Understanding Statistical Models and Mathematical Models
This course covers important techniques from both mathematical and statistical modeling, including the use of ordinary differential equations to model deterministic systems, classic local search and simulated annealing to explore large search spaces.
What you'll learn
Data science and data modeling are fast emerging as crucial capabilities that every enterprise and every technologist and it us important to choose the type of model most appropriate to your use-case. In this course, Understanding Statistical Models and Mathematical Models, you will gain the ability to differentiate between mathematical models and statistical models and pick the right type of model for your scenario.
First, you will learn the important characteristics of mathematical and statistical models and their applications. Next, you will discover how classic mathematical models find wide applicability in solving differential equations and modeling deterministic systems.
Then, you will also learn how statistical models are great for modeling systems with randomness, using business-based use-cases from risk management, and the use of Monte Carlo simulations. Finally, you will round out your knowledge performing hypothesis testing using T-tests and Z-tests on real-world data.
When you’re finished with this course, you will have the skills and knowledge to use powerful techniques from both mathematical and statistical modeling, including solving simple ordinary differential equations, the use of simulated annealing and classic hill climbing, as well as hypothesis testing and statistical tests such as the T-test.
Table of contents
- Version Check 0m
- Prerequisites and Course Outline 1m
- Understanding Mathematical Models and Statistical Models 8m
- Mathematical Models and Statistical Models: Differences and Applications 6m
- Data and Metadata 6m
- Demo: Creating an Environment to Run the R Kernel on Jupyter Notebooks 3m
- Demo: Associating Metadata Using the Comment Function 2m
- Demo: Querying and Setting Metadata Using the Meta Function 7m
- Recap: Ordinary Differential Equations 2m
- Demo: Calculating the Derivative of a Function 5m
- Demo: Solving Differential Equations 6m
- Demo: Solving Verhulst's Equation for Population Growth 6m
- The 8 Queens Problem 8m
- Local Search Optimization Techniques 6m
- Demo: Setting up Helper Functions to Solve the 8 Queens Optimization Problem 9m
- Demo: Applying Local Search Optimization to Solve the Eight Queens Problem 6m
- Data Mining Statistics and Machine Learning 5m
- Understanding Hypothesis Testing 6m
- The T-test and the Z-test 5m
- Demo: Exploring the Automobile Dataset 5m
- Demo: One Sample T-test 6m
- Demo: One Sample Z-test 4m
- Demo: Two Sample T-test 6m
- Demo: Paired Sample T-test and Z-test 5m
- Summary and Further Study 2m