Florent Leclercq

• Cours (07-08-2023): La théorie des probabilités : la logique de la découverte scientifique slides
• GitHub repository containing the Jupyter notebooks.

• Lecture (16-09-2021): Bayesian statistics, and some other aspects of probability theory slides
• GitHub repository containing the Jupyter notebooks.

• Homepage
• Supernova cosmology: data and simulations (pre-workshop exercise) notebook and inference with MCMC and HMC notebook
• The 1919 Eclipse: parameter inference and model comparison notebook

Resources

• GitHub repository containing the Jupyter notebooks.

Programme

Lecture 1: Tuesday 14 May 2019

• Aspects of probability theory slides
  ... a.k.a. why am I not allowed to "change the prior" or to "cut the data"?
  • Probability theory and Bayesian statistics: reminders
  • Ignorance priors notes, notebook and the maximum entropy principle notebook
  • Gaussian random fields (and a digression on non-Gaussianity) notes, notebook
  • Bayesian signal processing and reconstruction: de-noising notebook 1, notebook 2, de-blending notebook
  • Bayesian decision theory notes, notebook and Bayesian experimental design

Lecture 2: Tuesday 21 May 2019

• Aspects of probability theory slides
  ... a.k.a. why am I not allowed to "change the prior" or to "cut the data"?
  • Bayesian networks, Bayesian hierarchical models and Empirical Bayes

• 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
  • The test pdf notes
  • Slice sampling notebook, Gibbs sampling notebook
  • Hamiltonian sampling notebook
  • Approximate Bayesian Computation: Likelihood-free rejection sampling notebook

Lecture 3: Tuesday 28 May 2019

• Aspects of probability theory: Bayesian model comparison notes
  ... a.k.a. why am I not allowed to "change the prior" or to "cut the data"?
  • Nested models and the Savage-Dickey density ratio
  • Bayesian model selection as a decision analysis
  • Bayesian model averaging
  • (Dangers of) model selection with insufficient summary statistics
• Information theory slides
  ... a.k.a. how much is there to be learned in my data anyway?
  • The noisy binary symmetric channel notebook
  • Low-density parity check codes
  • Measures of entropy and information
  • Information-theoretic experimental design
  • Supervised machine learning basics notebook

Bibliography

• 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).

Resources

• Preliminary reading: Chapter 3 (except 3.4.) in my PhD thesis.
• GitHub repository containing the Jupyter notebooks.

Programme

Lecture 1: Monday 6 March 2017

• 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

Lecture 2: Wednesday 8 March 2017

• 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

Lecture 3: Friday 10 March 2017

• Information theory slides
  ... a.k.a. how much is there to be learned in my data anyway?
  • The noisy binary symmetric channel notebook
  • Low-density parity check codes
  • Measures of entropy and information
  • Information-theoretic experimental design
  • Machine learning basics notebook

Bibliography

• 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).