The AstroStat Slog

We organized a Special Session on Time Series in High Energy Astrophysics: Techniques Applicable to Multi-Dimensional Analysis on Sep 7, 2011, at the AAS-HEAD conference at Newport, RI. The talks presented at the session are archived at http://hea-www.harvard.edu/AstroStat/#head2011

A tremendous amount of information is contained within the temporal variations of various measurable quantities, such as the energy distributions of the incident photons, the overall intensity of the source, and the spatial coherence of the variations. While the detection and interpretation of periodic variations is well studied, the same cannot be said for non-periodic behavior in a multi-dimensional domain. Methods to deal with such problems are still primitive, and any attempts at sophisticated analyses are carried out on a case-by-case basis. Some of the issues we seek to focus on are methods to deal with are:
* Stochastic variability
* Chaotic Quasi-periodic variability
* Irregular data gaps/unevenly sampled data
* Multi-dimensional analysis
* Transient classification

Our goal is to present some basic questions that require sophisticated temporal analysis in order for progress to be made. We plan to bring together astronomers and statisticians who are working in many different subfields so that an exchange of ideas can occur to motivate the development of sophisticated and generally applicable algorithms to astronomical time series data. We will review the problems and issues with current methodology from an algorithmic and statistical perspective and then look for improvements or for new methods and techniques.

Here’s a cool illustration of how to use Bayesian analysis in the limit of very little data, when inferences are necessarily dominated by the prior. The question, via Tom Moertel, is: suppose I tell you that a coin always comes up heads, and you proceed to toss it and it does come up heads — how much more do you believe me now?

He also has the answer worked out in detail.

(h/t Doug Burke)

Andrew Gelman says,

Instead of “confidence interval,” let’s say “uncertainty interval”

There is an ambitious project afoot to build a 3D map of a meteor stream during the Perseids on Aug 11-12. I got this missive about it from the organizer, Chris Crawford:

This will be one of the better years for Perseids; the moon, which often interferes with the Perseids, will not be a problem this year. So I’m putting together something that’s never been done before: a spatial analysis of the Perseid meteor stream. We’ve had plenty of temporal analyses, but nobody has ever been able to get data over a wide area — because observations have always been localized to single observers. But what if we had hundreds or thousands of people all over North America and Europe observing Perseids and somebody collected and collated all their observations? This is crowd-sourcing applied to meteor astronomy. I’ve been working for some time on putting together just such a scheme. I’ve got a cute little Java applet that you can use on your laptop to record the times of fall of meteors you see, the spherical trig for analyzing the geometry (oh my aching head!) and a statistical scheme that I *think* will reveal the spatial patterns we’re most likely to see — IF such patterns exist. I’ve also got some web pages describing the whole shebang. They start here:

http://www.erasmatazz.com/page78/page128/PerseidProject/PerseidProject.html

I think I’ve gotten all the technical, scientific, and mathematical problems solved, but there remains the big one: publicizing it. It won’t work unless I get hundreds of observers. That’s where you come in. I’m asking two things of you:

1. Any advice, criticism, or commentary on the project as presented in the web pages.
2. Publicizing it. If we can get that ol’ Web Magic going, we could get thousands of observers and end up with something truly remarkable. So, would you be willing to blog about this project on your blog?
3. I would be especially interested in your comments on the statistical technique I propose to use in analyzing the data. It is sketched out on the website here:

http://www.erasmatazz.com/page78/page128/PerseidProject/Statistics/Statistics.html

Given my primitive understanding of statistical analysis, I expect that your comments will be devastating, but if you’re willing to take the time to write them up, I’m certainly willing to grit my teeth and try hard to understand and implement them.

Thanks for any help you can find time to offer.

Chris Crawford

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’ »