### Bayesian statistics and information theory

#### (Imperial College, 2019)

Last update: 28-05-2019#### Resources

- 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"?*- 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

- 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

- 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?* - 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).

#### Programme

##### Lecture 1: Tuesday 14 May 2019

##### Lecture 2: Tuesday 21 March 2019

##### Lecture 3: Tuesday 28 May 2019

#### Bibliography

### 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.
- 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).

#### Programme

##### Lecture 1: Monday 6 March 2017

##### Lecture 2: Wednesday 8 March 2017

##### Lecture 3: Friday 10 March 2017

#### Bibliography