Teaching

Bayesian statistics and information theory

(Imperial College, 2019)

Last update: 28-05-2019

Resources

  • GitHub repository containing the all 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 March 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).


Cosmology with Bayesian statistics and information theory

(ICG Portsmouth, 2017)

Last update: 10-03-2017

Resources

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