= Solution
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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