Archive for August 2007

Quote of the Week, Aug 31, 2007

Once again, the middle of a recent (Aug 30-31, 2007) argument within CHASC, on why physicists and astronomers view “3 sigma” results with suspicion and expect (roughly) > 5 sigma; while statisticians and biologists typically assume 95% is OK:

David van Dyk (representing statistics culture):

Can’t you look at it again? Collect more data?

Vinay Kashyap (representing astronomy and physics culture):

…I can confidently answer this question: no, alas, we usually cannot look at it again!!

Ah. Hmm. To rephrase [the question]: if you have a “7.5 sigma” feature, with a day-long [imaging Markov Chain Monte Carlo] run you can only show that it is “>3sigma”, but is it possible, even with that day-long run, to tell that the feature is really at 7.5sigma — is that the question? Well that would be nice, but I don’t understand how observing again will help?

David van Dyk :

No one believes any realistic test is properly calibrated that far into the tail. Using 5-sigma is really just a high bar, but the precise calibration will never be done. (This is a reason not to sweet the computation TOO much.)

Most other scientific areas set the bar lower (2 or 3 sigma) BUT don’t really believe the results unless they are replicated.

My assertion is that I find replicated results more convincing than extreme p-values. And the controversial part: Astronomers should aim for replication rather than worry about 5-sigma.

[ArXiv] Numerical CMD analysis, Aug. 28th, 2007

From arxiv/astro-ph:0708.3758v1
Numerical Color-Magnitude Diagram Analysis of SDSS Data and Application to the New Milky Way Satellites by J. T. A. de Jong et. al.

The authors applied MATCH (Dolphin, 2002[1] -note that the year is corrected) to M13, M15, M92, NGC2419, NGC6229, and Pal14 (well known globular clusters), and BooI, BooII, CvnI, CVnII, Com, Her, LeoIV, LeoT, Segu1, UMaI, UMaII and Wil1 (newly discovered Milky Way satellites) from Sloan Digital Sky Survey (SDSS) to fit Color Magnitude diagrams (CMDs) of these stellar clusters and find the properties of these satellites.
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  1. Numerical methods of star formation history measurement and applications to seven dwarf spheroidals,Dolphin (2002), MNRAS, 332, p. 91[]

The future of Very High Energy Gamma-Ray Astronomy

Quote of the Week, Aug 23, 2007

These are from two lively CHASC discussions on classification, or cluster analysis. The first was on Feb 7, 2006; the continuation on Dec 12, 2006, at the Harvard Statistics Department, as part of Stat 310 .

David van Dyk:

Don’t demand too much of the classes. You’re not going to say that all events can be well-classified…. It’s more descriptive. It gives you places to look. Then you look at your classes.

Xiao Li Meng:

Then you’re saying the cluster analysis is more like -

David van Dyk:

It’s really like you have a propsal for classes. You then investigate the physical processes more thoroughly. You may have classes that divide it [up]


David van Dyk:

But it can make a difference, where you see the clusters, depending on your [parameter] transformation.You can squish the white spaces, and stretch out the crowded spaces; so it can change where you think the clusters are.

Aneta Siemignowska:

But that is interesting.

Andreas Zezas:

Yes, that is very interesting.

These are particularly in honor of Hyunsook Lee‘s recent posting of Chattopadhyay et. al.’s new work about possible intrinsic classes of gamma-ray bursts. Are they really physical classes — or do they only appear to be distinct clusters because we view them through the “squished” lens (parameter spaces) of our imperfect instruments?

[ArXiv] Isochrone database, Aug. 20, 2007

From arxiv/astro-ph:0708.1204v3
An Isochrone Database and a Rapid Model for Stellar Population Synthesis by Li and Han

This paper emphasize the binary population: CMD fitting with the binary population synthetic model outperformed to the single population model. They used Hurley code (Hurley, Tout, and Pols (2002). Evolution of binary stars and the effect of tides on binary populations, MNRAS, 329(4), p.897-928). They mentioned that two color-color grids can disentangle the age-metallicity degeneracy via binary stellar populations. They fitted their isochrone database to M67 and NGC 1868 with the gT-grid and concluded that the database of binary stellar populations fitted the color magnitude diagrams better.
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Mmm.. donuts

Mmm.. chi-square!

The withering criticisms Hyunsook has been directing towards the faulty use of chisquare by astronomers brings to mind this classic comment by [astronomer] Jeremy Drake during the 2005 Chandra Calibration Workshop: Continue reading ‘Mmm.. donuts’ »

Cross-validation for model selection

One of the most frequently cited papers in model selection would be An Asymptotic Equivalence of Choice of Model by Cross-Validation and Akaike’s Criterion by M. Stone, Journal of the Royal Statistical Society. Series B (Methodological), Vol. 39, No. 1 (1977), pp. 44-47.
(Akaike’s 1974 paper, introducing Akaike Information Criterion (AIC), is the most often cited paper in the subject of model selection).
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An alternative to MCMC?

I think of Markov-Chain Monte Carlo (MCMC) as a kind of directed staggering about, a random walk with a goal. (Sort of like driving in Boston.) It is conceptually simple to grasp as a way to explore the posterior probability distribution of the parameters of interest by sampling only where it is worth sampling from. Thus, a major savings from brute force Monte Carlo, and far more robust than downhill fitting programs. It also gives you the error bar on the parameter for free. What could be better? Continue reading ‘An alternative to MCMC?’ »

[ArXiv] Data-Driven Goodness-of-Fit Tests, Aug. 1, 2007

From arxiv/
Data-Driven Goodness-of-Fit Tests by L. Mikhail

Goodness-of-Fit tests have been essential in astronomy to validate the chosen physical model to observed data whereas the limits of these tests have not been taken into consideration carefully when observed data were put into the model for estimating the model parameters. Therefore, I thought this paper would be helpful to have a thought on the different point of views between the astronomers’ practice of goodness-of-fit tests and the statisticians’ constructing tests. (Warning: the paper is abstract and theoretical.)
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[ArXiv] Poisson Mixture, Aug. 16, 2007

From arxiv/
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.

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

[ArXiv] Gamma-ray albedo of the moon, Aug. 15, 2007

From arxiv/astro-ph:0705.3856
Gamma-ray albedo of the moon by Moskalenko and Porter

The title sounds very interesting although the significance of albedo spectra is not recognized by a statistician. This study was performed to utilize GLAST and PAMELA via Monte Carlo simulations (the toolkit for MC was GEANT 8.2) with EGRET data.

Coverage issues in exponential families

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’ »

Astrostatistics: Goodness-of-Fit and All That!

During the International X-ray Summer School, as a project presentation, I tried to explain the inadequate practice of χ^2 statistics in astronomy. If your best fit is biased (any misidentification of a model easily causes such bias), do not use χ^2 statistics to get 1σ error for the 68% chance of capturing the true parameter.

Later, I decided to do further investigation on that subject and this paper came along: Astrostatistics: Goodness-of-Fit and All That! by Babu and Feigelson.
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[ArXiv] GRB host galaxies, Aug. 10, 2007

From arxiv/astro-ph:0708.1510v1
Connecting GRBs and galaxies: the probability of chance coincidence by Cobb and Bailyn

Without an optical afterglow, a galaxy within the 2 arc second error region of a GRB x-ray afterglow is identified as a host galaxy; however confusion can rise due to the facts that 1. the edge of a galaxy is diffused, 2. multiple sources could exist within 2 arc second error region, 3.the distance between the galaxy and the x-ray afterglow is measured by projection, and 4. lensing causes increase of brightness and position shifts. In this paper, the authors “investigated the fields of 72 GRBs in order to examine the general issue of associations between GRBs and host galaxies.”
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[Quote] Changing my mind (again)

From IMS Bulletin Vol. 36(7) p.10, Terence’s Stuff: Changing my mind (again)
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