The AstroStat Slog

Astrophysics, especially high-energy astrophysics, is all about counting photons. And this, it is said, naturally leads to all our data being generated by a Poisson process. True enough, but most astronomers don’t know exactly how it works out, so this derivation is for them. Continue reading ‘Poisson Likelihood [Equation of the Week]’ »

Not many this week, but there’s a great read. Continue reading ‘[ArXiv] 3rd week, May 2008’ »

The gamma function [not the Gamma -- note upper-case G -- which is related to the factorial] is one of those insanely useful functions that after one finds out about it, one wonders “why haven’t we been using this all the time?” It is defined only on the positive non-negative real line, is a highly flexible function that can emulate almost any kind of skewness in a distribution, and is a perfect complement to the Poisson likelihood. In fact, it is the conjugate prior to the Poisson likelihood, and is therefore a natural choice for a prior in all cases that start off with counts. Continue reading ‘gamma function (Equation of the Week)’ »

Scheming arXiv:astro-ph abstracts almost an year never offered me an occasion that the fit of the Poisson distribution is tested in different ways, instead it is taken for granted by plugging data and (source) model into a (modified) χ² function. If any doubts on the Poisson distribution occur, the following paper might be useful: Continue reading ‘tests of fit for the Poisson distribution’ »

To be exact, the title of this posting should contain 5th week, Oct, which seems to be the week of EGRET. In addition to astro-ph papers, although they are not directly related to astrostatistics, I include a few statistics papers which may be profitable for astronomical data analysis. Continue reading ‘[ArXiv] 1st week, Nov. 2007’ »

From arxiv/math.st:0708.2153v1
Estimating the number of classes by Mao and Lindsay

This study could be linked to identifying the number of lines from Poisson nature x-ray count data, one of the key interests for astronomers. However, as pointed by the authors, estimating the numbers of classes is a difficult statistical problem. I.J.Good^[1] said that

I don’t believe it is usually possible to estimate the number of species, but only an appropriate lower bound to that number. This is because there is nearly always a good chance that there are a very large number of extremely rare species.

Continue reading ‘[ArXiv] Poisson Mixture, Aug. 16, 2007’ »

1. courtesy of the paper: Estimating the number of species: A review by Bunge and Fitzpatrick (1993), JASA, 88, 364-373.[↩]

I’ve been heard so much, without knowing fundamental reasons (most likely physics), about coverage problems from astrostat/phystat groups. This paper might be an interest for those: Interval Estimation in Exponential Families by Brown, Cai,and DasGupta ; Statistica Sinica (2003), 13, pp. 19-49

Abstract summary:
The authors investigated issues in interval estimation of the mean in the exponential family, such as binomial, Poisson, negative binomial, normal, gamma, and a sixth distribution. The poor performance of the Wald interval has been known not only for discrete cases but for nonnormal continuous cases with significant negative bias. Their computation suggested that the equal tailed Jeffreys interval and the likelihood ratio interval are the best alternatives to the Wald interval. Continue reading ‘Coverage issues in exponential families’ »