, peaking in 2023. The fastest-growing topics are Markov Chains and Monte Carlo Methods.

19801990200020102020
grewheldshrank

The same series as a ribbon — one cell per year, darker for more. The line above answers how much; this answers when.

Which topics inside it are moving

Growth and decline on one axis around a shared zero. Two lists side by side hide the thing that matters: whether the growth dwarfs the decline, or the other way round.