Reading material

Different authors present content in different ways. Try a few and pick one that you find most readable/accessible.

Books about Bayesian inference


  • “Bayesian data analysis” (Gelman):

  • “Introduction to Probability” (Dimitri Bertsekas): covers basics: random variable, combinatorics, derived distributions, what is a PDF, how to work with them, expectation values

  • “Probability and Statistics” (Morris H. DeGroot): covers classical approaches to hypothesis testing and frequentist analysis, so you can really understand, e.g., the classical tests, what p-values really are, why are they used and how and when they are useful.

for physical sciences

  • “Bayesian Logical Data Analysis for the Physical Sciences” (Gregory)

  • “Data Analysis - A Bayesian Tutorial” (Sivia): building an intuition for how Bayesian statistics works

  • “Scientific Inference” (Simon Vaughan): basic probability theory, statistical thinking, model and data representation in computers. likelihood function, graphical summaries, basic Monte Carlo.

  • “Bayesian reasoning in data analysis - A critical introduction” (D’Agostini) differences in uncertainties, confidence vs. credible intervals, frequentist/maximum likelihood, Bayesian inference and how they relate

  • “An Introduction to Statistical Learning with Applications in R” (James, Witten, Hastie & Tibshirani) available online

  • “Machine Learning: An Algorithmic Perspective” (Stephen Marsland)

  • “Statistics, Data Mining, and Machine Learning in Astronomy” (Zeljko Ivezic, Andy Connolly, Jake VanderPlas, Alex Gray) for scikit-learn and astroml

  • “Wahrscheinlichkeitstheorie, Statistik und Datenanalyse”, von der Linden & Prüll


A similar course is available in full online at

Research Papers on State-of-the-Art Methods

In the course, we will go through some of these (you do not have to read them beforehand).

Markov Chain Monte Carlo

(see also the end of the 3-MCMC notebook for references)



Recommended state-of-the-art tools:

Importance Sampling

(there are many resources online)

Recommended tools:

Nested Sampling

LRPS techniques:


Recommended state-of-the-art, open-source tools:

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