Mixture models for magnetars …

A Bayesian-heavy dump on astro ph today but I did manage to squeeze in a read of one paper over lunch while simultaneously supervising various scripts running to generate our groups’ latest malaria incidence maps.  That paper was Daniela Huppenkothen’s “Dissecting magnetar variability with Bayesian hierarchical models“; overall this was an interesting read despite the hierarchy not actually extending to a simultaneous modelling of all magnetar bursts in their sample (flagged for future work).  One reason this paper was so interesting to me was that I was in fact present for the inception of the project at the MaxEnt2013 workshop.  The way I remember the banter regarding Daniela’s modelling problem (which may be some part simply a reflection of my skewed world view) the conversation as to how to represent these bursty time series was immediately ‘hijacked’ by the most charismatic speaker in the room and directed exclusively towards a discussion of Gaussian processes and their many wonders (*cough cough*).  When I finally got to talk with Daniela privately the next day I proposed a mixture model in which bursts were represented with a number of components sharing a common parametric form, which is surprisingly similar to the final model (except that I had suggested an infinite Dirichlet process mixture, whereas the authors ultimately choose a finite mixture representation) … and not a GP in sight. 🙂

All that aside the adopted mixture model (called a ‘superposition of bursts’ model in the paper) looks both well implemented with use of DNest3 (a version of diffusive nested sampling with birth/death proposals) and sufficiently flexible to extract the key features of these noisy bursts.  I’m not up to speed with the astrophysics literature on the physics of these bursts, but the final section caught my eye with its comparison to Self-Organised Criticality models (SOCs) since these are potentially an interesting case for Approximate Bayesian Computation; although for the particular types of bursts seen here they seem to be a poor model.  I look forward to reading the next instalment.

Minutiae: (i) There’s a typo in Equation 8: the sum should obviously be over N from N_min to N_max rather than n.  (ii) I would say that in (3.2) the spikes share a parameterisation rather than shape. (iii) The discussion of the truncated Cauchy [C(0,1)T(-21,21)] prior on log(mu_A) is a bit loose where it says “the Cauchy distribution ensures an ~0.5 chance of being close to unity.” [There’s an ~0.5 chance of log(mu_A) being >-1 and <1, i.e., close to zero, such that 0.5 of the prior mass on mu_A is between exp(-1) and exp(1), median of unity.]

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