The AstroStat Slog

Clauset, Shalizi, & Newman (2007, arXiv/0706.1062) have a very detailed description of what power-law distributions are, how to recognize them, how to fit them, etc. They are also making available their matlab and R codes that they use to do the fitting and such.

Looks like a very handy reference text, though I am a bit uncertain about their use of the K-S test to check whether a dataset can be described with a power-law or not. It is probably fine; perhaps some statisticians would care to comment?

Leccardi & Molendi (2007) have a paper in A&A (astro-ph/0705.4199) discussing the biases in parameter estimation when spectral fitting is confronted with low counts data. Not surprisingly, they find that the bias is higher for lower counts, for standard chisq compared to C-stat, for grouped data compared to ungrouped. Peter Freeman talked about something like this at the 2003 X-ray Astronomy School at Wallops Island (pdf1, pdf2), and no doubt part of the problem also has to do with the (un)reliability of the fitting process when the chisq surface gets complicated.

Anyway, they propose an empirical method to reduce the bias by computing the probability distribution functions (pdfs) for various simulations, and then averaging the pdfs in groups of 3. Seems to work, for reasons that escape me completely.

[Update: links to Peter's slides corrected]

Despite some recent significant advances in Statistics and its applications to Astronomy (Cash 1976, Cash 1979, Gehrels 1984, Schmitt 1985, Isobe et al. 1986, van Dyk et al. 2001, Protassov et al. 2002, etc.), there still exist numerous problems and limitations in the standard statistical methodologies that are routinely applied to astrophysical data. For instance, the basic algorithms used in non-linear curve-fitting in spectra and images have remained unchanged since the 1960′s: the downhill simplex method of Nelder & Mead (1965) modified by Powell, and methods of steepest descent exemplified by Levenberg-Marquardt (Marquardt 1963). All non-linear curve-fitting programs currently in general use (Sherpa, XSPEC, MPFIT, PINTofALE, etc.) with the exception of Monte Carlo and MCMC methods are implementations based on these algorithms and thus share their limitations.
Continue reading ‘On the unreliability of fitting’ »

Sometime early this year, Jeremy Drake asked this innocuous sounding question in the context of determining the bounds on the amplitude of an absorption line: Is the 3sigma error bar the same length as 3 times the 1sigma error bar?

In other words, if he measured the 99.7% confidence range for his model parameter, would it always be thrice as large as the nominal 1sigma confidence range? The answer is complicated, and depends on who you ask: Frequentists will say “yes, of course!”, Likelihoodists will say “Maybe, yeah, er, depends”, and Bayesians will say “sigma? what’s that?” So I think it would be useful to expound a bit more on this to astronomers, whose mental processes are generally Bayesian but whose computational tools are mostly Frequentist.
Continue reading ‘Is 3sigma the same as 3*1sigma?’ »