Bayesian analysis of lunar laser
ranging data
William H. Jefferys
Judit Gyorgyey Ries
ABSTRACT
In 1969, astronauts first placed a retroreflector on the moon for laser ranging
of the moon, and since then the McDonald Observatory of the University
of Texas has been ranging to these and other later-placed retroreflectors.
By determining the round-trip time of a very short but powerful laser
pulse, important and extremely precise information about lunar motion and
earth rotation can be obtained. The problem is an interesting one from the
point of view of signal-to-noise, for in unfavorable circumstances, nearly
all of the detected photons are not laser returns but simply background
photons. Other interesting features of this problem are the fact that the
data are censored; and that it is necessary to take into account the Poisson
nature of the data. Determining which photons are actual returns is critical
to the initial data analysis. In this paper we describe how a Bayesian
analysis of the return data can be used to improve the results.

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