Bayesian Statistics for Astrophysics 2025

This is the webpage of the course Bayesian Statistics for Astrophysics 2025.

Lecture Notes

• Chapter 1: Hypothesis Testing & Maximum Likelihood
  • Hypothesis Testing
  • Advantages and Disadvantages of Hypothesis Testing
  • Maximum likelihood
  • Maximum Likelihood Estimator
  • Generative model
  • Confidence intervals
• Chapter 2: Information Criterions and Bootstrap Confidence Intervals
  • Nested Models
  • Akaike Information Criterion (AIC)
  • Bayesian Information Criterion (BIC)
  • AIC vs BIC
  • Bootstrap and confidence intervals
• Chapter 3: Mathematical foundations of statistics
  • 3.1 Sample Spaces
  • 3.2 Derivation of Bayes theorem
  • 3.3 Law of total probability
  • 3.4 The difference between frequentist and Bayesian views
• Chapter 4: Bayesian inference
  • The steps of Bayesian inference
  • Visual example
  • Grid search
  • Simple astrophysical example
  • Computation of confidence intervals using a grid search in combination with an updated posterior
  • Complete example
  • Confidence intervals
  • Conclusions
  • References
• Chapter 5 - Priors
  • What is a prior
  • Strength of a prior
  • Type of priors
  • Computational examples of priors
  • Manual examples of (conjugate) priors
  • Sources
• Chapter 6: Markov Chain Monte Carlo
  • Introduction to Markov chains
  • Explanation of Metropolis-Hasting
  • Explanation of affine-invariant algorithms (used in emcee)
• Chapter 7: Advanced examples of Bayesian statistics
  • Bayesian Billiards
  • Sigma clipping
  • Rejecting Outliers with a Bayesian approach