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Astronomical Data Analysis Software and Systems IV
ASP Conference Series, Vol. 77, 1995
R. A. Shaw, H. E. Payne, and J. J. E. Hayes, eds.
Statistical Consulting Center for Astronomy
E. D. Feigelson
Department of Astronomy & Astrophysics, Penn State University,
University Park PA 16802
M. G. Akritas, J. L. Rosenberger
Department of Statistics, Penn State University, University Park PA
16802
Abstract. We announce the formation of a Statistical Consulting
Center for Astronomy (SCCA), designed to provide prompt high­quality
advice on statistical and methodological issues to the astronomical
community. Questions should be sent by e­mail to scca@stat.psu.edu.
Questions and answers can be examined on the World Wide Web 1 .
1. Introduction
The astronomer extracting scientifically useful information from astronomical
data often encounters complex and subtle problems. Statistical techniques such
as least­squares model fitting, Kolmogorov­Smirnov two­sample test and ü 2
goodness­of­fit test can be applied to many simple situations, but are inad­
equate for other problems. A few examples of such data analysis problems
are: satellite surveys with flux limits and nondetections; discrimination be­
tween stars and galaxies in digitized optical surveys; detection of weak sources in
photon­counting detectors with variable backgrounds; characterization of quasi­
periodic or stochastically variable objects; identification of filaments and voids
in anisotropically clustered galaxies; analysis of the Lyman­ff forest in quasar
spectra; repeated application of calibration regressions in the cosmic distance
scale; and error analysis in all of these situations.
The field of mathematical statistics and its many areas of application (bio­
metrics, econometrics, chemometrics, geostatistics, quality control, etc.) have
made huge advances in recent decades. Mathematics libraries have dozens of
journals and hundreds of monographs on specialized problems in statistics that
are rarely if ever read by the astronomer. The problem encountered by an as­
tronomer has often been addressed, and perhaps clearly resolved, by statisticians
working in other fields. In other cases, the astronomical problem is methodolog­
ically unique, and its treatment might challenge a top statistician specializing
in the relevant field.
1 http://www.stat.psu.edu/scca/homepage.html
1

2
We have created the Statistical Consulting Center for Astronomy (SCCA)
to help bridge the wide gap between the astronomical and statistical communi­
ties. Through the SCCA, astronomers can ask a team of statisticians questions
about the data analysis problems they are facing today. If a good solution is
readily known, the SCCA will respond rapidly with an answer and guidance
into the appropriate statistical literature. If the problem is particularly tricky
or important, the SCCA will seek out top quality statisticians to consult with,
and possibly collaborate with, the astronomer.
The need for improved statistical treatment of astronomical data is clear. A
scan of the Astronomy & Astrophysics Abstracts indicates that 100--200 papers
are published annually are principally concerned with methodological issues in
the astronomical literature, and dozens of additional observational papers have
discussions of statistical issues. Statistical issues arising in astronomical data
analysis have been presented at a growing number of conferences (e.g., Jaschek &
Murtagh 1990; Feigelson & Babu 1992; Subbarao 1995; various ADASS and Eu­
ropean workshop proceedings). Yet except for the 1991 Penn State conference,
there has been little involvement of the academic and professional statistical
community in addressing the problems arising in astronomy.
2. Operation of the SCCA
The SCCA is a team of Penn State faculty with interest and expertise in statis­
tical problems arising in astronomical research. The Center has contacts with
experts in the international statistical community. The goals of the Center
are to: (1) address the immediate statistical needs of astronomers by providing
prompt high­quality statistical advice, (2) make publicly available questions and
answers for the benefit of the wider astronomical community, and (3) encourage
interdisciplinary collaboration between the fields of statistics and astronomy.
Any individual in the astronomical community can submit a question to the
SCCA: a graduate student preparing a dissertation; a scientist confronted with a
tricky data set, preparing or revising a paper for publication; a scientist prepar­
ing software for an instrument or a data analysis software system; or a scientist
organizing a major observational program. Incoming questions are reviewed
by the members of the team and colleagues in the Department of Statistics at
Penn State. Many questions will be answered in­house, but particularly com­
plex and important problems will be sent to top­ranked experts worldwide. The
turn­around time for answering straightforward problems should be no more
than three weeks. Summaries of questions and answers will be made publicly
available through the Internet/WWW and publications.
The operation of the SCCA is partially supported by the NASA Astro­
physics Data Program starting in fall 1994. Initially, consulting can be free of
charge to U.S. astronomers. However, we strongly encourage questioners to pay
a nominal fee for the service. This will ensure the continuance of the Center
into the future, and the availability of top­quality external consultants.
When a question for the SCCA arises, astronomers should send e­mail to
scca@stat.psu.edu or FAX the Center at (814) 863--7114. Questions and an­
swers will be available by anonymous ftp at ftp.stat.psu.edu (cd to the pub/scca
directory) and on the World Wide Web at the SCCA Homepage.

3
3. Some Early Questions & Answers
Q: Can a partial correlation coefficient be applied to data with upper limits?
A: One can construct a partial correlation coefficient for censored data using
(say) the generalized Kendall's Ü bivariate coefficient implemented in the ASURV
package (LaValley et al. 1992), but no tests of significance are available. In fact,
no significance testing method is available for the partial Kendall's Ü even with
uncensored data (Hettmansperger 1984, p. 208). For uncensored data, we rec­
ommend instead either multiple regression (Murtagh & Heck 1987) or Pearson's
linear partial correlation coefficient (Anderson 1984). Unfortunately, the exten­
sion of multivariate analysis to censored data has proved to be quite difficult
and there are no available methods. Thus, no fully satisfactory answer to your
question exists, but an expert in the field has promised to work on developing a
method for testing the hypothesis that the partial Kendall's Ü is zero.
Q: How can one assess the likelihood and amplitude of variability of an X­ray
source from ROSAT observations consisting of 20 disjoint good time intervals?
100­1000 total counts are collected, which is a bit low for the ü 2 test.
A: If you can confidently assume that the underlying distribution of counts
follows a Poisson distribution, we recommend the likelihood ratio test. You
want to test that – 1 = \Delta \Delta \Delta = – 20 = –, where – i times the exposure time t i gives
the expected counts E(X i ) in the i­th interval. The likelihood ratio statistic is
LR = 2
n
X
i=1
X i log(
X i
“ –t i
): (1)
If the hypothesis of no variability is true, then LR has a ü 2 distribution with
19 degrees of freedom. Thus, the null hypothesis is rejected at significance level
ff = 0:01 if LR ? 36:2. If the hypothesis of constancy is rejected, the amplitude
of variability can be examined from the estimated parameters “
– i = X i =t i . The
likelihood ratio test is presented in Hogg & Tanis (1993), and its use in astron­
omy under the Poisson hypothesis is discussed by Cash (1979).
Q: Consider two clusters of galaxies, one with N 1 = 80 galaxies with 40% spirals
and the other with N 2 = 120 galaxies with 70% spirals. Is the spiral fraction
difference significant?
A: Let “
p 1 = X 1 =N 1 , and “
p 2 = X 2 =N 2 be the two proportions. We can suggest
two test statistics for determining if the proportions are significantly different
(Arnold 1990; Miller, Freund, & Johnson 1990):
T 1 = “
p 1 \Gamma “
p 2
[ “
p 1 (1\Gamma “
p 1 )
N 1
+ “
p 2 (1\Gamma “ p 2 )
N 2
] 1=2
(2)
T 2 = “
p 1 \Gamma “
p 2
[ “
p(1 \Gamma “
p)(N \Gamma1
1 + N \Gamma1
2 )] 1=2
(3)
where “
p = (X 1 + X 2 )=(N 1 + N 2 ). Under the null hypothesis, both statistics
have a normal distribution with mean zero and variance one. T 2 is equivalent to
Pearson's ü 2 and is more commonly used, though its applicability is limited to

4
testing the null hypothesis. T 1 is a Wald­type statistic and can be used to give
confidence intervals for the true difference p 1 \Gamma p 2 . For the problem at hand,
the two proportions would be declared significantly different at significance level
ff = 0:01 if jT 2 j ? 2:58. Miller, Freund, & Johnson (1990) also consider a k­
sample version of this statistic.
Q: I am teaching a graduate course on astronomical techniques, and would like
to include a short section on Bayesian analysis. Can you suggest a general
reference?
A: An excellent review of Bayesian inference in astronomy is given by Loredo
(1992) and further applications are discussed in Ripley (1992). Background
references might include Lindley (1965) and Howson & Urbach (1993).
Acknowledgments. The SCCA is partially funded by NASA grant NAS5­
32669.
References
Anderson, T. 1984, An Introduction to Multivariate Statistical Analysis (New
York, Wiley)
Arnold, S. 1990, Mathematical Statistics (Englewood Cliffs, Prentice­Hall), p.
386
Cash, W. 1979, ApJ, 228, 939
Feigelson, E. D., & Babu, G. J., eds. 1992, Statistical Challenges in Modern
Astronomy (New York, Springer­Verlag)
Hettmansperger 1984, Statistical Inference Based on Ranks (New York, Wiley)
Hogg, R., & Tanis, E. 1993, Probability and Statistical Inference (Macmillan)
Howson, C., & Urbach, P. 1993, Scientific Reasoning: The Bayesian Approach
(Chicago, Open Court)
Jaschek, C., & Murtagh, F. (eds.) 1990, Errors, Bias and Uncertainties in
Astronomy (Cambridge, Cambridge Univ. Press)
LaValley, M., Isobe, T., & Feigelson, E. 1992, BAAS (Software Report), 24, 839
Lindley, D. 1965, Introduction to Probability and Statistics from a Bayesian
Viewpoint, 2 vols., (Cambridge, Cambridge Univ. Press)
Loredo, T. 1992, in Statistical Challenges in Modern Astronomy, eds. E. D.
Feigelson & G. J. Babu (New York, Springer­Verlag), 275
Miller, I., Freund, J., & Johnson, R. 1990, Probability and Statistics for Engi­
neers (Englewood Cliffs, Prentice­Hall), p. 282
Murtagh, F., & Heck, A. 1987, Multivariate Data Analysis (Dordrecht, Kluwer)
Ripley, B. D. 1992, in Statistical Challenges in Modern Astronomy, eds. E. D.
Feigelson & G. J. Babu (New York, Springer­Verlag), p. 329
Subbarao, T., ed. 1995, Applications of Time Series Analysis to Astronomy and
Meteorology (New York, Chapman­Hall)