#### Overview of this book

Data Science with R aims to teach you how to begin performing data science tasks by taking advantage of Rs powerful ecosystem of packages. R being the most widely used programming language when used with data science can be a powerful combination to solve complexities involved with varied data sets in the real world. The book will provide a computational and methodological framework for statistical simulation to the users. Through this book, you will get in grips with the software environment R. After getting to know the background of popular methods in the area of computational statistics, you will see some applications in R to better understand the methods as well as gaining experience of working with real-world data and real-world problems. This book helps uncover the large-scale patterns in complex systems where interdependencies and variation are critical. An effective simulation is driven by data generating processes that accurately reflect real physical populations. You will learn how to plan and structure a simulation project to aid in the decision-making process as well as the presentation of results. By the end of this book, you reader will get in touch with the software environment R. After getting background on popular methods in the area, you will see applications in R to better understand the methods as well as to gain experience when working on real-world data and real-world problems.
Simulation for Data Science with R
Credits
www.PacktPub.com
Preface
Free Chapter
Introduction
R and High-Performance Computing
The Discrepancy between Pencil-Driven Theory and Data-Driven Computational Solutions
Simulation of Random Numbers
Monte Carlo Methods for Optimization Problems
Probability Theory Shown by Simulation
Resampling Methods
Applications of Resampling Methods and Monte Carlo Tests
The EM Algorithm
Simulation with Complex Data
System Dynamics and Agent-Based Models
Index

## The bootstrap

The bootstrap is the most popular resampling method to express the uncertainty of an estimate; in other words, to estimate the variance of an estimated statistic of interest. But why is it called bootstrap? Tall boots may have a tab, loop or handle at the top known as a bootstrap; see Figure 7.1:

This bootstrap allows us to use our fingers to pull the boots on. But the term is used as a synonym for more. In the 19th century, the idiom "to pull oneself up by one's bootstraps was already being used as an example of an impossible task:

"It is conjectured that Mr. Murphee will now be enabled to hand himself over the Cumberland river or a barn yard fence by the straps of his boots" (Freeman 2009). This is just what the bootstrap is about in statistics. We will see that we use a bootstrap to make inference just with our boots (sample data).

In the following section, we will show with a motivating example that we get basically the same results with the bootstrap in comparison to analytical...