The AstroStat Slog

Is there an objective method to combine measurements of the same quantity obtained with different instruments?

Suppose you have a set of N₁ measurements obtained with one detector, and another set of N₂ measurements obtained with a second detector. And let’s say you wanted something as simple as an estimate of the mean of the quantity (say the intensity) being measured. Let us further stipulate that the measurement errors of each of the points is similar in magnitude and neither instrument displays any odd behavior. How does one combine the two datasets without appealing to subjective biases about the reliability or otherwise of the two instruments? Continue reading ‘[Q] Objectivity and Frequentist Statistics’ »

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’ »

The Bootstrap and Modern Statistics Brad Efron (2000), JASA Vol. 95 (452), p. 1293-1296.

If the bootstrap is an automatic processor for frequentist inference, then MCMC is its Bayesian counterpart.

Continue reading ‘[Quote] Bootstrap and MCMC’ »

The paper about the Banff challenge [0712.2708] and the statistics tutorial for cosmologists [0712.3028] are the personal recommendations from this week’s [arXiv] list. Especially, I’d like to quote from Licia Verde’s [astro-ph:0712.3028],

In general, Cosmologists are Bayesians and High Energy Physicists are Frequentists.

I thought it was opposite. By the way, if you crave for more papers, click Continue reading ‘[ArXiv] 3rd week, Dec. 2007’ »

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?’ »