  We propose a general formalism for galaxy biasing and apply it to methods for
measuring cosmological parameters, such as regression of light versus mass, the
analysis of redshift distortions, measures involving skewness and the cosmic
virial theorem. The common 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 random fields, smoothed at a given
scale at a given time. The nonlinearity is characterized by the conditional
mean <g|d>=b(d)*d, while the local scatter is represented by the conditional
variance s_b^2(d) and higher moments. The scatter arises from hidden factors
affecting galaxy formation and from shot noise unless it has been properly
removed. 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,
a nonlinearity b_t, and a scatter s_b. The ratio of variances b_v^2 and the
correlation coefficient r mix these parameters. The nonlinearity and the
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 (=Omega^0.6/b_h). The nonlinear effects are
typically smaller. Local stochasticity affects the redshift-distortion analysis
only by limiting the useful range of scales, especially for power spectra. 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 nonlinear properties of biasing but in a weak way. Estimates of
the nontrivial features of the biasing scheme are made based on simulations and
toy models, and strategies for measuring them are discussed. They may partly
explain the range of estimates for beta.
