In this section, we test the VELMOD method on simulated data sets.
Kolatt et al. (1996)
have produced simulated catalogs that mimic the properties of
both the *IRAS* redshift survey and the Mark III samples. We briefly
review the salient points here.

The mass density distribution of the
simulated universe is based on the distribution of *IRAS* galaxies in
the real universe. This was achieved by first taking the present redshift
distribution of *IRAS* galaxies and solving for a 500 km
s^{-1} smoothed, real-space distribution via an iterative procedure
that applies nonlinear corrections and a power-preserving
filter (Sigad et
al. 1997).
The smoothed, filtered *IRAS* density field was then "taken
back in time" using the Zeldovich-Bernoulli algorithm of
Nusser & Dekel (1992)
to obtain the linear initial density field. The
method of constrained realization
(Hoffman & Ribak 1991;
Ganon & Hoffman 1993)
was used to restore small-scale power down to galactic scales.
The resulting initial conditions were then evolved forward as an
=
1 *N*-body simulation using the PM code
of Gelb & Bertschinger
(1994).
The present-day density field resulting from this procedure is displayed in
Figure 6 of
Kolatt et al. (1996).

We generated a suite of 20 mock Mark III
and mock *IRAS* catalogs from this simulated
universe. ^{(9)}
Each mock Mark III
TF sample was constructed to mimic the distribution on the sky and in
redshift space of the corresponding real sample, and the TF relations and
scatters of the mock samples were chosen to be similar to the observed
ones. The mock TF samples were subject to selection criteria similar to
those imposed on the real samples. The mock *IRAS* redshift catalogs
were generated so as to resemble the actual *IRAS* 1.2 Jy redshift
survey. They have the true *IRAS* selection and luminosity functions
applied, and lack data in the *IRAS*-excluded zones
(cf. Strauss et
al. 1990). These data were then put
through exactly the same code that is used to derive predicted
peculiar velocity and density fields for the real data
(Appendix A).
To simplify the interpretation of the mock
catalog tests, the mock *IRAS* galaxies were generated with
probability proportional to the mass density itself. Thus, the mock
*IRAS* galaxies are unbiased relative to the mass, i.e., for the mock
catalogs *b*_{I} = 1, and therefore the *true*
value of
_{I}
for the simulated data is unity.

^{9}
The 20 catalogs (of both types) are different statistical realizations
of the
same simulation. As a result, our simulations fully probe the effects of
*statistical* variance, because of distance indicator scatter, spatial
inhomogeneities, etc. However, they do not include the effects of
*cosmic* variance, because the density field of the region of space
surveyed may not be characteristic of the universe as a whole. However, as
we shall argue in Section 6, we expect that
cosmic variance will have minimal effect on our
-determination.
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