Summary of Feb. 8th meeting, by Tom Loredo

We had a productive meeting yesterday, with 10 group members present in person or teleconically (to coin a term).

A main topic of conversation regarding the two papers we discussed was the absence of the following characteristics of astronomical survey data in the existing literature applying survival analysis methods to such data:

• Accounting for measurement error for detected objects. It is not uncommon for the errors to be significant. E.g., for dim gamma-ray bursts (GRBs, the main area of application of the Efron-Petrosian work), the uncertainties can range from 20-50%. Since most sources are dim sources (due to the large volume sampling distant sources), the effect of these uncertainties is likely not negligible.
• Accounting for "soft" truncation. In some surveys an abrupt "cut" may adequately model the selection criteria. But often the cut is soft or probabilistic, and in many cases observers go to great lengths to accurately quantify this (e.g., via exposure maps and efficiency or selection functions).
• Accounting for "soft" censoring. For most objects treated as censored by the current methods, there is actually as much data (in the sense of numbers of pixels with photon counts) as there is for the detected objects. It's just that the data from an undetected source are consistent (at some confidence level) with there being no flux from the source. Put differently, there is a likelihood function for the source's flux that is not just a step function. It seems this information could be used, though it's not clear how much information it actually provides.

The statisticians present noted there is existing work on random truncation and random censoring that might address these issues. This will be the topic of future meetings, as will more explicit parametric treatment of of some of these complications.

Another significant topic was the "two cultures" of survey analysis: one approach ("model-based") that emphasizes forward modeling via likelihood and Bayesian methods and the survey selection function, the other ("design-based") based more on an "inverse problem" perspective, where the data get reweighted to account for unobserved objects. The model-based approach appears best suited for handling measurement error and is straightforward for parametric models, but there is little if any astrostat work on non- or semi-parametric modeling of surveys with this approach. In the design-based approach, nonparametric modelling is much more straightforward, but there is no astrostat work that brings to this approach the ability to handle biases due to source uncertainties (Malmquist, etc.) that is automatically handled in the model-based approach. We hope our group will find new directions to pursue to meld the two approaches, or at least transfer capability between them.

A few good sources of information (published and online) were cited in the discussion. The web page will soon have links to two papers by Martin Hendry and his colleagues on these topics, and information about how the 2MASS survey quantifies source uncertainties, both for detected and undetected objects.

I will again lead the next meeting. The topic will be a basic discussion of the effects of measurement error in size-frequency distributions (what astronomers often call "log N - log S" distributions).

In two weeks, we are tentatively scheduling presentations by Martin Hendry on Malmquist-Eddington bias, and Haywood Smith on Lutz-Kelker bias. The main goal is to communicate what astronomers mean by these terms to statisticians, in the hope that they have arisen and been treated in other disciplines, from which we might learn new techniques for handling them.

Future topics, without a firm date yet set:

• Random truncation and random censoring - Jogesh and Woncheol
• Frequentist model selection methods - Hyunsook
• Bayesian marginal likelihood computation - Hopefully with Merlise Clyde
• Cuts vs. weights - Tom and/or ???

If you'd like to prepare a presentation on any of these topics, or if there is another topic you'd like to lead a discussion on, please contact me. You needn't lead the full 1 1/2 hours; short contributions are very welcome (and perhaps preferable).

I'll send out a reminder soon about the next meeting.