Journal ArticleDOI
Bernstein Polynomials and Monte Carlo Integration
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TLDR
Two variance reducing techniques, control variates and importance sampling, are described in this paper, which are used in increasing the efficiency of a Monte Carlo evaluation of an integral, are shown under very general conditions that the Bernstein polynomials can serve as both a control variate and an importance sampling function.Abstract:
Two variance reducing techniques, the method of control variates and the method of importance sampling, which are used in increasing the efficiency of a Monte Carlo evaluation of an integral, are described. It is shown under very general conditions that the Bernstein polynomials can serve as both a control variate and an importance sampling function. In addition these methods can also be combined to further increase the efficiency of the Monte Carlo evaluation. An example is given to illustrate the method.read more
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Journal ArticleDOI
Numerical Evaluation of Multiple Integrals
TL;DR: A survey of the main methods for numerical evaluation of multiple integrals can be found in this article, where the Monte Carlo method and its generalizations are discussed, as well as number-theoretical methods, based essentially on the ideas of Diophantine approximation and equidistribution modulo 1; functional analysis approach, in which the quadrature error is regarded as a linear functional and one attempts to minimize its norm.
Journal ArticleDOI
Towards built-in capture–recapture mixed models in program E-SURGE
Rémi Choquet,Olivier Gimenez +1 more
TL;DR: It is shown that a frequentist approach using numerical integration can be tractable when independent clusters of individuals can be identified and the maximum likelihood approach is time-efficient because the dimension of the integral for the likelihood is small.
Journal ArticleDOI
Bernstein-type approximation using the beta-binomial distribution
TL;DR: In this article, both univariate and multivariate Bernstein-type approximations are studied, and the uniform convergence and degree of approximation are studied. And the Bernsteintype estimators of smooth functions of population means are also proposed and studied.
On the method of Ermakov and Zolotukhin for multiple integration
R. Cranley,T. N. L. Patterson +1 more
TL;DR: In this article, a practical assessment of the Ermakov and Zolotukhin method is made and the performance of the method is found to be unimpressive in comparison with a recent regression method.