Geodesic
Variance reduction techniques for estimation of integrals over a set of branching trajectories
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 54 (2014) no. 2, pp. 183-194 Cet article a éte moissonné depuis la source Math-Net.Ru

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Monte Carlo variance reduction techniques within the supertrack approach are justified as applied to estimating non-Boltzmann tallies equal to the mean of a random variable defined on the set of all branching trajectories. For this purpose, a probability space is constructed on the set of all branching trajectories, and the unbiasedness of this method is proved by averaging over all trajectories. Variance reduction techniques, such as importance sampling, splitting, and Russian roulette, are discussed. A method is described for extending available codes based on the von Neumann-Ulam scheme in order to cover the supertrack approach. 
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E. A. Tsvetkov. Variance reduction techniques for estimation of integrals over a set of branching trajectories. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 54 (2014) no. 2, pp. 183-194. http://geodesic.mathdoc.fr/item/ZVMMF_2014_54_2_a1/

[1] Booth T., “Monte Carlo variance reucation approaches for non-Boltzmann tallies”, Nuclear Sci. and Engng., 116 (1994), 113–124

[2] Valentine T., MCNP-DSP users manual, Tech. Rep. ORNL/TM-13334, Oak Ridge Nat. Lab., 1997

[3] Mori T., Okumura K., Magaya Y., “Development of the MVP Monte Carlo code at JAERI”, Trabs. of the ANS, 84 (2001), 45–46

[4] Ficaro E., KENO-NR: A Monte Carlo simulating the $^{252}\mathrm{Cf}$-source-driven noise analysis experimental method for determining subcriticality, Ph. D. thesis, University of Michigan, 1991

[5] Ermakov S. M., Mikhailov G. A., Statisticheskoe modelirovanie, Nauka, M., 1982 | MR

[6] Ermakov S. M., Metod Monte-Karlo i smezhnye voprosy, Nauka, M., 1975 | MR | Zbl

[7] Marchuk G. I., Mikhailov G. A., Nazarliev M. A. i dr., Metod Monte-Karlo v atmosfernoi optike, ed. G. I. Marchuk, Nauka, Novosibirsk, 1976 | Zbl

[8] Mikhailov G. A., Optimizatsiya vesovykh metodov Monte-Karlo, Nauka, M., 1987 | MR

[9] Sobol I. M., Chislennye metody Monte-Karlo, Nauka, M., 1973 | MR

[10] Uchaikin V. V., Lagutin A. A., Stokhasticheskaya tsennost, Energoatomizdat, M., 1993 | MR

[11] Lappa A. V., Burmistrov D. S., “Novye fluktuatsionnye vesovye metody Monte-Karlo i ikh primenenie k kaskadnym protsessam perenosa chastits sverkhvysokikh energii”, Matem. modelirovanie, 7:5 (1995), 100–114

[12] Lappa A. V., “Vesovaya otsenka metoda Monte-Karlo dlya rascheta vysshikh momentov additivnykh kharakteristik perenosa chastits s razmnozheniem”, Zh. vychisl. matem. i matem. fiz., 30:1 (1990), 122–134 | MR

[13] Borisov N. M., Panin M. P., “Adjoint Monte Carlo calculations for pulse-height-spectrum”, Monte Carlo Methods and Applications, 4:3 (1998), 273–284 | DOI | MR | Zbl

[14] Borisov N. M., Primenenie sopryazhennykh metodov Monte-Karlo v zadachakh perenosa fotonov s uchetom vtorichnogo izlucheniya, Diss. ... kand. fiz-matem. nauk, MIFI, M., 1999

[15] Booth T., Pulse height tally variance reduction in MCNP5, Tech. Rep. LA-13995, Los Alamos Nat. Lab., 1994

[16] Hendricks J., McKinney G. W., “Pulse height tallies with variance reduction”, Proc. of Monte Carlo 2005 (Chattanooga, Tennesse, USA, April 17–21, 2005)

[17] Shuttleworth E., “The pulse height distribution tally in MCBEND”, Proc. of International Conference on Radiation Schielding ICRS'9 (Tsukuba, Japan, 17–22 October, 1999)

[18] Szieberth M., Kloosterman J., “New methods for the Monte Carlo simulation of neutron noise experiments”, Proc. of Seventh Information Exchange Meeting on Actinide and Fission Product Partitioning and transmutation (Jeju, Korea, October 14–16, 2002)

[19] Nekrutkin V. V., “Vychislenie integralov po prostranstvu derevev metodom Monte-Karlo”, Metody Monte-Karlo v vychislitelnoi matematike i matematicheskoi fizike, VTs SO AN SSSR, 1974, 94–102

[20] Ermakov S. M., Nekrutkin V. V., Sipin A. S., Sluchainye protsessy dlya resheniya klassicheskikh uravnenii matematicheskoi fiziki, Nauka, M., 1984 | MR

[21] Dynkin E. B., Osnovaniya teorii markovskikh protsessov, Fizmatgiz, M., 1959 | MR

[22] Kharris T., Teoriya vetvyaschikhsya sluchainykh protsessov, Mir, M., 1966

[23] J. Briesmeister (ed.), MCNP. A general Monte Carlo $N$-particle transport code. Version 4C, Manual LA-13709-M, Los Alamos Nat. Lab., 2000

[24] Tsvetkov E. A., Shakhovskii V. V., “Obosnovanie DXTRAN-modifikatsii metoda Monte-Karlo na osnove sootnoshenii vzaimnosti dlya razlichayuschikhsya sistem”, Trudy MFTI, 1:2 (2009), 207–215 | MR