Cosmology with Bayesian statistics and information theory
(ICG Portsmouth, 2017)Last update: 10-03-2017
- Preliminary reading: Chapter 3 (except 3.4.) in my PhD thesis.
- GitHub repository containing the all Jupyter notebooks.
- Aspects of probability theory slides
... a.k.a. why am I not allowed to "change the prior" or to "cut the data"?
- Ignorance priors and the maximum entropy principle notebook
- Bayesian signal processing and reconstruction notebook: de-noising notebook 1, notebook 2, de-blending notebook
- Bayesian decision theory notebook
- Hypothesis testing beyond the Bayes factor
- Bayesian networks, Bayesian hierarchical models and Empirical Bayes method
- Probabilistic computations slides
... a.k.a. how much do I know about the likelihood?
- Which inference method to choose?
- Monte-Carlo integration, importance sampling, rejection sampling notebook
- Markov Chain Monte Carlo: Metropolis-Hastings algorithm & Gelman-Rubin test notebook
- Slice sampling notebook, Gibbs sampling notebook
- Hamiltonian sampling notebook
- Likelihood-free methods and Approximate Bayesian Computation notebook
- Information theory slides
... a.k.a. how much is there to be learned in my data anyway?
- E. T. Jaynes, Probability Theory: The Logic of Science, edited by G. L. Bretthorst (Cambridge University Press, 2003).
- A. Gelman, J. B. Carlin, H. S. Stern, D. B. Dunson, A. Vehtari, D. B. Rubin, Bayesian Data Analysis, Third Edition (Taylor & Francis, 2013).
- B. D. Wandelt, Astrostatistical Challenges for the New Astronomy (Springer, 2013) Chap. Gaussian Random Fields in Cosmostatistics, pp. 87–105.
- R. M. Neal, Handbook of Markov Chain Monte Carlo (Chapman & Hall/CRC, 2011) Chap. MCMC Using Hamiltonian Dynamics, pp. 113–162.
- D. J. C. MacKay, Information Theory, Inference, and Learning Algorithms (Cambridge University Press, 2003).
- G. E. Crooks, On Measures of Entropy and Information (Tech Note, 2016).
Lecture 1: Monday, March 6th
Lecture 2: Wednesday, March 8th
Lecture 3: Friday, March 10th