  We propose an extension of umbrella sampling in which the pertinent range of
states is subdivided in windows that are sampled consecutively and linked
together. Extrapolating results from one window we estimate a weight function
for the neighboring window. We present a detailed analysis and demonstrate that
the error is controlled and independent from the window sizes. The analysis
also allows us to detect sampling difficulties. The efficiency of the algorithm
is comparable to a multicanonical simulation with an ideal weight function. We
exemplify the computational scheme by simulating the liquid-vapor coexistence
in a Lennard--Jones system.
