#### 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

## Why use simulation?

Simulation can save huge amounts of time and provides very accurate answers to our questions.

Statistical inference is often handled by asymptotic normal theory, which may provide formulas for the standard errors that allow us to construct confidence intervals around point estimates. For the simple case of the simple estimator of the arithmetic mean, we can immediately choose the formula for an observational vector x with n values, the arithmetic and s being the standard deviation of x. However, this formula to express the confidence interval for the arithmetic mean is only true for independent identical distributed samples, sampled with simple random sampling from a population. However, in many situations the (asymptotic) distribution of the parameter of interest might not be known, and often we do not have the expertise to derive even an approximation of a formula to express the standard error of an estimator of interest. For example, this might be true for the Huber mean (Huber 1981) from data sampled with a multi-stage cluster sampling design. In other words, if the quantity of interest is a very complex function of the data or if the data is of a very complex nature, we may be able to benefit substantially from the use of a Monte Carlo simulation. Even when a formula may exist in the statistical literature to express the confidence interval, we might not be aware of it.

A very prominent resampling method is the bootstrap, intensively discussed in Chapter 7, Resampling Methods. In this approach, the sampling distribution of the parameter estimate is simulated by repeated sampling with replacement from the current data, and re-computing parameter estimates from each sampled data set. The distribution of these estimations expresses the variability of the estimation, thus this distribution can be used to express confidence intervals.

The approach is very similar for hypothesis tests. The distribution of the test statistics is not always known for a test. With the Monte Carlo approach to testing, data is simulated in a way that it mimics the null hypothesis, and parameters for data generation are used from the empirical data. The test statistic is calculated on the data and compared to the repeatedly simulated data. It's then a straightforward topic in Chapter 8, Applications of Resampling Methods and Monte Carlo Tests, Monte Carlo Tests) to receive a p-value for the test.