Monte Carlo sampling

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1: 8.24 Physical Applications

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§8.24(ii) Incomplete Beta Functions

►The function $I_x(a,b)$ appears in: Monte Carlo sampling in statistical mechanics (Kofke (2004)); analysis of packings of soft or granular objects (Prellberg and Owczarek (1995)); growth formulas in cosmology (Hamilton (2001)). …

2: 35.10 Methods of Computation

… ►See Yan (1992) for the ${}_1{}^{}F_1^{}$ and ${}_2{}^{}F_1^{}$ functions of matrix argument in the case $m=2$, and Bingham et al. (1992) for Monte Carlo simulation on $𝐎(m)$ applied to a generalization of the integral (35.5.8). …

3: 27.19 Methods of Computation: Factorization

… ►Type I probabilistic algorithms include the Brent–Pollard rho algorithm (also called Monte Carlo method), the Pollard $p-1$ algorithm, and the Elliptic Curve Method (ecm). …

4: 3.5 Quadrature

§3.5 Quadrature

… ►For integrals in higher dimensions, Monte Carlo methods are another—often the only—alternative. The standard Monte Carlo method samples points uniformly from the integration region to estimate the integral and its error. In more advanced methods points are sampled from a probability distribution, so that they are concentrated in regions that make the largest contribution to the integral. With $N$ function values, the Monte Carlo method aims at an error of order $1/\sqrt{N}$, independently of the dimension of the domain of integration. …

5: Bibliography I

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Statistical Field Theory: Strong Coupling, Monte Carlo Methods, Conformal Field Theory, and Random Systems. Vol. 2, Cambridge University Press, Cambridge.

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External Links:

ISBN 0-521-37012-4; 0-521-40806-7, MathReview (C. A. Hurst), ZentralBlatt

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2nd item.

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6: 12.16 Mathematical Applications

… ►Integral transforms and sampling expansions are considered in Jerri (1982).

7: Bibliography S

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Adaptive Quasi-Monte Carlo Integration Based on MISER and VEGAS. In Monte Carlo and Quasi-Monte Carlo Methods 2002, pp. 393–406.

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External Links:

MathReview Entry, ZentralBlatt

Referenced by:

§3.5(x).

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BibTeX

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8: DLMF Project News

error generating summary

9: Guide to Searching the DLMF

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Table 3: A sample of recognized symbols

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Symbols	Comments
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10: Bibliography J

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Distributions of matrix variates and latent roots derived from normal samples. Ann. Math. Statist. 35 (2), pp. 475–501.

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External Links:

FullText, MathReview (I. Olkin), ZentralBlatt

Referenced by:

§35.11, §35.4(i), §35.4(ii), §35.8(i), §35.8(ii), §35.8(iv), §35.9, Ch.35.

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BibTeX

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A note on sampling expansion for a transform with parabolic cylinder kernel. Inform. Sci. 26 (2), pp. 155–158.

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External Links:

ISSN 0020-0255, Document, MathReview, ZentralBlatt

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§12.16.

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BibTeX

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