Simulation for Data Science with R电子书

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

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Why 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 code

Downloading the color images of this book

Errata

Piracy

Questions

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 environment

Basics in R

Some very basic stuff about R

Installation and updates

Help

The R workspace and the working directory

Data types

Vectors in R

Factors in R

list

data.frame

array

Missing values

Generic functions, methods, and classes

Data manipulation in R

Apply and friends with basic R

Basic data manipulation with the dplyr package

dplyr – creating a local data frame

dplyr – selecting lines

dplyr – order

dplyr – selecting columns

dplyr – uniqueness

dplyr – creating variables

dplyr – grouping and aggregates

dplyr – window functions

Data manipulation with the data.table package

data.table – variable construction

data.table – indexing or subsetting

data.table – keys

data.table – fast subsetting

data.table – calculations in groups

High performance computing

Profiling to detect computationally slow functions in code

Further benchmarking

Parallel computing

Interfaces to C++

Visualizing information

The graphics system in R

The graphics package

Warm-up example – a high-level plot

Control of graphics parameters

The ggplot2 package

References

3. The Discrepancy between Pencil-Driven Theory and Data-Driven Computational Solutions

Machine numbers and rounding problems

Example – the 64-bit representation of numbers

Convergence in the deterministic case

Example – convergence

Condition of problems

Summary

References

4. Simulation of Random Numbers

Real random numbers

Simulating pseudo random numbers

Congruential generators

Linear and multiplicative congruential generators

Lagged Fibonacci generators

More generators

Simulation of non-uniform distributed random variables

The inversion method

The alias method

Estimation of counts in tables with log-linear models

Rejection sampling

Simulating values from a normal distribution

Simulating random numbers from a Beta distribution

Truncated distributions

Metropolis - Hastings algorithm

A few words on Markov chains

The Metropolis sampler

The Gibbs sampler

The two-phase Gibbs sampler

The multiphase Gibbs sampler

Application in linear regression

The 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 optimization

Gradient ascent/descent

Newton-Raphson methods

Further general-purpose optimization methods

Dealing with stochastic optimization

Simplified procedures (Star Trek, Spaceballs, and Spaceballs princess)

Metropolis-Hastings revisited

Gradient-based stochastic optimization

Summary

References

6. Probability Theory Shown by Simulation

Some basics on probability theory

Probability distributions

Discrete probability distributions

Continuous probability distributions

Winning the lottery

The weak law on large numbers

Emperor penguins and your boss

Limits and convergence of random variables

Convergence of the sample mean – weak law of large numbers

Showing the weak law of large numbers by simulation

The central limit theorem

Properties of estimators

Properties of estimators

Confidence intervals

A note on robust estimators

Summary

References

7. Resampling Methods

The bootstrap

A motivating example with odds ratios

Why the bootstrap works

A closer look at the bootstrap

The 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 jackknife

The delete-d jackknife

Jackknife after bootstrap

Cross-validation

The classical linear regression model

The basic concept of cross validation

Classical cross validation – 70/30 method

Leave-one-out cross validation

k-fold cross validation

Summary

References

8. Applications of Resampling Methods and Monte Carlo Tests

The bootstrap in regression analysis

Motivation to use the bootstrap

The most popular but often worst method

Bootstrapping 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 example

The permutation test as a special kind of MC test

A Monte Carlo test for multiple groups

Hypothesis testing using a bootstrap

A test for multivariate normality

Size of the test

Power comparisons

Summary

References

9. The EM Algorithm

The basic EM algorithm

Some prerequisites

Formal definition of the EM algorithm

Introductory 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 example

A model-based example with mixtures

Model-based approach to simulate data

An example of simulating high-dimensional data

Simulating finite populations with cluster or hierarchical structures

Model-based simulation studies

Latent model example continued

A simple example of model-based simulation

A model-based simulation study

Design-based simulation

An example with complex survey data

Simulation of the synthetic population

Estimators of interest

Defining the sampling design

Using stratified sampling

Adding contamination

Performing 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