#### 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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# Approaching cross-validation techniques

Cross-validation is a method used in model selection procedures based on the principle of predictive accuracy. A sample is divided into two subsets, of which the first (training set) is used for construction and estimation, while the second (validation set) is used to verify the accuracy of the predictions of the estimated model. Through a synthesis of repeated predictions, a measure of the accuracy of the model is obtained. A cross-validation method is like jackknife, in that it leaves one observation out at a time. In another method, known as K-fold validation, the sample is divided into K subsets and, in turn, each of them is left out as a validation set.

Important Note

Cross validation can be used to estimate the Mean Squared Error (MSE) test (or, in general, any measure of precision) of a statistical learning technique in order to evaluate its performance or select its level of flexibility.

Cross validation can be used for both...