Module 3: Bayesian Statistics
Introduction
In this module, we'll explore an alternative approach to statistics: the Bayesian perspective. Unlike the frequentist approach we've been using so far, Bayesian statistics treats probability as a measure of belief that can be updated as new evidence emerges.
Bayesian statistics provides a powerful framework for reasoning about uncertainty and making predictions based on incomplete information. It allows us to incorporate prior knowledge and update our beliefs in light of new data, which is particularly valuable in real-world scenarios where perfect information is rarely available.
Learning Objectives
By the end of this module, you should be able to:
- Explain the fundamental differences between Bayesian and frequentist statistical approaches
- Apply Bayes' Theorem to calculate conditional probabilities
- Update prior probabilities based on new evidence
- Calculate likelihood ratios and posterior odds
- Interpret Bayesian results in terms of belief updates
- Apply Bayesian reasoning to real-world problems
- Use Python to implement basic Bayesian analyses
Guided Project
Project Resources
Open DS_123_Bayesian_Statistics.ipynb in the GitHub repository below to follow along with the guided project:
GitHub: Bayesian StatisticsKey Concepts
- Bayes' Theorem and its components: prior, likelihood, evidence, and posterior
- Conditional probability and independence
- Prior and posterior distributions
- Subjective vs. objective probability
- Bayesian updating process
- Bayesian inference vs. frequentist inference
- Applications of Bayesian statistics in data science
Module Project
Project Tasks
In this module's project, you will be asked to:
- Apply Bayes' Theorem to calculate conditional probabilities
- Use Bayesian reasoning to solve probabilistic problems
- Calculate prior, likelihood, and posterior probabilities
- Update beliefs in response to new evidence
- Interpret Bayesian results in real-world contexts
- Compare Bayesian and frequentist approaches to inference
- Implement Bayesian methods using Python
Complete all tasks in the Jupyter notebook provided in the GitHub repository.