It’s been a few weeks since my last blog entry here, largely on account of the one person hack-a-thon I’ve been on in an attempt to extract every last drop of signal from an amazing serological dataset. Unlike parasite positivity for *Pf.* malaria which is detectable with slide microscopy for only a matter of weeks after infection, the antigenic response targeted by serological measurements can be present for decades (depending on the specific antigen); this means we can use observations of the age-seroprevalence function at a given location to infer a detailed history of transmission intensity, not just that of the present day. To do so one needs an efficient solver (uniformization algorithm) for the inhomogeneous, continuous-time, discrete-state Markov models that describe the acquisition and loss of the antigenic response. But once you have this it can be embedded in an almost arbitrarily complex hierarchical model such as those we use to build our *Pf*PR space-time cubes. So far my initial efforts in this direciton have been extremely encouraging, revealing intriguing heterogeneities in the malaria control history for a particular SE Asian country at both the regional and national scale. But enough about me!

The title of this particular blog post refers to Weijia’s new paper on the star cluster mass to galactocentric redius relation (on which I was a minor coauthor) accepted a couple of weeks by ApJ. A motivation for this work was to challenge the dubious analysis (and unusually strongly worded conclusions) of this paper by Pflamm-Altenburg et al. (the subject of a couple [1][2] of past blog posts here), and more importantly to make a rigorous investigation of the stochasticity of star cluster formation across the best available datasets from nearby galaxies (M33, M51, M83, and the Large Magellanic Cloud). The refereeing for this paper was appropriately challenging (given the controversial nature of the topic) but Weijia & Richard made a huge final push and ultimately carried this one over the line. Of particular interest from an astro-statistics perspective is that this analysis represents perhaps the first use of quantile regression in an astronomical context—and in doing so highlights the sophistication of this binless method in contrast to the clunkiness of the ad hoc alternative often adopted in astronomy of making a least squares fit against some arbitrary binning of the data.

[Thanks to facebook’s ‘history’ feature I was recently reminded how many years it was since I was fortunate to receive a tutorial in quantile regression from Koenker himself at the 5th R/Rmetrics conference in Meielisalp.]

Another blog-worthy happening in the past weeks was the visit of Jason Wyse from Dublin, who was invited to Oxford by Chris Holmes to share his tricks for efficient inference for Gaussian Markov Random Fields and in particular to describe his work on removing spurious signals (foreground dust, galactic synchrotron emission, etc.) from Cosmic Microwave Background maps. (An early version of this project appears on arXiv as Wilson & Yoon.) Amongst our discussions was the topic of how the SPDE approach to approximation of Gaussian processes on continuous domains by sparse GMRFs on appropriate discrete basis functions might be achievable for matter density power spectrum reconstructions. Almost surely this will involve a bespoke coding project rather than a quick application of the existing INLA tools, but Jason has experience with this since his CMB analysis was already coded outside the INLA library. In leiu of doing actual work for this nascent collaboration (which is really just talk and dreams at this stage) I am posting below some neat visualizations of the galaxy density field in a thin redshift slice modelled with INLA as a log Gaussian Cox process on a portion of the sphere (that is, a spherical manifold in 3D). This is one reason why the SPDE idea is so cool: you can define fields on manifolds directly as GMRFs for which the equivalent GP defined in covariance matrix form may be intractible or non-existant! Compare this to standard analyses confined to regular grids on the whole sphere (to take advantage of a circulant matrix structure) or on regular boxes/cubes (to take advantage of fast Fourier transformation techniques).

[A a density image texture wrapped on the sphere, or what OpenGL on a machine with a potato for a graphics card calls a sphere.]

[In orthographic projection on the sphere as a contour plot.]