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.

Introduction to random variables

np.random.choice()

Poisson random variable

Shuffling a deck of cards

Simulation basics

Throwing a fair die

Throwing two fair dice

Simulating the dice game

Using simulation for decision-making

Simulating one lottery drawing

Should we buy?

Calculating a break-even lottery price

Basics of Randomness & Simulation

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.

Probability basics

Queen and spade

Two of a kind

Game of thirteen

More probability concepts

The conditional urn

Birthday problem

Full house

Data generating process

Driving test

National elections

Fitness goals

eCommerce Ad Simulation

Sign up Flow

Purchase Flow

Probability of losing money

Probability & Data Generation Process

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.

Introduction to resampling methods

Sampling with replacement

Probability example

Bootstrapping

Running a simple bootstrap

Non-standard estimators

Bootstrapping regression

Jackknife resampling

Basic jackknife estimation - mean

Jackknife confidence interval for the median

Permutation testing

Generating a single permutation

Hypothesis testing - Difference of means

Hypothesis testing - Non-standard statistics

Resampling Methods

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.

Simulation for Business Planning

Modeling Corn Production

Modeling Profits

Optimizing Costs

Monte Carlo Integration

Integrating a Simple Function

Calculating the value of pi

Simulation for Power Analysis

Factors influencing Statistical Power

Power Analysis - Part I

Power Analysis - Part II

Applications in Finance

Portfolio Simulation - Part I

Portfolio Simulation - Part II

Portfolio Simulation - Part III

Wrap Up

Advanced Applications of Simulation

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.

<h2>Get to Grips with Random Variables</h2>
Simulations are a class of computational algorithms that use random sampling to solve increasingly complex problems. Although simulations have been around for a long time, interest in this area has recently grown due to the rise in computational power and the applications across Artificial Intelligence, Physics, Computational Biology and Finance just to name a few. 
<br><br>
This course provides hands-on experience with simulations using real-world applications, starting with an introduction to random variables and the tools you need to run a simulation. 
<br><br>
<h2>Gain an Introduction to Probability Concepts </h2>
The second chapter in this course provides an overview of probability concepts, using practice exercises based on card games and well-known probability puzzles to provide a framework for your new knowledge. You’ll finish this chapter by modeling an eCommerce advertising simulation. 
<br><br>
<h2>Discover Resampling Methods and Applications </h2>
The third chapter looks at different resampling methods, including bootstrap resampling, jackknife resampling, and permutation testing. Once you’ve completed this course, you’ll be able to add these methods to your data analysis process. 
<br><br>
<h2>Learn to Use Simulation for Business and Build Your Portfolio </h2>
Simulation has many real-world applications, especially in the world of business. The final chapter in this course looks at these, and takes you through a business planning problem to get you used to using your new skills in a business setting. You’ll look at modeling profits, optimizing costs, and getting started with power analysis.

Sampling in Python

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

Statistical Simulation in Python

Data Scientist

Monte Carlo integration

Definite integration

Let's practice!

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Advanced Applications of Simulation - Monte Carlo Integration

Monte Carlo Integration

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