Most high-dimensional phase space has negligible equilibrium probability. Uniform sampling spends nearly all its work in these irrelevant regions and seldom visits the small subset that dominates the partition function or the numerator of an equilibrium average. The resulting estimator can have enormous variance.
Importance sampling places samples where the product of statistical weight and observable matters. Sampling the Boltzmann distribution, for example, converts a weighted phase-space integral into an equilibrium expectation. If a Markov chain Monte Carlo algorithm is used, adequate exploration of separate free-energy basins and allowance for autocorrelation remain necessary.
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