•  #### Hands-On Simulation Modeling with Python #### Overview of this book

Simulation modeling helps you to create digital prototypes of physical models to analyze how they work and predict their performance in the real world. With this comprehensive guide, you'll understand various computational statistical simulations using Python. Starting with the fundamentals of simulation modeling, you'll understand concepts such as randomness and explore data generating processes, resampling methods, and bootstrapping techniques. You'll then cover key algorithms such as Monte Carlo simulations and Markov decision processes, which are used to develop numerical simulation models, and discover how they can be used to solve real-world problems. As you advance, you'll develop simulation models to help you get accurate results and enhance decision-making processes. Using optimization techniques, you'll learn to modify the performance of a model to improve results and make optimal use of resources. The book will guide you in creating a digital prototype using practical use cases for financial engineering, prototyping project management to improve planning, and simulating physical phenomena using neural networks. By the end of this book, you'll have learned how to construct and deploy simulation models of your own to overcome real-world challenges.
Preface Section 1: Getting Started with Numerical Simulation  Free Chapter
Chapter 1: Introducing Simulation Models Chapter 2: Understanding Randomness and Random Numbers Chapter 3: Probability and Data Generation Processes Section 2: Simulation Modeling Algorithms and Techniques Chapter 4: Exploring Monte Carlo Simulations Chapter 5: Simulation-Based Markov Decision Processes Chapter 6: Resampling Methods Chapter 7: Using Simulation to Improve and Optimize Systems Section 3: Real-World Applications Chapter 8: Using Simulation Models for Financial Engineering Chapter 9: Simulating Physical Phenomena Using Neural Networks Chapter 10: Modeling and Simulation for Project Management Chapter 11: What's Next? Other Books You May Enjoy # Demystifying bootstrapping

The most well-known resampling technique is the one defined as bootstrapping, as introduced by B. Efron in 1993. The logic of the bootstrap method is to build samples that are not observed, but statistically like those observed. This is achieved by resampling the observed series through an extraction procedure where we reinsert the observations.

## Introducing bootstrapping

This procedure is like extracting a number from an urn, with subsequent reinsertion of the number before the next extraction. Once a statistical test has been chosen, it is calculated both on the observed sample and on a large number of samples of the same size as that observed and obtained by resampling. The N values of the test statistic then allow us to define the sample distribution; that is, the empirical distribution of the chosen statistic.

Important Note

A statistical test is a rule for discriminating samples that, if observed, lead to the rejection of an initial hypothesis...