Bayesian inference is a statistical method that updates probabilities based on evidence. It's rooted in Bayes' Theorem, which provides a mathematical framework for calculating conditional probabilities. Here's a breakdown of its core concepts:
Key Principles
- Prior Knowledge: Initial beliefs about parameters before observing data
- Likelihood: Probability of observing data given a hypothesis
- Posterior Distribution: Updated beliefs after incorporating evidence
- Evidence (Marginal Likelihood): Normalizing factor for Bayesian updating
Applications
- Machine Learning: Used in probabilistic models like Naive Bayes classifiers
- Medical Diagnosis: Calculating disease probabilities based on symptoms
- Finance: Risk assessment and predictive modeling
- Natural Language Processing: Spam filtering and text classification
Comparison with Frequentist Approach
| Feature | Bayesian Inference | Frequentist Statistics |
|---|---|---|
| Uncertainty Handling | Probabilistic (Bayesian) | Frequentist (confidence intervals) |
| Prior Knowledge | Incorporates prior beliefs | Does not use prior knowledge |
| Computation | Often uses MCMC methods | Relies on analytical solutions |
For further reading, explore our guide on Bayesian Networks or Markov Chain Monte Carlo (MCMC) Methods. Dive deeper into probability theory with Probability Fundamentals.