Pioneers-pp: Bayesian statistics and ABC talk

The repo contains the examples and computer exercise that are associated with the An Introduction to Bayesian Statistics and Approximate Bayesian Computing Meetup event (https://www.meetup.com/Pioneers-of-Probabilistic-Programming/events/264336086/).

File structure

• presentation.ipynb: notebook with the presentation.
• examples.ipynb: notebook with the code for the examples in the presentation.
• computer exercise.ipynb: the computer exercise (implementing ABC rejection sampling for the g-and-k distribution).
• computer exercise solutions.ipynb: solutions for computer exercise.
• cars.csv: the speed and stopping distance for 1920s cars dataset (see https://stat.ethz.ch/R-manual/R-patched/library/datasets/html/cars.html).
• /fig: figures for the presentation and computer exercise.

Software

We will use Julia 1.0.3 (https://julialang.org/) for the examples and exercise.

The easiest way to run the code for the examples and the exercise is to use JuliaBox (https://www.juliabox.com/). To run the code that we use with JuliaBox then:

1. Go to https://www.juliabox.com/ and create a free account.
2. Clone (or download) this repo to your local computer.
3. In the JuliaBox start scree, click on the launch button and upload following files to your jupyter environment: computer exercise.ipynd, computer exercise solutions.ipynd, examples.ipynd, and cars.csv.
4. You can now run the examples and work on the computer exercise.

To get started with Julia there are some tutorials provided in JuliaBox.

An alternative is to run everything on your local computer, which might be preferable if you already have installed Julia.

Resources and further reading

Bayesian statistics:

Carpenter, Bob, et al. "Stan: A probabilistic programming language." Journal of statistical software 76.1 (2017. - Stan is a probabilistic programming framework for building Bayesian models.

Bernardo, José M.. BAYESIAN STATISTICS https://www.uv.es/bernardo/BayesStat.pdf - A nice and easy to read introduction paper, however, I would skip the objective Bayesian part.

Gabry, Jonah, et al. "Visualization in Bayesian workflow." Journal of the Royal Statistical Society: Series A (Statistics in Society) 182.2 (2019): 389-402. - A good paper on how run a Bayesian analysis, including prior and posterior checks.

Gelman, Andrew, Daniel Simpson, and Michael Betancourt. "The prior can often only be understood in the context of the likelihood." Entropy 19.10 (2017): 555. - A very good paper on how to interpretation the prior and how the prior and posterior and combined in a Bayesian analysis.

Robert, Christian P.. The Bayesian Choice. - A quite theory-heavy book on Bayesian statistics.

Yildirim, Ilker. "Bayesian Inference: Metropolis-Hastings Sampling." Dept. of Brain and Cognitive Sciences, Univ. of Rochester, Rochester, NY (2012) - A easy-to-read note on the Metropolis-Hastings algorithm

ABC:

Drovandie, Christopher C. "Approximate Bayesian Computation." In wiley StatsRef: Statistics References Online. John Wiley & Sons Lt,Ltd. pp 1-9, 2017. - A nice and easy-to-read introduction paper.

Marin, Jean-Michel, et al. "Approximate Bayesian computational methods." Statistics and Computing 22.6 (2012): 1167-1180. - A good (but slightly old review paper).

Sisson, Scott A., and Yanan Fan. "Likelihood-free markov chain monte carlo." arXiv preprint arXiv:1001.2058 (2010). - A paper on ABC-MCMC.

Sisson, Scott A., Yanan Fan, and Mark Beaumont. Handbook of approximate Bayesian computation. Chapman and Hall/CRC, 2018. - The handbook of ABC, a book on ABC that covers many topics.

https://xianblog.wordpress.com/2019/07/28/introductory-overview-lecture-the-abc-of-abc/ - The slides from Christian P. Robert'sgit JMS lectur.