演講訊息 TALKS

Let X be a finite space and π be an underlying probability on X. For any real-valued function f defined on X , we are interested in calculating the expectation of f under π. Let X(1), X(2), …, X(n),… be a Markov chain generated by some transition matrix P with invariant distribution π. The time average, 1/n(f (X(1))+ f (X(2))+…+ f (X(n))), is a reasonable approximation to the expectation, E_π[f (X)]. Which matrix P minimizes the asymptotic variance of 1/n(f (X(1))+ f (X(2))+…+ f (X(n)))? The answer depends on f. Rather than a worst-case analysis, we will identify the set of P that minimize the average asymptotic variance, averaged with respect to a uniform distribution on f. A simulation study of a new algorithm called locally optimal sampler is presented. This is a joint work with Ting-Li Chen, Wei-Kuo Chen, and Hui-Ming Pai.