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.

Abstracts are due Sep 17.

Meeting Justification

We propose to highlight the growing use of ‘non-parametric’ techniques to distill meaningful science from today’s astronomical data. Challenges range from Kuiper objects to cosmology. We have chosen just a few ‘teaching’ examples from this lively interdisciplinary area.

Meeting Notes

This ‘Astro-Statistics’ special session is proposed in concert with an ‘Astro-Informatics’ Special Session, organized by Kirk Bourne. In this proposed ‘Non-Parametrics for the Non-Specialist’ session, we are highlighting just a few of the new, outstanding, applications. Many are coming to fruition just now, in this age of large data-sets, complex instruments, and subtleties of distilling accurate science from indirect measurements. We chose to highlight: complex models (cosmology, black hole mass distributions); and complex data, such as image (spatial); and timing analyses (e.g. transients such as the distribution of Kuiper objecs) from surveys. We invited a mixture of newer and seasoned speakers; and ones that will make good ‘teaching examples’. At the same time, we left out many new areas. Hence we are planning a lively, associated, poster session. The format will be: An Intro by one of the seasoned statisticians; followed by ‘examples’ talks by two astronomers and a physicist. Following, another of the senior statisticians will discuss the principles. Finally, a senior astrophysicist will summarize challenges for the future. We plan to leave time for one-minute poster advertisements highlighting other areas. Expected participants include: Eric Feigelson, Brandon Kelly, Meyer Pesenson, Stanislav (George) Djorgovski, Tom Loredo, Alanna Connors, Pavlos Protopapas, Katrin Heitmann, Chad Schaefer, Xiao Li Meng.

When it comes to survey, the first thing comes in my mind is the census packet although I only saw it once (an easy way to disguise my age but this is true) but the questionaire layouts are so carefully and extensively done so as to give me a strong impression. Such survey is designed prior to collecting data so that after collection, data can be analyzed according to statistical methodology suitable to the design of the survey. Strategies for response quantification is also included (yes/no for 0/1, responses in 0 to 10 scale, bracketing salaries, age groups, and such, handling missing data) for elaborated statistical analysis to avoid subjective data transformation and arbitrary outlier eliminations.

In contrast, survey in astronomy means designing a mesh, not questionaires, unable to be transcribed into statistical models. This mesh has multiple layers like telescope, detector, and source detection algorithm, and eventually produces a catalog. Designing statistical methodology is not a part of it that draws interpretable conclusion. Collecting what goes through that mesh is astronomical survey. Analyzing the catalog does not necessarily involve sophisticated statistics but often times adopts chi-sq fittings and cast aways of unpleasant/uninteresting data points.

As other conflicts in jargon, –a simplest example is H_o: I used to know it as Hubble constant but now, it is recognized first as a notation for a null hypothesis — survey has been one of them and like the measurement error, some clarification about the term, survey is expected to be given by knowledgeable astrostatisticians to draw more statisticians involvement in grand survey projects soon to come. Luckily, the first opportunity will be given soon at the Special Session: Meaning from Surveys and Population Studies: BYOQ during the 213 AAS meeting, at Long Beach, California on Jan. 5th, 2009.

   $$\frac{1}{N(\theta)}\int_{\Omega} f(x;\theta)dx=1$$
   $$\frac{1}{N(x)}\int_{\Theta} f(x;\theta)d\theta=1$$
If you are Beyesian, Θ is the focus; otherwise, Ω. Regardless, finding N that satisfies the above relations is called normalization. And the difference between astronomers and statisticians is how Θ or Ω is treated.

For astronomers, in general, the integration occurs in the range of observed minimum (or zero, depending on what physics tells you) and observed maximum. Statisticians, generally, integrate over the whole parameter space that satisfies the measure theory; for example, if f(x;θ) is in the form of gaussian distribution, then (-∞, ∞).

This different trend occurs because of the different view points toward f(x;θ)/N (hereafter, f). For statisticians, the integration occurs over a properly defined measure space and f is a proper density function. For astronomers, the integration happens over a physically meaningful space and f is a viable model subject to the law of physics.

However, I want to warn astronomers transforming f defined on a physically meaningful space for statistical inference. Sometimes, statistical inferences is performed on f while this model f is the result of fitting, not a probability density function because astronomer’s f was not defined based on measure theory. It is clear that the variance from the truncated normal distribution is different from the one from the regular normal distribution. This will give different confidence interval at a given confidence level and the size of the interval, astronomers care so much about will vary.

The astronomers’ f is not necessarily to be pmf or pdf unless f is defined on a proper probability measure space. Without checking whether the normalized f is measurable, often times the 2nd derivative of f is derived for a fisher information or a covariance matrix from which error bars with a given confidence level are built. Due to the fact that astronomers’ f may not satisfy the basic probability axioms, the nominal coverage that one likes to compare with other results can be underestimated (in my opinion, it is the primary reason for the claim of improvement in the results in astronomical papers thanks to narrow intervals; however, one cannot claim such victory because underlying assumptions are inconsistent).

Since astronomers are so keen on error bars and coverage, I wish them to care fundamentals of probability theory on which statistical inference is built in their normalization process.

A disclaimer of mine is that I often see astronomers are well aware of the properties of pdfs in general. Narrow error bars from other types of statistical analysis are most likely legitimate.

— This is my last posting on my first AAS

I was browsing posters; there were so many but the acronym ANOVA couldn’t miss my eyes. I decided to take a look. The poster was made by an education graduate student who designed experiments on children and performed a statistical analysis (ANOVA) with collected data to find a factor that affects children (testing the significance of a factor via the F-test). Frankly, I didn’t read it through but was desperate to know the occasion in astronomy where ANOVA can be utilized. I was half excited because ANOVA appeared in the AAS meeting and half disappointed because ANOVA was not performed as a part of astronomical research. A train of thoughts, nonetheless, came along.

ANOVA or statistical methods from design of experiments may be of no use in astronomical experiments (collecting data by observations, i.e. collecting random incidents seems to not allow experiment designing stages). However, these methods can be used in evaluating proposals, summaries of projects’ quality, standardizing decision making processes, improving usages of instrument times, and so on. These statistical experiment design tools could be a servant to improve the procedures of collecting data and allocating time slots, and could amplify already tremendous efforts of renovating/creating expensive instruments.

Experiment design has never been of my interest because I could not see any chance of using them in astronomy. Upon finding ANOVA at the AAS, my second thought combined with my experience at CfA is now quite opposite to my first thought. There are plenty of rooms where well sought experiment design can be adopted in the astronomical society.

I saw a poster that said their result excels because they used the maximum likelihood test (hereafter, MLT) for a contour plot. At least this was my understanding after casual reading of the poster whilst I was focusing in finding the definition of the MLT. My guess was they obtained estimaties from maximum likelihood principles, such as using Cash statistics in X-ray data analysis.

It was interesting to see a dialect that gave me hard time to associate with the original meanings.

I’m not going to name the session, the speaker, nor the topic. Only relevant story related to regression analysis.

One of sessions, a speaker showed a slide with a headline, … test H_o…. My expectation was that H_o indicated a null hypothesis related to the expansion of the universe so that he was going to do a hypothesis testing. I was wrong. This H_o was the Hubble constant and his plan was estimating it with his carefully executed astrometry.

After a few slides later, I saw a straight line overplotted on top of scattered points. If I dissect the given space into 4×4, the most of points were occupied in the lower left corner section, and there was only one point placed in the section of the upper right corner. This single point had the most leverage that determines the slope of the line. Without verification, such as using Cook’s distance, I wondered what would happen with the estimated slope. Even with that high leverage point, I wondered if he still could claim with real statistics that his slope (H_o) estimate prefers the model by Freedman to the model by Sandage? To my naive eyes, the differences between the estimated slope from data and the two theoretical slopes are hardly distinguishable.

I saw papers in astronomy/astrophysics that carefully explain caveats of regression analysis on their target data and describe statistical tests to show the differences and similarities. Probably, the speaker didn’t want to disturb the audience with boring statistics. Yet, this was one of the occasions where my doubts toward astronomers who practice statistics in their own ways without consulting scholarly works in statistics sufficiently. The other likelihood is that I myself is biased to see things. I bet I’m the only one who expected that …test H_o… would accompany a null hypothesis and hypothesis tests, instead of estimating the Hubble constant.

The meeting website is at: http://www.confcon.com/head2008/.The abstract submission deadline is January 25, 2008 (now past, but late abstracts are not unheard of among astronomers).

If you are attending the meeting, and plan to present posters or talks that deal with astrostatistical methods or techniques, we welcome you to participate in this session. When you submit an abstract, be sure to indicate a category of “Other” and in the comments field state that it belongs with the AstroStatistics special session.If you have questions, please contact Aneta or me. There is also a page for this session on the astrostat google groups site.

Update (1/22): The abstract submission page currently says that only one abstract is allowed per person. We have been informed that this is incorrect, and that people can submit two abstracts, one for the special session and one as a regular contribution. Note that posters will be up only one day, and those associated with a special session will be put up the day of the session.

Update (1/26): A detailed program is not yet available, but here is a description of the session:

Astrostatistics: Methods and Techniques

This session will provide a forum for the discussion and presentation of statistical challenges in high energy astrophysics, highlighting the great deal of progress that has been made in methods and techniques over the past decade. The one hour session will cover the current and future directions in Astrostatistics, and will include a discussion of MCMC methods in the context of specific applications (such as propagating calibration errors, defining the significance of image features, etc.); a discussion of standardized methods for computing detection limits, upper limits, and confidence intervals for weak sources; and hypothesis testing and its limitations (including the significance testing of emission lines).

Update (2/19): We have been allocated the mid-day slot of March 31. The session will run from 12:30pm till 1:30pm2pm. The tentative program is as follows:

• Remarks on current and future trends in AstroStatistics, by Eric Feigelson
• Poster haiku
• F-Test theory and usage, by David van Dyk
• Discussion on MCMC techniques, led by Andy Ptak

Update (2/26): The final program is out, and the AstroStat session is scheduled for 12:30pm-2pm at the Museum/Bunker Hill Room.

Update (4/1): The talks and posters associated with the AstroStat special session are now online at
http://hea-www.harvard.edu/AstroStat/HEAD2008/. Additional comments and descriptions will be archived there.