The AstroStat Slog

I watched a movie in which one of the characters said, “country A has nukes with 80% chance” (perhaps, not 80% but it was a high percentage). One of the statements in that episode is that people will not eat lettuce only if the 1% chance of e coli is reported, even lower. Therefore, with such a high percentage of having nukes, it is right to send troops to A. This episode immediately brought me a thought about astronomers’ null hypothesis probability and their ways of concluding chi-square goodness of fit tests, likelihood ratio tests, or F-tests.

First of all, I’d like to ask how you would like to estimate the chance of having nukes in a country? What this 80% implies here? But, before getting to the question, I’d like to discuss computing the chance of e coli infection, first. Continue reading ‘The chance that A has nukes is p%’ »

[stat.AP:0811.1663]
Open Statistical Issues in Particle Physics by Louis Lyons

My recollection of meeting Prof. L. Lyons was that he is very kind and listening. I was delighted to see his introductory article about particle physics and its statistical challenges from an [arxiv:stat] email subscription. Continue reading ‘[ArXiv] Particle Physics’ »

From Protassov et al. (2002, ApJ, 571, 545), here is a formal expression for the Likelihood Ratio Test Statistic,

T_LRT = -2 ln R(D,Θ₀,Θ)

R(D,Θ₀,Θ) = [ sup_θεΘ0 p(D|Θ₀) ] / [ sup_θεΘ p(D|Θ) ]

where D are an independent data sample, Θ are model parameters {θ_i, i=1,..M,M+1,..N}, and Θ₀ form a subset of the model where θ_i = θ_i⁰, i=1..M are held fixed at their nominal values. That is, Θ represents the full model and Θ₀ represents the simpler model, which is a subset of Θ. R(D,Θ₀,Θ) is the ratio of the maximal (technically, supremal) likelihoods of the simpler model to that of the full model.
Continue reading ‘Likelihood Ratio Test Statistic [Equation of the Week]’ »

Why is it that detection of emission lines is more reliable than that of absorption lines?

That was one of the questions that came up during the recent AstroStat Special Session at HEAD2008. When you look at the iconic Figure 1 from Protassov et al (2002), which shows how the null distribution of the Likelihood Ratio Test (LRT) and how it holds up for testing the existence of emission and absorption lines. The thin vertical lines are the nominal F-test cutoffs for a 5% false positive rate. The nominal F-test is too conservative in the former case (figures a and b; i.e., actual existing lines will not be recognized as such), and is too anti-conservative in the latter case (figure c; i.e., non-existent lines will be flagged as real). Continue reading ‘The Flip Test’ »

One of the speakers from the google talk series exemplified model based clustering and mentioned the likelihood ratio test (LRT) for defining the number of clusters. Since I’ve seen the examples of ill-mannerly practiced LRTs from astronomical journals, like testing two clusters vs three, or a higher number of components, I could not resist indicating that the LRT is improperly used from his illustration. As a reply, the citation regarding the LRT was different from his plot and the test was carried out to test one component vs. two, which closely observes the regularity conditions. I was relieved not to find another example of the ill-used LRT. Continue reading ‘The LRT is worthless for …’ »

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