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On large scales a nonlinear transformation of matter density field can beviewed as a biased tracer of the density field itself. A nonlineartransformation also modifies the redshift space distortions in the same limit,giving rise to a velocity bias. In models with primordial nongaussianity anonlinear transformation generates a scale dependent bias on large scales. Wederive analytic expressions for these for a general nonlinear transformation.These biases can be expressed entirely in terms of the one point distributionfunction (PDF) of the final field and the parameters of the transformation. Ouranalysis allows one to devise nonlinear transformations with nearly arbitrarybias properties, which can be used to increase the signal in the large scaleclustering limit. We apply the results to the ionizing equilibrium model ofLyman-alpha forest, in which Lyman-alpha flux F is related to the densityperturbation delta via a nonlinear transformation. Velocity bias can beexpressed as an average over the Lyman-alpha flux PDF. At z=2.4 we predict thevelocity bias of -0.1, compared to the observed value of -0.13 +/- 0.03. Biasand primordial nongaussianity bias depend on the parameters of thetransformation. Measurements of bias can thus be used to constrain theseparameters, and for reasonable values of the ionizing background intensity wecan match the predictions to observations. Matching to the observed values wepredict the ratio of primordial nongaussianity bias to bias to have theopposite sign and lower magnitude than the corresponding values for the highlybiased galaxies, but this depends on the model parameters and can also vanishor change the sign.

Bias, redshift space distortions and primordial nongaussianity of nonlinear transformations: application to Lyman alpha forest