The fundamental relations of the sampling process in the multicanonical ensemble and simulated tempering have been studied in the expanded ensembles formalism. The simulated tempering is identified as the multicanonical sampling with the generalized weight determined by a Laplace transform of the temperature weight. The characteristic dynamics of both sampling methods has been verified in the stochastic formulation of the sampling process. Our study gives a necessary and sufficient condition for the weights to realize a uniform sampling in the energy and temperature spaces. Based on the stochastic model, robust force biased iteration schemes have been proposed to allow automatic determinations of uniform sampling weights.