Introducing the mathematics of Bayesian field inference & astro ph round-up …

Happily I can announce the arXiving of my conference proceedings from the IAUS306 meeting in Lisbon: link.  The title of this short (4 page) article is “What we talk about when we talk about fields”, and its purpose is to provide a brief introduction to the mathematics of Bayesian inference over infinite-dimensional fields (functions, or random measures) and to point out a few contemporary techniques for field inference from the statistics literature.  More specifically the aim is to bring to the attention of astronomers/cosmologists the measure-theoretic language used to describe field inference in mainstream statistics, as contrasting with the informal language of path-integration which we’ve inherited from physics.  Whether or not anyone actually reads this I’m satisfied that I’ve written it down because it’s exactly what I would have wanted to read (but couldn’t find anywhere) when I first started my research in this area.  I’d probably also have liked to be pointed towards Rosenthal’s “First Look at Rigorous Probability Theory”: I highly recommend it!

Interesting development over at a fellow young Bayesian’s blog, entsophy.net (warning: not safe for work). At face value it looks like the author has finally put voice to the feelings many of us in low-paid/stressful/uncertain untenured positions hold towards that fraction (perhaps 50%?) of senior scientists in well-paid tenured positions that we see taking a free ride: if we had the opportunity you have we’d sure not be resting on our laurels!  On the other hand, there’s not much explanation so it could be his account was hacked? Hmmm …

A few interesting papers on astro ph recently (other than my conference proceedings).  Daniel Kelson has a paper looking at how the tightness of the SFR to stellar mass relation might be a simple consequence of the central limit theorem, assuming that star formation follows some sort of stochastic process.  In some ways I didn’t feel that the paper was very successful in the sense that it presents a long review of stochastic processes and martingales (sans measure) yet ultimately there seems to be little physical motivation to explain what sort of stochastic process should best represent star formation in galaxies and in what circumstances this approach would provide better insights than the current default of non-stochastic star formation used for modelling.  Nevertheless, good to see martingales appearing in astronomy; it will make us more attractive to the financial institutions which can be an important source of jobs for those leaving the academic path.  Another interesting paper was that by Fournier et al. on stochastic excitation models for solar oscillations. I haven’t fully digested this one yet but I was excited myself to see that recurrence relations were key to their solutions: the ability to recognise problems amenable to solution by recurrence relations is an important skill for the applied mathematician!

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