### 6. GRAVITATIONAL LENS STATISTICS

It is the opinion of the author that the statistics of lenses as a
method for determining the cosmological model has largely
ceased to be interesting. However, it is important to understand the
underlying physics because it determines the types of lenses we detect.
While most recent analyses have found cosmological results
consistent with the concordance model (Chae et al.
[2002],
Chae
[2003],
Davis, Huterer & Krauss
[2003],
Mitchell et al.
[2004])
there are still large statistical uncertainties
and some dangerous systematic assumptions. More importantly, there is
little prospect
at present of lens statistics becoming competitive with other methods.
Gravitational lenses statistics arguably begins with Press & Gunn
([1973]),
although the "modern" era begins with the introduction of
magnification bias (Turner
[1980]),
the basic statistics of normal galaxy lenses (Turner, Ostriker & Gott
[1984]),
cross sections and optical depths
for more general lenses (Blandford & Kochanek
[1987a],
Kochanek & Blandford
[1987]),
explorations of the effects of general cosmologies (Fukugita et al.
[1990],
Fukugita & Turner
[1991])
and lens structure (Maoz & Rix
[1993],
Kochanek
[1996a])
and the development of the general methodology of interpreting
observations (Kochanek
[1993b],
[1996a]).