Archive for Roberto Trotta

Bayesian methods in cosmology

Posted in Statistics with tags , , , , , , , , , , , , on January 18, 2017 by xi'an

A rather massive document was arXived a few days ago by Roberto Trotta on Bayesian methods for cosmology, in conjunction with an earlier winter school, the 44th Saas Fee Advanced Course on Astronomy and Astrophysics, “Cosmology with wide-field surveys”. While I never had the opportunity to give a winter school in Saas Fee, I will give next month a course on ABC to statistics graduates in another Swiss dream location, Les Diablerets.  And next Fall a course on ABC again but to astronomers and cosmologists, in Autrans, near Grenoble.

The course document is an 80 pages introduction to probability and statistics, in particular Bayesian inference and Bayesian model choice. Including exercises and references. As such, it is rather standard in that the material could be found as well in textbooks. Statistics textbooks.

When introducing the Bayesian perspective, Roberto Trotta advances several arguments in favour of this approach. The first one is that it is generally easier to follow a Bayesian approach when compared with seeking a non-Bayesian one, while recovering long-term properties. (Although there are inconsistent Bayesian settings.) The second one is that a Bayesian modelling allows to handle naturally nuisance parameters, because there are essentially no nuisance parameters. (Even though preventing small world modelling may lead to difficulties as in the Robbins-Wasserman paradox.) The following two reasons are the incorporation of prior information and the appeal on conditioning on the actual data.

trottaThe document also includes this above and nice illustration of the concentration of measure as the dimension of the parameter increases. (Although one should not over-interpret it. The concentration does not occur in the same way for a normal distribution for instance.) It further spends quite some space on the Bayes factor, its scaling as a natural Occam’s razor,  and the comparison with p-values, before (unsurprisingly) introducing nested sampling. And the Savage-Dickey ratio. The conclusion of this model choice section proposes some open problems, with a rather unorthodox—in the Bayesian sense—line on the justification of priors and the notion of a “correct” prior (yeech!), plus an musing about adopting a loss function, with which I quite agree.

the latest Significance: Astrostats, black swans, and pregnant drivers [and zombies]

Posted in Books, Kids, pictures, Statistics, Travel, University life with tags , , , , , , , , , , on February 4, 2015 by xi'an

Reading Significance is always an enjoyable moment, when I can find time to skim through the articles (before my wife gets hold of it!). This time, I lost my copy between my office and home, and borrowed it from Tom Nichols at Warwick with four mornings to read it during breakfast. This December issue is definitely interesting, as it contains several introduction articles on astro- and cosmo-statistics! One thing I had not noticed before is how a large fraction of the papers is written by authors of books, giving a quick entry or interview about their book. For instance, I found out that Roberto Trotta had written a general public book called the Edge of the Sky (All You Need to Know About the All-There-Is) which exposes the fundamentals of cosmology through the 1000 most common words in the English Language.. So Universe is replaced with All-There-Is! I can understand and to some extent applaud the intention, but it nonetheless makes for a painful read, judging from the excerpt, when researcher and telescope are not part of the accepted vocabulary. Reading the corresponding article in Significance let me a bit bemused at the reason provided for the existence of a multiverse, i.e., of multiple replicas of our universe, all with different conditions: multiplying the universes makes our more likely, while it sounds almost impossible on its own! This sounds like a very frequentist argument… and I am not even certain it would convince a frequentist. The other articles in this special astrostatistics section were of a more statistical nature, from estimating the number of galaxies to the chances of a big asteroid impact. Even though I found the graphical representation of the meteorite impacts in the past century because of the impact drawing in the background. However, when I checked the link to Carlo Zapponi’s website, I found the picture was a still of a neat animation of meteorites falling since the first report.

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