  A variant of multiscale analysis for ergodic Schr\"odinger operators is
developed. This enables us to prove positivity of Lyapunov exponents given
initial scale estimates and an initial Wegner estimate. This is then applied to
high dimensional skew-shifts at small coupling, where initial conditions are
checked using the Pastur--Figotin formalism. Furthermore, it is shown that for
potentials generated by the doubling map one has positive Lyapunov exponent
except in a superpolynomially small set.
