#### 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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# Explaining permutation tests

When observing a phenomenon belonging to a set of possible results, we ask ourselves what the law of probability is that we can assign to this set. Statistical tests provide a rule that allows us to decide whether to reject a hypothesis based on the sample observations.

Parametric approaches are very uncertain about the experiment plan and the population model. When these assumptions are not respected, particularly when the data law does not conform to the needs of the test, the parametric results are less reliable. When the hypothesis is not based on knowledge of the data distribution and assumptions have not been verified, nonparametric tests are used. Nonparametric tests offer a very important alternative since they need fewer hypotheses.

Permutation tests are a special case of randomization tests that use series of random numbers formulated from statistical inferences. The computing power of modern computers has made their widespread application...