Monte Carlo and Quasi-Monte Carlo Methods.

Caflisch, R. E. (1998). Monte Carlo and Quasi-Monte Carlo Methods. Acta Numerica, 7, 1-49.

Type

Journal article

Intellectual base

Primary research

Year

1998

Volume

7

Pages

1-49

DOI

10.1017/s0962492900002804

DOI registrant

Cambridge University Press

Link

https://doi.org/10.1017/S0962492900002804

Cited from

data_science

Cited by

2 citations across 2 artifacts.

Each citation links to the sentence it supports in the citing article.

Primes

• Curse Of Dimensionality
  • In numerical analysis, deterministic quadrature scales exponentially in dimension, which is precisely why Monte Carlo and quasi-Monte Carlo methods exist.

    This sourceExplains the exponential cost of deterministic quadrature in dimension and why Monte Carlo and quasi-Monte Carlo methods escape it.

    Supported in partVerified against the work's full text

    Supplies Monte Carlo's dimension-independent O(N^-1/2) convergence rate and quasi-Monte Carlo as a deterministic alternative; it says nothing about Bellman, dynamic programming, or mitigation families.

    “Its convergence rate, O ( N −1/2 ), is independent of dimension, which shows Monte Carlo to be very robust but also slow. ... Accelerated convergence for Monte Carlo quadrature is attained using quasi-random (also called low-discrepancy) sequences, which are a deterministic alternative to random or pseudo-random sequences.”

    Read by an automated reader; not a human review. How support was checked

Domain-specific

• Monte Carlo integration
  • Monte Carlo integration rewrites an integral as an expectation under a chosen sampling distribution and estimates it with a sample average, often using importance, stratified, or quasi-random variants.

Verification

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