## Preface

"Everybody seems to think I'm lazy

I don't mind, I think they're crazy

Running everywhere at such a speed

Till they find there's no need (There's no need)"

The Beatles in their song "I'm only sleeping"

The Monte Carlo way and simulation approach are ways to stay lazy and efficient at the same time. "Lazy", since a simulation approach is generally much easier to carry out as compared to an analytical approach—there is mostly no need for analytical approaches, and one might be crazy to neglect the whole world of statistical simulation. "Efficient", since it costs minimal efforts to get reliable results, and often simulation is the only approach to get results. The simulation approach in data science and statistics is generally a more intuitive approach compared to analytical solutions. It is not hidden behind a wall of mathematics, and using a simulation approach is often the only way to solve complex problems.

Statistical simulation has thus become an essential area in data science and statistics. It can be seen as a data-driven approach to many practical problems in data science and statistics.

In this book, theory is also explained with illustrative examples using the software environment R, for which advanced data processing features are shown in the book.

This book will thus provide a computational and methodological framework for statistical simulation to users with a computational statistics and/or data science background.

More precisely, the aim of this book is to lay into the hands of the readers a book that explains methods, give advice on the usage of the methods, and provide computational tools to solve common problems in statistical simulation and computer-intense methods.

The core issues are on simulating distributions and datasets, Monte Carlo methods for inference statistics, microsimulation and dynamical systems, and presenting solutions using computer-intense approaches. You will see applications in R not only to better understand the methods but also to gain experience when working on real-world data and real-world problems.

The author of the book has tried to make humorous and amusing examples in certain chapters in order to increase interest, staying catchy and memorable. Next to serious text on methods, curious examples on individual mortality and fertility rates of the author of the book are also present as is the system dynamics from the love/hate story of Prince Henry and Chelsy Davy, the Australian guy in the Austrian mountain trying to reach the highest mountain through an optimization problem, or the weak law of winning the lottery are presented as well.

## What this book covers

Chapter 1, *Introduction*, discusses the general aim of simulation experiments in data science and statistics, why and where simulation is used, and the special case of dealing with big data.

Chapter 2, *R and High-Performance Computing*, consists of comprehensive text on advanced computing, data manipulation, and visualization with R.

Chapter 3, *The Discrepancy between Pencil-Driven Theory and Data-Driven Computational Solutions*, reports problems on numerical precision, rounding, and convergence in a deterministic setting.

Chapter 4, *Simulation of Random Numbers*, starts with the simulation of uniform random numbers and transformation methods to obtain other kinds of distributions. It includes a discussion of various types of Markov chain Monte Carlo (MCMC) methods.

Chapter 5, *Monte Carlo Methods for Optimization Problems*, introduces deterministic and stochastic optimization methods.

Chapter 6, *Probability Theory Shown by Simulation*, has a strong focus on basic theorems in statistics; for example, the concept of the weak law of large numbers and the central limit theorem are shown by simulation.

Chapter 7, *Resampling Methods*, is a comprehensive view on the bootstrap, the jackknife and cross-validation.

Chapter 8, *Applications of Resampling Methods and Monte Carlo Tests*, shows applications in various fields such as regression, imputation, and time series analysis. In addition, Monte Carlo tests and their variants such as permutation tests and bootstrap tests are presented.

Chapter 9, *The EM Algorithm*, introduces the expectation maximum method to iteratively obtain an optima. Applications in clustering and imputation of missing values are given.

Chapter 10, *Simulation with Complex Data*, shows how to simulate synthetic data as well as population data that can be used for the comparison of methods in general or also serve as input for agent-based microsimulation models.

Chapter 11, *System Dynamics and Agent-Based Models*, discusses agent-based microsimulation models and shows basic models in system dynamics to study complex dynamical systems.

## What you need for this book

This book heavily depends on the software environment R, version 3.2 or newer (https://cran.r-project.org/). In most chapters, independent and standalone code is written to show methods and execute examples, and no additional packages of R are needed. For a few chapters, additional R packages such as deSolve, cvTools, laeken, VIM, and few others must be installed within R. The packages dplyr and ggplot2 are used throughout the book.

Optionally, the use of a script editor for R, such as RStudio (https://www.rstudio.com/) or Architect + Eclipse (https://www.openanalytics.eu/architect), is recommended.

## Who this book is for

This book is for users who are familiar with computational methods and R. If you want to learn about the advanced features of R, along with computer-intense Monte Carlo methods and tools for statistical simulation, and if you prefer data-driven solutions, then this book is for you.

## Conventions

In this book, you will find a number of text styles that distinguish between different kinds of information. Here are some examples of these styles and an explanation of their meaning.

R code words in text, filenames, file extensions, pathnames, and dummy URLs are shown as follows:

A block of code is set as follows:

[default] love <- function(t, x, parms){ with(as.list(c(parms, x)), { dPrince_Harry <- a * Chelsy_Davy dChelsy_Davy <- -b * Prince_Harry res <- c(dPrince_Harry, dChelsy_Davy) list(res) }) }

Any command-line input or output is written as follows:

dat <- matrix(c(104,11037,189,11034),2,2, byrow=TRUE)## Loading required package: grid> confint(oddsratio(dat, log=FALSE))## 2.5 % 97.5 %## 0.4324132 0.6998549

### Note

Warnings or important notes appear in a box like this.

### Tip

Tips and tricks appear like this.

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