CTmod : Mathematical Foundations (original) (raw)
Related papers
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.
2017
β α 1 +α 2 +α 3 Γ(α 1)Γ(α 2)Γ(α 3). (10.5) Note 10.2. Since the joint probability/density function at the observed sample point is defined as the likelihood function, once the point is substituted then the function
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.
Monte Carlo Methods and Applications
Monte Carlo Methods and appliCations is a quarterly published journal presenting original articles on the theory and applications of Monte Carlo and quasi-Monte Carlo methods. Launched in 1995 the journal covers all stochastic numerics topics with emphasis on the theory of Monte Carlo methods and new applications in all branches of science and technology. The following topics will be covered: theory of Monte Carlo methods, quasi-Monte Carlo methods, integration, boundary value problems for PDE's, numerics of stochastic differential equations, simulation of random variables, stochastic processes and fields, and stochastic models in all fields of applied sciences. All information regarding notes for contributors, subscriptions, Open access, back volumes and orders is available online at www.degruyter.com/mcma.