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.

Bayesian_Statistics
Probability_Distribution