Notes on basic ABC

[drphilmarshall]

Let's write some notes together. Feel free to suggest reading material below, and keep track of your own progress. Note that this issue will only be complete when all of our checkboxes are ticked!

Phil's reading list @drphilmarshall:

• [ ] Wikipedia page
• [x] Darren Wilkinson's introduction

Adam's reading list @abmantz :

• [ ]
• [ ]

Doug's reading list @deapplegate :

• [ ]
• [ ]

[drphilmarshall]

OK, the Wilkinson introductory blog post does indeed seem like a nice place to start with ABC - certainly enough to code up some toy examples. The idea is simply to simulate mock datasets from the prior and sampling distributions, and for each one compute a summary statistic (or a vector of them). In the simplest possible ABC routine, you simply reject X% of them for having summary statistics greater than epsilon different from the summary statistic computed on the real data, leaving you with an approximate posterior PDF for the model parameters. The size of epsilon (and therefore X) determine 1) how good an approximate posterior you end up with and 2) how many simulations you have to do to make it.

In the simple toy problem of inferring the width parameter of a Gaussian, a good summary statistic would be the variance of the simulated data points, but another could be the KS statistic, etc. The skill seems to be in defining summary statistics, and then later, doing better than just rejection sampling.

[ipashchenko]

Hi all! Concerning selection of summary statistic - you could be interested in this article. It uses ABC (explicitly:) for astrophysical study and explains how one can choose the best summary statistic in more-or-less human readable form:) "Best" means it permits the most accurate posterior mean determination and getting highest information content in posterior. There are also references to the original (mainly statistical) papers, describing selection of summary statistic in details.

P.S. By the way, one of the authors promotes the use of ABC in astronomy in his blog.

[drphilmarshall]

Thanks Ilya!

On Fri, May 22, 2015 at 10:55 PM, Ilya notifications@github.com wrote:

Hi all! Concerning selection of summary statistic - you could be interested in this article http://arxiv.org/abs/1202.1426. It uses ABC (explicitly:) for astrophysical study and explains how one can choose the best summary statistic in more-or-less human readable form:) "Best" means it permits the most accurate posterior mean determination and getting highest information content in posterior. There are also references to the original (mainly statistical) papers, describing selection of summary statistic in details.

P.S. By the way, one of the authors promotes the use of ABC in astronomy in his blog https://astrostatistics.wordpress.com/category/abc/.

— Reply to this email directly or view it on GitHub https://github.com/drphilmarshall/ABC/issues/2#issuecomment-104784826.