The AstroStat Slog

This question came to the CfA Public Affairs office, and I am sharing it with y’all because I think the solution is instructive.

A student had to figure out the name of a stellar object as part of an assignment. He was given the following information about it:

• apparent [V] magnitude = 5.76
• B-V = 0.02
• E(B-V) = 0.00
• parallax = 0.0478 arcsec
• radial velocity = -18 km/s
• redshift = 0 km/s

He looked in all the stellar databases but was unable to locate it, so he asked the CfA for help.

Just to help you out, here are a couple of places where you can find comprehensive online catalogs:

• Vizier
• W3Browse
• SIMBAD

See if you can find it!

Continue reading ‘An Instructive Challenge’ »

Sherpa is a fitting environment in which Chandra data (and really, X-ray data from any observatory) can be analyzed. It has just undergone a major update and now runs on python. Or allows python to run. Something like that. It is a very powerful tool, but I can never remember how to use it, and I have an amazing knack for not finding what I need in the documentation. So here is a little cheat sheet (which I will keep updating as and when if I learn more): Continue reading ‘Everybody needs crampons’ »

The Vatican adopts the FITS standard. Yes, really.

(via /.)

The Solar Dynamics Observatory, which promises a flood of data on the Sun, was launched today from Cape Kennedy.

A postdoc job announcement from Prof. Joshua Bloom of UC Berkeley:
http://members.aas.org/JobReg/JobDetailPage.cfm?JobID=26225
Continue reading ‘[Jobs] postdoc position at UC Berkeley’ »

The 2009 Physics Nobel is shared (along with Charles Kao, who is cited for suggesting optic fibers) by Willard Boyle and George Smith, inventors of the Charge-coupled Device.

The CCD, of course, is the workhorse of modern Astronomy. I cannot even imagine how things would be without it.
Continue reading ‘Boyle & Smith (1969)’ »

From a poem submitted to the Chinese National Bureau of Statistics:

因为有了统计
我可以把天上的星星重新梳理

Because of statistics
I can rearrange the stars in the skies above

Indeed. Especially so when the PSF is broad and the stars overlap.

(via)

Is Calculus the ultimate goal of mathematical education? Arthur Benjamin has a slightly subversive suggestion in this TED presentation.
Continue reading ‘Mt. Mathematics’ »

For someone who doesn’t know any grammar, I can be a bit of a Grammar nazi sometimes. And one of my pet peeves is when people use the word data in the singular. No! Data are!

Or so I used to believe. Continue reading ‘Datums’ »

http://www.tricki.org/

The wikipedia-like repository for mathematical “tricks” has now gone live. Their mission statement:

The main body of the Tricki will be a (large, if all goes according to plan) collection of articles about methods for solving mathematical problems. These will be everything from very general problem-solving tips such as, “If you can’t solve the problem, then try to invent an easier problem that sheds light on it,” to much more specific advice such as, “If you want to solve a linear differential equation, you can convert it into a polynomial equation by taking the Fourier transform.”

Probability density functions are another way of summarizing the consequences of assuming a Gaussian error distribution when the true distribution is Poisson. We can compute the posterior probability of the intensity of a source, when some number of counts are observed in a source region, and the background is estimated using counts observed in a different region. We can then compare it to the equivalent Gaussian.

The figure below (AAS 472.09) compares the pdfs for the Poisson intensity (red curves) and the Gaussian equivalent (black curves) for two cases: when the number of counts in the source region is 50 (top) and 8 (bottom) respectively. In both cases a background of 200 counts collected in an area 40x the source area is used. The hatched region represents the 68% equal-tailed interval for the Poisson case, and the solid horizontal line is the ±1σ width of the equivalent Gaussian.

Clearly, for small counts, the support of the Poisson distribution is bounded below at zero, but that of the Gaussian is not. This introduces a visibly large bias in the interval coverage as well as in the normalization properties. Even at high counts, the Poisson is skewed such that larger values are slightly more likely to occur by chance than in the Gaussian case. This skew can be quite critical for marginal results. Continue reading ‘Poisson vs Gaussian, Part 2’ »

We astronomers are rather fond of approximating our counting statistics with Gaussian error distributions, and a lot of ink has been spilled justifying and/or denigrating this habit. But just how bad is the approximation anyway?

I ran a simple Monte Carlo based test to compute the expected bias between a Poisson sample and the “equivalent” Gaussian sample. The result is shown in the plot below.

The jagged red line is the fractional expected bias relative to the true intensity. The typical recommendation in high-energy astronomy is to bin up events until there are about 25 or so counts per bin. This leads to an average bias of about 2% in the estimate of the true intensity. The bias drops below 1% for counts >50. Continue reading ‘Poisson vs Gaussian’ »

The iPhone App Store has a couple of apps that make life significantly easier for those of us inundated and overwhelmed by the stream of daily arXiv preprints. These are ArXivReader.app and ArXiv.app, both providing a means to browse and search the arXiv preprint database and both selling for 99c with the first selling for 99c and the second free. Check them out! The former even lets you save papers for off-line reading.

For me at least, the hardest part of going through the arXiv emails every day was to pick out the interesting papers in the deluge of text. These apps do the right thing and segregate the categories and highlight the titles. Fitts’ Law in action — suddenly the daily ritual is orders of magnitude more pleasant!

What XKCD says:


The mouseover text on the original says “Correlation doesn’t imply causation, but it does waggle its eyebrows suggestively and gesture furtively while mouthing ‘look over there’.”

It is a bad habit, hard to break, the temptation is great.

You would think that something like “measurement error” is a well-defined concept, and everyone knows what it means. Not so. I have so far counted at least 3 different interpretations of what it means.

Suppose you have measurements X={X_i, i=1..N} of a quantity whose true value is, say, X₀. One can then compute the mean and standard deviation of the measurements, E(X) and σ_X. One can also infer the value of a parameter θ(X), derive the posterior probability density p(θ|X), and obtain confidence intervals on it.

So here are the different interpretations:

1. Measurement error is σ_X, or the spread in the measurements. Astronomers tend to use the term in this manner.
2. Measurement error is X₀-E(X), or the “error made when you make the measurement”, essentially what is left over beyond mere statistical variations. This is how statisticians seem to use it, essentially the bias term. To quote David van Dyk
   

   For us it is just English. If your measurement is different from the real value. So this is not the Poisson variability of the source for effects or ARF, RMF, etc. It would disappear if you had a perfect measuring device (e.g., telescope).

3. Measurement error is the width of p(θ|X), i.e., the measurement error of the first type propagated through the analysis. Astronomers use this too to refer to measurement error.

Who am I to say which is right? But be aware of who you may be speaking with and be sure to clarify what you mean when you use the term!