Statistical Simulation in Python

Overview

Learn to solve increasingly complex problems using simulations to generate and analyze data.

Simulations are a class of computational algorithms that use the relatively simple idea of random sampling to solve increasingly complex problems. Although they have been around for ages, they have gained in popularity recently due to the rise in computational power and have seen applications in multiple domains including Artificial Intelligence, Physics, Computational Biology and Finance just to name a few. Students will use simulations to generate and analyze data over different probability distributions using the important NumPy package. This course will give students hands-on experience with simulations using simple, real-world applications.

Syllabus

Basics of Randomness & Simulation

This chapter gives you the tools required to run a simulation. We'll start with a review of random variables and probability distributions. We will then learn how to run a simulation by first looking at a simulation workflow and then recreating it in the context of a game of dice. Finally, we will learn how to use simulations for making decisions.

Probability & Data Generation Process

This chapter provides a basic introduction to probability concepts and a hands-on understanding of the data generating process. We'll look at a number of examples of modeling the data generating process and will conclude with modeling an eCommerce advertising simulation.

Resampling Methods

In this chapter, we will get a brief introduction to resampling methods and their applications. We will get a taste of bootstrap resampling, jackknife resampling, and permutation testing. After completing this chapter, students will be able to start applying simple resampling methods for data analysis.

Advanced Applications of Simulation

In this chapter, students will be introduced to some basic and advanced applications of simulation to solve real-world problems. We'll work through a business planning problem, learn about Monte Carlo Integration, Power Analysis with simulation and conclude with a financial portfolio simulation. After completing this chapter, students will be ready to apply simulation to solve everyday problems.