book

Simulation for Data Science with R

Name: Simulation for Data Science with R
Author: Matthias Templ
ISBN: 9781785881169

by Matthias Templ

June 2016

Beginner to intermediate

398 pages

8h 51m

English

Packt Publishing

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Simulation for Data Science with R
Table of Contents
Simulation for Data Science with R
Credits
About the Author
About the Reviewer
www.PacktPub.com
eBooks, discount offers, and moreWhy subscribe?
Preface
What this book covers
What you need for this book
Who this book is for

Conventions
Reader feedback
Customer support
Downloading the example codeDownloading the color images of this bookErrataPiracyQuestions
1. Introduction
What is simulation and where is it applied?
Why use simulation?
Simulation and big data
Choosing the right simulation technique
Summary
References
2. R and High-Performance Computing
The R statistical environmentBasics in RSome very basic stuff about RInstallation and updatesHelpThe R workspace and the working directoryData typesVectors in RFactors in Rlistdata.framearrayMissing values
Generic functions, methods, and classes
Data manipulation in R
Apply and friends with basic RBasic data manipulation with the dplyr packagedplyr – creating a local data framedplyr – selecting linesdplyr – orderdplyr – selecting columnsdplyr – uniquenessdplyr – creating variablesdplyr – grouping and aggregatesdplyr – window functionsData manipulation with the data.table packagedata.table – variable constructiondata.table – indexing or subsettingdata.table – keysdata.table – fast subsettingdata.table – calculations in groups
High performance computing
Profiling to detect computationally slow functions in codeFurther benchmarkingParallel computingInterfaces to C++
Visualizing information
The graphics system in RThe graphics packageWarm-up example – a high-level plotControl of graphics parametersThe ggplot2 package
References
3. The Discrepancy between Pencil-Driven Theory and Data-Driven Computational Solutions
Machine numbers and rounding problemsExample – the 64-bit representation of numbersConvergence in the deterministic caseExample – convergence
Condition of problems
Summary
References
4. Simulation of Random Numbers
Real random numbers
Simulating pseudo random numbers
Congruential generatorsLinear and multiplicative congruential generatorsLagged Fibonacci generatorsMore generators
Simulation of non-uniform distributed random variables
The inversion methodThe alias methodEstimation of counts in tables with log-linear modelsRejection samplingSimulating values from a normal distributionSimulating random numbers from a Beta distributionTruncated distributionsMetropolis - Hastings algorithmA few words on Markov chainsThe Metropolis samplerThe Gibbs samplerThe two-phase Gibbs samplerThe multiphase Gibbs samplerApplication in linear regressionThe diagnosis of MCMC samples
Tests for random numbers
The evaluation of random numbers – an example of a test
Summary
References
5. Monte Carlo Methods for Optimization Problems
Numerical optimizationGradient ascent/descentNewton-Raphson methodsFurther general-purpose optimization methods
Dealing with stochastic optimization
Simplified procedures (Star Trek, Spaceballs, and Spaceballs princess)Metropolis-Hastings revisitedGradient-based stochastic optimization
Summary
References
6. Probability Theory Shown by Simulation
Some basics on probability theory
Probability distributions
Discrete probability distributionsContinuous probability distributions
Winning the lottery
The weak law on large numbers
Emperor penguins and your bossLimits and convergence of random variablesConvergence of the sample mean – weak law of large numbersShowing the weak law of large numbers by simulation
The central limit theorem
Properties of estimators
Properties of estimatorsConfidence intervalsA note on robust estimators
Summary
References
7. Resampling Methods
The bootstrapA motivating example with odds ratiosWhy the bootstrap worksA closer look at the bootstrapThe plug-in principle
Estimation of standard errors with bootstrapping
An example of a complex estimation using the bootstrap
The parametric bootstrap
Estimating bias with bootstrap
Confidence intervals by bootstrap
The jackknife
Disadvantages of the jackknifeThe delete-d jackknifeJackknife after bootstrap
Cross-validation
The classical linear regression modelThe basic concept of cross validationClassical cross validation – 70/30 methodLeave-one-out cross validationk-fold cross validation
Summary
References
8. Applications of Resampling Methods and Monte Carlo Tests
The bootstrap in regression analysisMotivation to use the bootstrapThe most popular but often worst methodBootstrapping by draws from residuals
Proper variance estimation with missing values
Bootstrapping in time series
Bootstrapping in the case of complex sampling designs
Monte Carlo tests
A motivating exampleThe permutation test as a special kind of MC testA Monte Carlo test for multiple groupsHypothesis testing using a bootstrapA test for multivariate normalitySize of the testPower comparisons
Summary
References
9. The EM Algorithm
The basic EM algorithmSome prerequisitesFormal definition of the EM algorithmIntroductory example for the EM algorithm
The EM algorithm by example of k-means clustering
The EM algorithm for the imputation of missing values
Summary
References
10. Simulation with Complex Data
Different kinds of simulation and software
Simulating data using complex models
A model-based simple exampleA model-based example with mixturesModel-based approach to simulate dataAn example of simulating high-dimensional dataSimulating finite populations with cluster or hierarchical structures
Model-based simulation studies
Latent model example continuedA simple example of model-based simulationA model-based simulation study
Design-based simulation
An example with complex survey dataSimulation of the synthetic populationEstimators of interestDefining the sampling designUsing stratified samplingAdding contaminationPerforming simulations separately on different domains
Inserting missing values
Summary
References
11. System Dynamics and Agent-Based Models
Agent-based models
Dynamics in love and hate
Dynamic systems in ecological modeling
Summary
References
Index

Content preview from Simulation for Data Science with R

Cross-validation

Cross-validation is a resampling method as well, similar to the jackknife. However, the aim is now not to make inference statistics but to estimate prediction errors.

Cross-validation is mainly used for the comparison of methods or to find the optimal values of parameters in an estimation model.

In the following section, we will explain cross-validation based on regression analysis. For readers who have never heard of regression analysis, we recommend to read a basic textbook about regression analysis. We only point out some very basic issues.

The classical linear regression model

The classical linear regression model in its simplest case with one response and one predictor is given by with . In matrix notation, this is

, with the ...

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Simulation for Data Science with R

by Matthias Templ

Cross-validation

The classical linear regression model

Become an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
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