Geodesic
Investigation and reduction of variance of a weighted estimate in numerical statistical simulation
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 46 (2006) no. 8, pp. 1519-1536

Voir la notice de l'article provenant de la source Math-Net.Ru

The efficiency of the “value” and “partial value” modeling related to the construction of a modeling distribution for an auxiliary random variable by multiplying the initial density by a value function is investigated. The value function usually corresponds to a solution of the adjoint equation. Conditions under which the value modeling of the initial distribution reduces the variance compared to the direct simulation are obtained. It is proved that the variance of the weighted estimate is bounded in the case of the partial value modeling. This proposition provides a basis for a method for determining whether or not the variance of the weighted estimate is bounded. This method uses the majorizing adjoint equation. Using a practically important problem in transport theory as an example, the asymptotic optimization of the distribution of the mean free path is presented. The application of the proposed method of the investigation of the variance boundedness for the analysis of the classical exponential transformation method of simulating the mean free path of a particle in the one-dimensional and the spherical variants is discussed. 
@article{ZVMMF_2006_46_8_a12,
     author = {I. N. Medvedev and G. A. Mikhailov},
     title = {Investigation and reduction of variance of a~weighted estimate in numerical statistical simulation},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1519--1536},
     publisher = {mathdoc},
     volume = {46},
     number = {8},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_8_a12/}
}
TY  - JOUR
AU  - I. N. Medvedev
AU  - G. A. Mikhailov
TI  - Investigation and reduction of variance of a weighted estimate in numerical statistical simulation
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2006
SP  - 1519
EP  - 1536
VL  - 46
IS  - 8
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_8_a12/
LA  - ru
ID  - ZVMMF_2006_46_8_a12
ER  - 
%0 Journal Article
%A I. N. Medvedev
%A G. A. Mikhailov
%T Investigation and reduction of variance of a weighted estimate in numerical statistical simulation
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2006
%P 1519-1536
%V 46
%N 8
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_8_a12/
%G ru
%F ZVMMF_2006_46_8_a12
I. N. Medvedev; G. A. Mikhailov. Investigation and reduction of variance of a weighted estimate in numerical statistical simulation. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 46 (2006) no. 8, pp. 1519-1536. http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_8_a12/