  Reweighting is not a new method in lattice QCD, but a comprehensive analysis
is missing in the literature. We close this gap by presenting: (i) a proof of
an integral representation of the complex determinant of a complex matrix, (ii)
a method to control the stochastic error of its Monte Carlo estimation, (iii)
expansions of the stochastic error and the ensemble fluctuations of the one
flavor reweighting factor. Based on (iii) we present a detailed scaling
analysis and optimized reweighting strategies. As an application we analyze the
ensemble fluctuations of the reweighting factor corresponding to the sea
contribution to isospin splitting and predict at physical quark masses a
standard deviation of +-20%.
