The AstroStat Slog

Almost two year long scrutinizing some publications by astronomers gave me enough impression that astronomers live in the Gaussian world. You are likely to object this statement by saying that astronomers know and use Poisson, binomial, Pareto (power laws), Weibull, exponential, Laplace (Cauchy), Gamma, and some other distributions.^[1] This is true. I witness that these distributions are referred in many publications; however, when it comes to obtaining “BEST FIT estimates for the parameters of interest” and “their ERROR (BARS)”, suddenly everything goes back to the Gaussian world.^[2]

Borel Cantelli Lemma (from Planet Math): because of mathematical symbols, a link was made but any probability books have the lemma with proofs and descriptions.

Continue reading ‘Borel Cantelli Lemma for the Gaussian World’ »

1. It is a bit disappointing fact that not many mention the t distribution, even though less than 30 observations are available.[↩]
2. To stay off this Gaussian world, some astronomers rely on Bayesian statistics and explicitly say that it is the only escape, which is sometimes true and sometimes not – I personally weigh more that Bayesians are not always more robust than frequentist methods as opposed to astronomers’ discussion about robust methods.[↩]

Physicists believe that the Gaussian law has been proved in mathematics while mathematicians think that it was experimentally established in physics — Henri Poincare

Continue reading ‘Why Gaussianity?’ »

What if R. A. Fisher was hired by the Royal Observatory in spite that his interest was biology and agriculture, or W. S. Gosset^[1] instead of brewery? An article by E.L. Lehmann made me think this what if. If so, astronomers could have handled errors better than now. Continue reading ‘On the history and use of some standard statistical models’ »

1. Gosset’s pen name was Student, from which the name, Student-t in t-distribution or t-test was spawned.[↩]

I have been observing some sorts of misconception about statistics and statistical nomenclature evolution in astronomy, which I believe, are attributed to the lack of references in the astronomical society. There are some textbooks designed for junior/senior science and engineering students, which are likely unknown to astronomers. Example-wise, these books are not suitable, to my knowledge. Although I never expect astronomers to learn standard graduate (mathematical) statistics textbooks, I do wish astronomers go beyond Numerical Recipes (W. H. Press, S. A. Teukolsky, W. T. Vetterling, & B. P. Flannery) and Error Data Reduction and Analysis for the Physical Sciences (P. R. Bevington & D. K. Robinson). Here are some good ones written by astronomers, engineers, and statisticians: Continue reading ‘Books – a boring title’ »

Seven preprints were chosen this week and two mentioned model selection. Continue reading ‘[ArXiv] 3rd week, Jan. 2008’ »

This will be the last [ArXiv] of this year (for some of you, the previous year). Continue reading ‘The last [ArXiv] of 2007’ »