CTmod : Mathematical Foundations (original) (raw)
Another special method to sample probability density functions
Computing, 1979
Another Special Method to Sample Probability Density Functions. A modified rejection technique is proposed, to sample certain probability density functions. The general drawing up of the method and some applications, specific to reactor physical Monte Carlo calculations, are given. In a special case the efficiency of the new method is compared to that of the conventional rejection technique. Eine weitere spezielle Methode flit die Modellierung yon Wahrscheinlichkeitsdichtefunktionen. Eine modifizierte Rejektionstechnik zur Modellierung einiger Wahrscheinlichkeitsdichten wird vorgeschlagen. Die Grundztige der Methode sowie einige Anwendungen sind mit spezieller Rticksicht auf die Monte Carlo Rechnungen der Reaktorphysik angegeben. In einem Spezialfalle wird die Wirkungsffihigkeit der neuen Methode mit der der konventionellen Rejektionstechnik vergliehen.
A special method to sample some probability density functions
Computing, 1978
A Special Method to Sample Some Probability Density Functions. A special method is described to sample some probability density functions by help of their first derivatives. Two general theorems and some special applications, giving practical sampling procedures, are presented along with a number of illustrative examples. Eine spezielle Methode zur Modellierung einiger Wahrscheinlichkeitsdichtefunktionen. Eine spezielle Methode fiir Modellierung einiger Wahrscheinlichkeitsdichtefunktionen mittels ihren ersten Ableitungen zu nehmen, wird beschrieben. Zwei allgemeine Theoreme und einige spezielle Anwendungen, die praktische Verfahren geben, werden zusammen mit einer Reihe von verdeutlichenden Beispielen gegeben.
Random sampling from the generalized gamma distribution
Computing, 1979
Random Sampling from the Generalized Gamma Distribution. This paper presents a simple and easy to implement algorithm for sampling from the generalized four parameter gamma distribution proposed by Stacy. The proposed method is based on a generalization of Von Neumann's rejection method where the first stage sampling is done from the log logistic distribution. The proposed method is simple, easy to implement and faster than the traditional methods for generating generalized gamma variates.
Communications in Statistics - Simulation and Computation, 1994
Theoretical considerations and empirical results show that the one-dimensional quality of non-uniform random numbers is bad and the discrepancy is high when they are generated by the ratio of uniforms method combined with linear congruential generators. This observation motivates the suggestion to replace the ratio of uniforms method by transformed rejection (also called exact approximation or almost exact inversion), as the above problem does not occur for this method. Using the function G(x) = a 1?x + b x with appropriate a and b as approximation of the inverse distribution function the transformed rejection method can be used for the same distributions as the ratio of uniforms method. The resulting algorithms for the normal, the exponential and the t-distribution are short and easy to implement. Looking at the number of uniform deviates required, at the code length and at the speed the suggested algorithms are superior to the ratio of uniforms method and compare well with other algorithms suggested in literature.
A Review on the Exact Monte Carlo Simulation
Bayesian Inference [Working Title]
Perfect Monte Carlo sampling refers to sampling random realizations exactly from the target distributions (without any statistical error). Although many different methods have been developed and various applications have been implemented in the area of perfect Monte Carlo sampling, it is mostly referred by researchers to coupling from the past (CFTP) which can correct the statistical errors for the Monte Carlo samples generated by Markov chain Monte Carlo (MCMC) algorithms. This paper provides a brief review on the recent developments and applications in CFTP and other perfect Monte Carlo sampling methods.
An Introduction to Monte Carlo Methods
American Journal of Physics, 1974
These lectures given to graduate students in high energy physics, provide an introduction to Monte Carlo methods. After an overview of classical numerical quadrature rules, Monte Carlo integration together with variance-reducing techniques is introduced. A short description on the generation of pseudo-random numbers and quasi-random numbers is given. Finally, methods to generate samples according to a specified distribution are discussed. Among others, we outline the Metropolis algorithm and give an overview of existing algorithms for the generation of the phase space of final state particles in high energy collisions.
IEEE Transactions on Nuclear Science, 2000
In this paper, we propose a hybrid approach to simulate multiple scattering of photons in objects under X-ray inspection, without recourse to parallel computing and without any approximation sacrificing accuracy. Photon scattering is considered from two points of view: it contributes to X-ray imaging and to the dose absorbed by the patient. The proposed hybrid approach consists of a Monte Carlo stage followed by a deterministic phase, thus taking advantage of the complementarity between these two methods. In the first stage, a set of scattering events occurring in the inspected object is determined by means of classical Monte Carlo simulation. Then this set of scattering events is used to compute the energy imparted to the detector, with a deterministic algorithm based on a "forced detection" scheme. As regards dose evaluation, we propose to assess separately the energy deposited by direct radiation (using a deterministic algorithm) and by scattered radiation (using our hybrid approach). The results obtained in a test case are compared to those obtained with the Monte Carlo method alone (Geant4 code) and found to be in excellent agreement. The proposed hybrid approach makes it possible to simulate the contribution of each type (Compton or Rayleigh) and order of scattering, separately or together, with a single PC, within reasonable computation times (from minutes to hours, depending on the required detector resolution and statistics). It is possible to simulate radiographic images virtually free from photon noise. In the case of dose evaluation, the hybrid approach appears particularly suitable to calculate the dose absorbed by regions of interest (rather than the entire irradiated organ) with computation time and statistical fluctuations considerably reduced in comparison with conventional Monte Carlo simulation.
Discretization of Probability Distributions: Random, Deterministic and Randomistic Sampling
ForsChem Research Reports, 2019
Sampling procedures are commonly used to extract a finite number of elements from a particular probability distribution. This discretization of the probability distribution is usually performed using pseudo-random number generators. This type of discretization, known as random sampling, requires suitable functions for transforming standard uniform random numbers into random numbers following any arbitrary probability distribution. While random sampling resembles the natural behavior of experimentation, individual samples do not necessarily preserve all the properties of the original probability distribution. Those properties include the cumulative probability and the moments of the distribution. The match between the cumulative probability observed in a sample and that of the original distribution can be determined using the random goodness-of-fit criterion. Random samples seldom achieve a 100% fit to the original distribution. Deterministic sampling methods, on the other hand, always present a 100% random goodness-of-fit, but their values are always the same, depending on the size of the sample. One particular case of deterministic sampling is optimal sampling, which ensure goodness-of-fit but also allows preserving the moments of the original distribution. Finally, randomistic sampling combines the fitness of deterministic sampling with the changing behavior of random samples, resulting in an interesting alternative for representing random variables, particularly in applications involving Monte Carlo methods, where the sample is expected to represent the properties of the full distribution.