The Monte Carlo Method
Abstract
We shall present here the motivation and a general description of a method dealing with a class of problems in mathematical physics. The method is, essentially, a statistical approach to the study of differential equations, or more generally, of integro-differential equations that occur in various branches of the natural sciences.
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Frequently, the study of thermodynamical properties and observables, such as adsorption isotherms, Henry constants, heats of adsorption, is carried out via Monte Carlo simulations, which are based on statistical mechanics.
“Frequently, the study of thermodynamical properties and observables, such as adsorption isotherms, Henry constants, heats of adsorption, is carried out via Monte Carlo simulations, which are based on statistical mechanics.344−346”
From Zeolites in Adsorption Processes: State of the Art and Future Prospects (2022) · cites this paper as [344]
Because bootstrapping of standard errors of indirect effects was not possible with Lavaan, 95% confidence intervals for indirect effects in the multiple imputed datasets were estimated using the Monte Carlo sampling method.
“Because bootstrapping of standard errors of the indirect effects was not possible with Lavaan, con fi dence intervals (95%) for indirect effects in the multiple imputed datasets were estimated using the Monte Carlo sampling method (Metropolis & Ulam, 1949).”
From Mindfulness, Self-compassion, and Psychological Wellbeing as Correlates of Paternal Bonding in Pregnancy. (2025) · cites this paper as Metropolis & Ulam, 1949
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- Authors
- Metropolis, N., & Ulam, S.
- Affiliations
- Los Alamos National Laboratory (US)
- Venue
- Journal of the American Statistical Association
- Publisher
- Informa UK Limited
- Published
- 1949-09
- Volume
- 44
- Issue
- 247
- Pages
- 335-341
- ISSN
- 0162-1459 (ISSN-L)
- 1537-274X
- OpenAlex
- W2051203581
- Cited by
- 6,474
- References
- 0
- Citations by year
- 2026: 368 · 2025: 419 · 2024: 327 · 2023: 345 · 2022: 333 · 2021: 343 · 2020: 318 · 2019: 304 · 2018: 270 · 2017: 252 · 2016: 258 · 2015: 249 · 2014: 254 · 2013: 283 · 2012: 262
- FWCI
- 8.97
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Journal of the American Statistical Association (publishedVersion)
- PubMed (publishedVersion)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Markov Chains and Monte Carlo Methods
- Physical Sciences › Mathematics › Numerical Analysis › Mathematical Approximation and Integration
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Theoretical and Computational Physics
- Keywords
- Monte Carlo methods, integro-differential equations, mathematical physics, numerical solution of partial differential equations
- MeSH terms
- Biometry, Humans, Monte Carlo Method, Statistics as Topic
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