What this book covers
Chapter 1, Introduction, analyzes the basics of numerical simulation and highlights the difference between modeling and simulation and the strengths of simulation models such as defects. The different types of models are analyzed, and we study practical modeling cases to understand how to elaborate a model starting from the initial considerations.
Chapter 2, Understanding Randomness and Random Numbers, defines stochastic processes and explains the importance of using them to address numerous real-world problems. The main methods for generating random numbers with practical examples in Python code, and the generation of uniform and generic distributions, are both explored. It also explains how to perform a uniformity test using the chi-square method.
Chapter 3, Probability and the Data Generating Process, shows how to distinguish between the different definitions of probabilities and how they can be integrated to obtain useful information in the simulation of real phenomena.
Chapter 4, Monte Carlo Simulations, explores techniques based on Monte Carlo methods for process simulation. We will first learn the basic concepts, and then we will see how to apply them to practical cases.
Chapter 5, Simulation-Based Markov Decision Process, shows how to deal with decision-making processes with Markov chains. We will analyze the concepts underlying Markovian processes and then analyze some practical applications to learn how to choose the right actions for the transition between different states of the system.
Chapter 6, Resampling Methods, shows how to apply resampling methods to approximate some characteristics of the distribution of a sample in order to validate a statistical model. We will analyze the basics of the most common resampling methods and learn how to use them by solving some practical problems.
Chapter 7, Use of Simulation to Improve and Optimize Systems, shows how to use the main optimization techniques to improve the performance of our simulation models. We will see how to use the gradient descent technique, the Newton-Raphson method, and stochastic gradient descent. We will also see how to apply these techniques with practical examples.
Chapter 8, Simulation Models for Financial Engineering, shows practical cases of using simulation methods in a financial context. We will learn how to use Monte Carlo methods to predict stock prices and how to assess the risk associated with a portfolio of shares.
Chapter 9, Simulating Physical Phenomena with Neural Networks, shows how to develop models based on artificial neural networks to simulate physical phenomena. We will start by exploring the basic concepts of neural networks, and we will examine their architecture and its main elements. We will see how to train a network to update its weights.
Chapter 10, Modeling and Simulation for Project Management, deals with practical cases of project management using the tools we learned how to use in the previous chapters. We will see how to evaluate in advance the results of the actions undertaken in the management of a forest using Markov processes, and then move on to evaluating the time required for the execution of a project using the Monte Carlo simulation.
Chapter 11, What’s Next?, provides a better understanding of the problems associated with building and deploying simulation models and additional resources and technologies to learn how to hone your machine learning skills.