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

### General¶

• “Bayesian data analysis” (Gelman): http://www.stat.columbia.edu/~gelman/book/

• “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) https://www.roma1.infn.it/~dagos/WSPC/ 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) http://www-bcf.usc.edu/~gareth/ISL/ available online

• “Machine Learning: An Algorithmic Perspective” (Stephen Marsland) http://seat.massey.ac.nz/personal/s.r.marsland/MLbook.html

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

• https://itp.tugraz.at/LV/wvl/Statistik/A_WS_pdf.pdf “Wahrscheinlichkeitstheorie, Statistik und Datenanalyse”, von der Linden & Prüll

## Lectures¶

A similar course is available in full online at https://kipac.github.io/StatisticalMethods/

## 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¶

Talks:

Diagnostics:

Recommended state-of-the-art tools:

### Importance Sampling¶

(there are many resources online)

Recommended tools:

### Nested Sampling¶

LRPS techniques:

Diagnostics

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

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