Introduction to Scientific Programming and Simulation Using R

Jones, Owen; Maillardet, Robert; Robinson, Andrew

doi:10.1201/b17079

Cited by 16 publications

(6 citation statements)

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“…The golden‐section method is used as the line search algorithm in the AEM and QN2 algorithms. The R code of the method is provided in Jones et al (2009).…”

Section: Numerical Experimentsmentioning

confidence: 99%

Acceleration of the EM algorithm

Kuroda

Geng

2023

WIREs Computational Stats

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The expectation–maximization (EM) algorithm is a well‐known iterative algorithm for finding maximum likelihood estimates from incomplete data and is used in several statistical models with latent variables and missing data. The algorithm also exhibits a monotonic increase in a likelihood function and satisfies parameter constraints for its convergence. The popularity of the EM algorithm can be attributed to its stable convergence, simple implementation and flexibility in interpreting data incompleteness. Despite these computational advantages, the algorithm is linear convergent and suffers from very slow convergence when a statistical model has many parameters and a high proportion of missing data. Various algorithms have been proposed to accelerate the convergence of the EM algorithm. We introduce the acceleration of the EM algorithm using root‐finding and vector extrapolation algorithms. The root‐finding algorithms include Aitken's method and the Newton–Raphson, quasi‐Newton and conjugate gradient algorithms. These algorithms with faster convergence rates allow the EM algorithm to be sped up. The vector extrapolation algorithms transform the sequence of estimates from the EM algorithm into a fast convergent sequence and can accelerate the convergence without modifying the EM algorithm. We describe the derivation of these acceleration algorithms and attempt to apply them to two examples.This article is categorized under: Statistical and Graphical Methods of Data Analysis > EM Algorithm

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“…The golden‐section method is used as the line search algorithm in the AEM and QN2 algorithms. The R code of the method is provided in Jones et al (2009).…”

Section: Numerical Experimentsmentioning

confidence: 99%

Acceleration of the EM algorithm

Kuroda

Geng

2023

WIREs Computational Stats

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“…R is an object oriented functional programming language, convenient for high-level scientific programming, data analysis as well as modelling. For computationally cumbersome tasks, languages like C, C++, Python and Fortran could be linked and called up as required [21,22,23].…”

Section: Model Description and Developmentmentioning

confidence: 99%

Prediction of Hole Expansion Ratio of Titanium Alloys Using R Programming

Kwame¹,

Yakushina

Blackwell

2020

J. Model. Optim.

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The hole expansion ratio (HER) is an important material property which defines the extent of edge formability of sheet metals. The stress states observed at the hole edge after the hole expansion test are similar to those seen during traditional uniaxial tensile deformation. This observation has provoked research, directed at ascertaining a correlation between the HER and tensile properties. In order to account for the forming behaviour of complex materials like titanium, a highly robust model that takes into account the material formability in all sheet-processing directions must be considered. The R programming language was used in this research to build a model fitting expression capable of predicting the HER as well as generating a regression model equation for titanium alloys, based on their thickness and Erichsen index number. The proposed regression model equation for predicting HER of titanium alloys exhibited an excellent statistical significance (p= 0.00076), indicating the robustness of the model fitting expression to predict HER values of titanium alloys. An accompanying adjusted R squared value of 0.9987 for the generated regression model equation also shows how well the regression line fits the data for accurate prediction of the HER of titanium alloys. A numerical validation analysis of the strength of the relationship derived between the predicted and the experimental HERs gave a correlation coefficient of 0.9884. This result shows a strong linear relationship between the experimental and predicted HER values of the titanium alloys with an average absolute error of 8.8%.

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“…Furthermore, the choice of the 𝑑 value is ambiguous. Some popular stochastic simulation books do not present an explicit criterion to determine the sample size in MC simulations, but limit themselves to proposing the use of the CLT and confidence intervals to evaluate the convergence of the estimators, with little emphasis on the details [1], [14].…”

Section: Introductionmentioning

confidence: 99%

Criterio para determinar el tamaño de muestra en procesos de simulación estocástica

Molina-Muñoz

Christen

2022

IyU

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Objetivo: Proponer un criterio para determinar el tamaño de muestra en simulaciones estocásticas de MC (Monte Carlo) y MCMC (Markov chain Monte Carlo), garantizando una determinada precisión en la estimación de parámetros. Se busca que la precisión se garantice de forma adimensional. Materiales y métodos: El presente artículo propone un criterio buscando cumplir con el objetivo planteado. Además, de una metodología para la aplicación del mismo. Resultados y discusión: Se presenta la aplicación de la metodología en 3 contextos diferentes: Simulación de MC en que la muestra de interés presenta variabilidad moderada, simulación de MC en que la muestra de interés presenta variabilidad excesiva y simulación de MCMC. En todos los casos se obtienen adecuadas estimaciones del número de corridas MC y MCMC a partir de muestras relativamente pequeñas. Además, la aplicación de la metodología representa únicamente un costo computacional adicional marginal. Conclusiones: El criterio presentado en este artículo permite determinar el tamaño de muestra en simulaciones estocásticas, garantizando precisión adimensional en la estimación de parámetros.

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Introduction to Scientific Programming and Simulation Using R

Cited by 16 publications

References 0 publications

Acceleration of the EM algorithm

Acceleration of the EM algorithm

Prediction of Hole Expansion Ratio of Titanium Alloys Using R Programming

Criterio para determinar el tamaño de muestra en procesos de simulación estocástica

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