Determination of normalizing constants for simulated tempering

In this paper, we propose to estimate the normalizing constants for simulated tempering by a modified histogram algorithm, the so-called contour Monte Carlo algorithm, and compare the efficiency of simulated tempering and parallel tempering. Our analysis reveals that simulated tempering tends to mix faster than parallel tempering at low temperature levels for simulating from complex systems. The reason why simulated tempering is better than parallel tempering is discussed at length.