[ArXiv] 2nd week, Apr. 2008
Markov chain Monte Carlo became the most frequent and stable statistical application in astronomy. It will be useful collecting tutorials from both professions.
- [astro-ph:0804.0620] Q. Wu et al.
Late transient acceleration of the universe in string theory on $S^{1}/Z_{2}$ (MCMC) - [astro-ph:0804.0692] Corless, Dobke & King
The Hubble constant from galaxy lenses: impacts of triaxiality and model degeneracies (MCMC, Bayesian Modeling) - [astro-ph:0804.0788] Zamfir, Sulentic, & Marziani
New Insights on the QSO Radio-Loud/Radio-Quiet Dichotomy: SDSS Spectra in the Context of the 4D Eigenvector1 Parameter Space - [astro-ph:0804.0965] Bloom, Butler, & Perley
Gamma-ray Bursts, Classified Physically (instead of statistics, it relies on physics to grow a (classification) tree) - [astro-ph:0804.1089] G.K.Skinner
The sensitivity of coded mask telescopes - [astro-ph:0804.1197] Bagla, Prasad and Khandai
Effects of the size of cosmological N-Body simulations on physical quantities – III: Skewness - [astro-ph:0804.1447] Marsh, Ireland, & Kucera
Bayesian Analysis of Solar Oscillations - [astro-ph:0804.1532] C. LцЁpez-Sanjuan, C. E. Garcцa-DabцЁ, M. Balcells
A maximum likelihood method for bidimensional experimental distributions, and its application to the galaxy merger fraction - [astro-ph:0804.1536] V.J.Martinez (One of my favorite astronomers who brings in mathematics and statistics)
The Large Scale Structure in the Universe: From Power-Laws to Acoustic Peaks
vlk:
Glad to see that Larry Bretthorst’s Bayesian Fourier periodogram is finally being put to good use (Marsh, Ireland, & Kucera, astro-ph:0804.1447). I remember coming across it first in 1995! (There is an IDL implementation too by Paul Barrett from c.1996) It is easy to implement, and easy to run, and produces a natural probability for each frequency (unlike FFTs where you have to appeal to various sketchy statistics), though there is that limitation of the assumption of Gaussian noise. Also, background flux is not included, though that is not such a big problem for frequency analysis.
04-11-2008, 12:25 pmTomLoredo:
Vinay et al.-
We (my collaboration with the Duke folks) have been using Larry’s more general algorithm to build a “Kepler periodogram” for exoplanet detection and measurement. Jeff Scargle and I independently came up with the idea several years ago, for SIM exoplanet proposals, but never developed it (there was no public data and no funding at the time). In the meantime, Andrew Cumming invented something similar, and more recently, Ford and Gregory have made great progress with classic MCMC algorithms. We’re using it, not so much to get final answers, but as a step in accelerating an adpative MCMC algorithm.
I think the application that has been dying for application of the Bretthorst algorithm is asteroseismology using Whole Earth Telescope (WET) data. That whole field has been relying on primitive time series methods for way too long. In fact, one can argue that the case for the WET rested on mediocre time series methods; methods like the Bretthorst algorithm can handle gaps in data that the WET was designed to try to fill in. Brendon Brewer, who participated in the SAMSI astrostat program in 2006, recently published a paper bringing Bayesian ideas into asteroseismology. I haven’t looked at it in detail, but my recollection is that it was an MCMC-based approach. I suspect a Bretthorst-like approach might have more impact, in that it might be more easily understood by astronomers used to thinking about periodograms. This is an area on my “to do” list to explore—if I only I didn’t have to spend so much of my time writing proposals!
04-11-2008, 3:35 pmTomLoredo:
PS: My Python Inference package has a Bretthorst algorithm module that makes it nearly trivial to implement the general algorithm—you just pass a list of basis functions (sin and cos for the basic periodogram; Keplerian orbit terms for a Kepler periodogram, etc.), and it creates an object that processes data to give you the log posterior for nonlinear parameters (periodogram for the sin/cos basis), estimated amplitudes, info for Bayes factors, etc.. Inference also has a “Bayesian harmonic analysis” module that makes some optimizations for the “sum of harmonic sinusoids” case. The Inference package is too “alpha” to be really useful at the moment, but those two packages are farther along than the rest.
04-11-2008, 3:40 pm