Change Point Problem
X-ray summer school is on going. Numerous interesting topics were presented but not much about statistics (Only advice so far, “use implemented statistics in x-ray data reduction/analysis tools” and “it’s just a tool”). Nevertheless, I happened to talk two students extensively on their research topics, finding features from light curves. One was very empirical from comparing gamma ray burst trigger time to 24kHz observations and the other was statistical and algorithmic by using Bayesian Block. Sadly, I could not give them answers but the latter one dragged my attention.
Recently I went to JSM 2007 and tried to attend talks about (bayesian) change point problems, which frequently appears in time series models, often found in economics. With ARCH (autoregressive conditional heteroskedecity) or GARCH (generalized ARCH) and by adding a parameter indicates a change point, I thought bayesian modeling could handle astronomical light curves.
Developing algorithms based on statistical theories, writing algorithms down in a heuristics way, making the code public, and finding/processing proper datum examples from huge astronomical data archives should come simultaneously, and this multiple steps make proposing new statistics to astronomical society difficult. I’m glad to know that there are individuals who are devoting themselves to make these steps happened. Unfortunately, they are loners.
vlk:
Yaming and Xiao-li have proposed just such an ARCH-like model (I do not know enough about ARCH to tell who I am insulting by comparing the two) to characterize astronomical light curves. See Poster 16.31, AAS-HEAD 2004. I believe that their method is actually more general than ARCH, and even works in the Poisson regime. Unfortunately, it needs to be validated, coded, and written up in an astronomer friendly way. Yaming started to do the validation using sunspot number data, but that exercise morphed into something completely different.
08-09-2007, 1:03 amhlee:
I received another type of changing point problem, defining a peak precisely, from a x-ray school student, who tried bayesian block but said it didn’t work. Defining peaks sounds like point estimation from functional data analysis. Eyes could tell the peak most easily and accurately but when it comes to automatization, I wonder what approaches were taken in astronomy. By the way, the student was interested in gamma ray burst light curves.
08-14-2007, 10:37 amvlk:
Finding the peak is indeed a huge problem. That is what is keeping us from a completely general algorithm for line and source detection (in spectra and images respectively). By its very nature, it is a multiscale problem, because it is not sufficient to just find the largest excursions in histograms of the data, but it needs to be done robustly. That is, a single large fluctuation in one bin should NOT overwhelm a nearby lower plateau where a number of adjacent bins are all showing similar deviations. This leads to the same issues encountered when trying to determine whether an extended feature in an image is real or not (see van Dyk & Connors, 2007, on Poisson Goodness-of-fit, SCMA IV)
08-14-2007, 1:11 pmvlk:
The Connors & van Dyk SCMA4 paper (with color figures) is now accessible online as a pdf document at the CHASC website.
08-17-2007, 6:09 pm