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Convergence of adaptive mixtures of importance sampling schemes. (English) Zbl 1132.60022
Let π be a probability distribution, π is dominated by a reference measure μ, π(dx)=π(x)dμ(x), where π(x) is density. Let π(f)=f(x)π(dx)· If we can obtain an i.i.d. sample x 1 ,,x N simulated from π, then N -1 i=1 N f(x i )=π ^ N (f) converges to π(f) as N with probability one and we can approximate π(f) by π N (f)· As the normalizing constant of the distribution π is unknown, it is not possible to use the estimator π ^ N (f) directly. The authors propose an algorithm for the estimation π(f)· The authors derive sufficient convergence conditions for adaptive mixtures of population Monte Carlo algorithms and show that Rao-Blackwellized asymptotically achieve an optimum in terms of a Kullback divergence criterion.
MSC:
60F05Central limit and other weak theorems
65C40Computational Markov chains (numerical analysis)