  I describe a general formalism for galaxy biasing (Dekel & Lahav 1998) and
its application to measurements of beta (=Omega^0.6/b), e.g. via direct
comparisons of light and mass and via redshift distortions. The linear and
deterministic relation g=b*d between the density fluctuation fields of galaxies
g and mass d is replaced by the conditional distribution P(g|d) of these as
random fields, smoothed at a given scale and at a given time. The mean biasing
and its nonlinearity are characterized by the conditional mean <g|d>=b(d)*d and
the local scatter by the conditional variance s_b^2(d). This scatter arises
from hidden effects on galaxy formation and from shot noise. For applications
involving second-order local moments, the biasing is defined by three natural
parameters: the slope b_h of the regression of g on d (replacing b), a
nonlinearity parameter b_t, and a scatter parameter s_b. The ratio of variances
b_v^2 and the correlation coefficient r mix these parameters. The nonlinearity
and scatter lead to underestimates of order b_t^2/b_h^2 and s_b^2/b_h^2 in the
different estimators of beta, which may partly explain the range of estimates.
Local stochasticity affects the redshift-distortion analysis only by limiting
the useful range of scales. In this range, for linear stochastic biasing, the
analysis reduces to Kaiser's formula for b_h (not b_v) independent of the
scatter. The distortion analysis is affected by nonlinearity but in a weak way.
Estimates of the nontrivial features of the biasing scheme are made based on
simulations and toy models, and a new method for measuring them via
distribution functions is proposed.
