Sampling from a Discrete Distribution While Preserving Monotonicity

Fishman, George S.; Moore, Louis R.

doi:10.1080/00031305.1984.10483208

Cited by 19 publications

(9 citation statements)

References 11 publications

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“…The resulting CDF is therefore reflective of the shaped beam, and sampling from this shaped beam distribution eliminates the inefficient step of tracking particles through the secondary collimators. As a result of the large number of discrete fluence values in the CDF an efficient sampling algorithm, the cut-point method, 19,20 is used for generating a random sample from the discrete distribution. Once the source particle's position has been chosen, the particle's energy is sampled from the cumulative bremsstrahlung distribution of the nearest ring or point detector.…”

Section: Beam Characterization and Reconstruction Of The Phase Spacementioning

confidence: 99%

A virtual source model for Monte Carlo modeling of arbitrary intensity distributions

2000

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A photon virtual source model was developed for simulating arbitrary, external beam, intensity distributions using the Monte Carlo method. The source model consists of a photon fluence grid composed of a matrix of square elements, located 25-cm downstream from the linear accelerator target. Each particle originating from the fluence map is characterized by the seven phase space parameters, position (x, y, z), direction (u, v, w), and energy. The map was reconstructed from fluence and energy spectra acquired by modeling components of the linear accelerator treatment head using the Monte Carlo code MCNP4B. The effect of contaminant electrons is accounted for by the use of a sub-source derived from a phase-space simulation of a 25-MV linac treatment head using the code BEAM. The BEAM sub-source was incorporated into the MCNP4B phase-space model and is sampled using a field-size dependent sampling ratio. A Gaussian blurring kernel is convolved with the photon fluence map to account for the finite focal spot size and scattering effects from structures such as the flattening filter and MLC leaves. Depth dose and profile source calculations for 6-MV and 25-MV photon beams, for 5 x 5 cm2, 10 x 10 cm2, and 15 x 15 cm2 field sizes, are in good agreement with measurement and are well within acceptability criteria suggested by the AAPM Task Group Report No. 53. Irregular field calculations compared with film measurement and with a 3-D pencil beam algorithm show that the source model is capable of accurately simulating arbitrary MLC fields.

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Section: Beam Characterization and Reconstruction Of The Phase Spacementioning

confidence: 99%

A virtual source model for Monte Carlo modeling of arbitrary intensity distributions

2000

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“…One is the time to sample a capacity state B U) = b {l) from [P{b); b 6 fi) and the other is the time to determine A(6 (() ) and thereby <t>(b 0) . Both the alias method (Walker [14]) and the cutpoint method (Fishman and Moore [4]) allow this sampling in O(n) time. Once the capacity state b (l) is given, A(b u) ) can be determined via a maximal flow algorithm.…”

Section: Monte Carlo Methodsmentioning

confidence: 99%

Evaluating Reliability of Stochastic Flow Networks

Fishman

Shaw

1989

Prob. Eng. Inf. Sci.

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This paper describes a highly efficient Monte Carlo sampling plan for evaluating the probability that the flow value in a stochastic flow network is greater than or equal to a prespecified level d. A stochastic flow network can characterize communication, transportation, and water or oil distribution systems. The paper first derives lower and upper bounds on the probability of interest and then describes how one can concentrate sampling in a specialized region of the arc capacity state space to increase the statistical efficiency of the resulting estimate. The paper also gives expressions for worst-case sample sizes needed to meet specified bounds on variances and coefficients of variation and illustrates the proposed sampling plan with an example.

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“…The overall time and space both are 0(n) . By a dynamic version of the guide table method (see [3] or [13], for the raw guide table method}, D (lag n ) expected space is achievable provided that we can update the guide table in 0(1) amortized time . This is easy to achieve if we take care to rebuild the table every log nth (or mth) entry .…”

Section: 2mentioning

confidence: 99%

On the Generation of Random Binary Search Trees

Devroye¹,

Robson²

1995

SIAM J. Comput.

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We consider the computer generation of random binary search trees with n nodes for the standard random permutation model. The algorithms discussed here output the number of external nodes at each level, but not the shape of the tree. This is important, for example, when one wishes to simulate the height of the binary search tree. Various paradigms are proposed, including depth-first search with pruning, incremental methods in which the tree grows with random-sized jumps, and a tree growing procedure gleaned from birth-and-death processes. The last method takes O (logo n) expected time .

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Sampling from a Discrete Distribution While Preserving Monotonicity

Cited by 19 publications

References 11 publications

A virtual source model for Monte Carlo modeling of arbitrary intensity distributions

A virtual source model for Monte Carlo modeling of arbitrary intensity distributions

Evaluating Reliability of Stochastic Flow Networks

On the Generation of Random Binary Search Trees

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