Monte Carlo Statistical Methods¶
Robert, C. P., & Casella, G. (2004). Monte Carlo Statistical Methods. Springer.
Cited by¶
4 citations across 4 artifacts.
Each citation links to the sentence it supports in the citing article.
Primes¶
- Law of Large Numbers
- Monte Carlo and randomized algorithms. Estimating an integral, a rare-event probability, or a posterior expectation by averaging simulated draws works because the law applies to the average of the simulated integrand, and the standard error falls as σ/√n regardless of how many dimensions the domain has.
This sourceGrounds Monte Carlo integration in the law of large numbers, with the error of the simulated average falling as sigma over root n irrespective of the dimension of the domain.
- Monte Carlo and randomized algorithms. Estimating an integral, a rare-event probability, or a posterior expectation by averaging simulated draws works because the law applies to the average of the simulated integrand, and the standard error falls as σ/√n regardless of how many dimensions the domain has.
- Monte Carlo Simulation
- By the late 1990s, MCMC had become the dominant tool for Bayesian inference across statistics, physics, epidemiology, and machine learning
This sourceRobert-Casella foundational monograph MCMC theory and practice.
Supported in partVerified against the publisher's abstract
The book's own abstract supports only that MCMC methods are an essential part of statisticians' standard toolkit, not that MCMC had become the dominant tool for Bayesian inference by the late 1990s across four disciplines.
“Monte Carlo statistical methods, particularly those based on Markov chains, are now an essential component of the standard set of techniques used by statisticians.”
- By the late 1990s, MCMC had become the dominant tool for Bayesian inference across statistics, physics, epidemiology, and machine learning
Mechanisms¶
- Monte Carlo Simulation Method
- Its strength is generality and honesty: given any forward model and defensible input distributions, it returns an unbiased picture of the output distribution, and its error is quantifiable and shrinks predictably by the law of large numbers
This sourceDerives basic Monte Carlo approximation from the law of large numbers.
- Its strength is generality and honesty: given any forward model and defensible input distributions, it returns an unbiased picture of the output distribution, and its error is quantifiable and shrinks predictably by the law of large numbers
- Simulation Rollout Evaluation
- Its value is precisely in exposing what an expected-value formula hides — the shape of the distribution
This sourceUses Monte Carlo simulation to characterize a target distribution beyond a single expected value.
- Its value is precisely in exposing what an expected-value formula hides — the shape of the distribution
Verification¶
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