#### 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
Free Chapter
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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# Applying Monte Carlo simulation

Monte Carlo simulation used to study the response of a model to randomly generated inputs. The simulation process takes place in the following three phases:

1. N inputs are generated randomly.
2. A simulation is performed for each of the N inputs.
3. The outputs of the simulations are aggregated and examined. The most common measures include estimating the average value of an output and distributing the output values, as well as the minimum or maximum output value.

Monte Carlo simulation is widely used for the analysis of financial, physical, and mathematical models.

## Generating probability distributions

The generation of probability distributions that cannot be found with analytical methods can easily be addressed with Monte Carlo methods. For example, let's say we want to estimate the probability distribution of the damage caused by earthquakes in a year in Japan.

Important Note

In this type of analysis, there are two...