Bayesian statistics is a powerful approach to statistical inference that incorporates prior knowledge and updates it with observed data to form posterior probabilities. Unlike frequentist methods, it treats probability as a measure of belief, making it particularly useful in scenarios with uncertainty.
Key Concepts
- Prior Probability: The initial belief about an event before observing new data.
- Likelihood: The probability of observing the data given a specific hypothesis.
- Posterior Probability: Updated belief after combining prior knowledge and observed data.
- Bayes' Theorem: The mathematical foundation linking these concepts:
$$ P(H|D) = \frac{P(D|H) \cdot P(H)}{P(D)} $$
Applications
Bayesian methods are widely applied in:
- Medical research (e.g., diagnostic testing)
- Machine learning (e.g., spam filtering)
- Finance (e.g., risk assessment)
- Natural language processing (e.g., topic modeling)
Further Reading
For a deeper dive, explore our Introduction to Statistics course or Machine Learning resources.