#### 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
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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?
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# Performing numerical integration using Monte Carlo

Monte Carlo simulations represent a numerical solution for calculating integrals. In fact, with the use of the Monte Carlo algorithm, it is possible to adopt a numerical procedure for the solution of mathematical problems, with many variables that do not present an analytical solution. The efficiency of the numerical solution increases compared to other methods when the size of the problem increases.

Important Note

Let's analyze the problem of a definite integral. In the simplest cases, there are methods for integration that foresee the use of techniques such as integration by parts, integration by replacement, and so on. In more complex situations, however, it is necessary to adopt numerical procedures that involve the use of a computer. In these cases, the Monte Carlo simulation provides a simple solution that's particularly useful in cases of multidimensional integrals.

However, it is important to highlight that...