#### 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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# Summary

In this chapter, we addressed the basic concepts of Monte Carlo simulation. We explored the Monte Carlo components used to obtain a simulation with satisfactory results. Hence, we used Monte Carlo methods to estimate the value of pi.

We then tackled two fundamental concepts of Monte Carlo simulation: the law of large numbers and the central limit theorem. For example, the law of large numbers allows us to determine the centers and weights of a Monte Carlo analysis for the estimate of definite integrals. The central limit theorem is of great importance and it is thanks to this that many statistical procedures work.

Next, we analyzed practical applications of using Monte Carlo methods in real life: numerical optimization and project management. Finally, we learned how to perform numerical integration using Monte Carlo techniques.

In the next chapter, we will learn the basic concepts of the Markov process. We will understand the agent-environment interaction process...