Friday, December 5, 2014

Beyond Monte Carlo: Solve high dimensional integrals efficiently

Adaptive umbrella sampling and incremental umbrella sampling are stochastic sampling methods to efficiently solve high dimensional integrals.
  • Directed: Focus on sampling of important states, i.e., states with large contributions to the intrgral that have so far been sampled comparatively little.
  • Incremental: Additional samples of states are combined with previous samples to form an augmented set that provides an improved estimate of the integral.
  • High dimensional integrals: Enhancement of stochastic integration method such as Monte Carlo or Metropolis Monte Carlo integration methods, which are particularly suited to solve high dimensional integrals.
  • Example applications: value at risk in finance; normalizing constants in Bayesian statistics; free energy differences in statistical physics, ...
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