Yousef's Notes / SMUC

Module I - Introduction & Random Variables Simulation

Elements of a Simulation Model
Generating Random Numbers
Inferential Statistics and Models
Introduction to Simulation and Modelling
Key Features and Components of a Model
Model
Modelling Methodology
Random Variable Simulation
Simulation
Simulation & Modelling Applications
System
Types of Simulation Models

Module II - Monte Carlo Simulation

A Game of Chance - Monte Carlo Simulation
Characteristics of a Monte Carlo Simulation
Finding pi Using Monte Carlo Simulation
Monte Carlo Simulation in Python
Sleepless in Seattle Experiment
Steps in a Monte Carlo Simulation
The Choice Function
The Monte Carlo Method
The Taxi Problem Experiment
Using Monte Carlo Simulation for Inference

Module III - Discrete Events Simulation

Discrete Events Simulation Modeling Approaches
Discrete Events Simulation Python
Discrete Events Simulation Use Cases
SimPy
SimPy Elements for Discrete Events Simulation
SimPy for Discrete Events Simulation

Module IV - Model Building

1. Functions vs Models
2. Reading Models
3. Model Design
4. Understanding the Data
5. Variation Analysis
6. Covariation Analysis
7. Patterns and Models
8. Cross Validation

Module V - Regression Models

1. Simple Linear Regression
2. Multiple Linear Regression
3. Residual Analysis
4. Categorical Variables
5. Interaction Terms and Polynomial Effects
6. Model Selection and Validation

Module VI - Classification Models

1. Introduction to Logistic Regression (Binary)
2. Sigmoid Function and Logit Transformation
3. Build the Model
4. Model Evaluation
5. Model Predictions
6. Multiple Logistic Regression Use Case

Test of Randomness in Python

Test of Randomness in Python

We want to test if our sequence of random numbers complies with uniformity and independence.

Testing Uniformity
Testing Independence

Properties of Random Numbers

Testing Independence Next

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