Bayesian Statistics for Astrophysics 2024

This is the webpage of the course Bayesian Statistics for Astrophysics 2024. Here we will subsequently add more and more lecture material, and in particular the lecture notes that you will be working on in small groups.

Lecture Notes

• Chapter 1: Hypothesis Testing & Maximum Likelihood
  • Hypothesis Testing
  • p-values
  • Advantages and Disadvantages of Hypothesis Testing
  • Example: sceptical astronomer
  • 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