By Joseph M. Hilbe (auth.), Joseph M. Hilbe (eds.)

Astrostatistical demanding situations for the hot Astronomy offers a set of monographs authored by way of a number of of the disciplines major astrostatisticians, i.e. by means of researchers from the fields of information and astronomy-astrophysics, who paintings within the statistical research of astronomical and cosmological information. 8 of the 10 monographs are improvements of displays given by way of the authors as invited or precise themes in astrostatistics papers on the ISI global facts Congress (2011, Dublin, Ireland). the outlet bankruptcy, via the editor, was once tailored from an invited seminar given at Los Alamos nationwide Laboratory (2011) at the historical past and present nation of the self-discipline; the second one bankruptcy by means of Thomas Loredo used to be tailored from his invited presentation on the Statistical demanding situations in glossy Astronomy V convention (2011, Pennsylvania country University), providing insights concerning frequentist and Bayesian tools of estimation in astrostatistical research. the rest monographs are study papers discussing a variety of issues in astrostatistics. The monographs give you the reader with a very good evaluation of the present country astrostatistical examine, and provide instructions as to matters of destiny examine. Lead authors for every bankruptcy respectively comprise Joseph M. Hilbe (Jet Propulsion Laboratory and Arizona kingdom Univ); Thomas J. Loredo (Dept of Astronomy, Cornell Univ); Stefano Andreon (INAF-Osservatorio Astronomico di Brera, Italy); Martin Kunz ( Institute for Theoretical Physics, Univ of Geneva, Switz); Benjamin Wandel ( Institut d'Astrophysique de Paris, Univ Pierre et Marie Curie, France); Roberto Trotta (Astrophysics staff, Dept of Physics, Imperial collage London, UK); Phillip Gregory (Dept of Astronomy, Univ of British Columbia, Canada); Marc Henrion (Dept of arithmetic, Imperial collage, London, UK); Asis Kumar Chattopadhyay (Dept of information, Univ of Calcutta, India); Marisa March (Astrophysics staff, Dept of Physics, Imperial collage, London, UK).

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Normal distributions with two different variances). More sophisticated versions have since been developed for diverse applications. An astronomical example building on some of this expertise is the finite mixture modeling of stellar populations by [36], mentioned above. The most immediate lessons astronomers may draw from this literature are probably computational; for example, algorithms using data augmentation (which involves a kind of guided, iterative 36 Thomas J. Loredo Monte Carlo sampling of the class labels and weights) may be more effective for implementing BEAMS than the weight-stepping approach currently used.

I discussed this at some length at SCMA IV in 2006 [22], but even as of that time there was relatively little work in astronomy using hierarchical Bayesian methods, and for the most part only the simplest such models were used. The last few years mark a change-point in this respect, and evidence of the change is apparent in the contributions to the summer 2011 Bayesian sessions at both SCMA V and the ISI World Congress. Several presentations in both forums described recent and ongoing research developing sophisticated hierarchical models 2 Bayesian Astrostatistics 29 for complex astronomical data.

Together, these papers point to hierarchical Bayesian modeling as an important emerging research direction for astrostatistics. To illustrate the notion of a hierarchical model—also known as a multilevel model (MLM) — we start with a simple parametric density estimation problem, and then promote it to a MLM by adding measurement error. xI Â/ for an observable x. , a probability density rather than a galaxy number density). Consider first the case where we have a set of precise measurements of the observables, fxi g (and no selection effects).

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