The AstroStat Slog

This is a quite long paper that I separated from [Arvix] 4th week, Feb. 2008:
      [astro-ph:0802.3916] P. Carvalho, G. Rocha, & M.P.Hobso
      A fast Bayesian approach to discrete object detection in astronomical datasets – PowellSnakes I
As the title suggests, it describes Bayesian source detection and provides me a chance to learn the foundation of source detection in astronomy.

First, I’d like to point out that my initial concerns from [astro-ph:0707.1611] Probabilistic Cross-Identification of Astronomical Sources are explained in sections 2, 3 and 6 about parameter space, its dimensionality, and priors in Bayesian model selection.

Second, I’d rather concisely list the contents of the paper as follows: (1) priors, various types but rooms were left for further investigations in future; (2) templates (such as point spread function, I guess), crucial for defining sources, and gaussian random field for noise; (3) optimization strategies for fast computation (source detection implies finding maxima and integration for evidence); (4) comparison with other works; (5) upper bound, tuning the threshold for acceptance/rejection to minimize the symmetric loss; (6) challenges of dealing likelihoods in Fourier space from incorporating colored noise (opposite to white noise); (7) decision theory from computing false negatives (undetected objects) and false positives (spurious objects). Many issues in computing Bayesian evidence, priors, tunning parameter relevant posteriors, and the peaks of maximum likelihoods; and approximating templates and backgrounds are carefully presented. The conclusion summarizes their PowellSnakes algorithm pictorially.

Thirdly, although my understanding of object detection and linking it to Bayesian techniques is very superficial, my reading this paper tells me that they propose some clever ways of searching full 4 dimensional space via Powell minimization (It seems to be related with profile likelihoods for a fast computation but it was not explicitly mentioned) and the detail could direct statisticians’ attentions for the improvement of computing efficiency and acceleration.

Fourth, I’d like to talk about my new knowledge that I acquired from this paper about errors in astronomy. Statisticians usually surprise at astronomical catalogs that in general come with errors next to single measurements. These errors are not measurement errors (errors calculated from repeated observations) but obtained from Fisher information owing to Cramer-Rao Lower Bound. The template likelihood function leads this uncertainty measure on each observation.

Lastly, in astronomy, there are many empirical rules, effects, and laws that bear uncommon names. Generally these are sophisticated rules of thumb or approximations of some phenomenon (for instance, Hubble’s law, though it’s well known) but they have been the driving away factors when statisticians reading astronomy papers. On the other hand, despite overwhelming names, when it gets to the point, the objective of mentioning such names is very statistical like regression (fitting), estimating parameters and their uncertainty, goodness-of-fit, truncated data, fast optimization algorithms, machine learning, etc. This paper mentions Sunyaev-Zel’dovich effect, which name scared me but I’d like to emphasize that this kind nomenclature may hinder from understanding details but could not block any collaborations.