On The Weak Law Of Large Numbers For Unbounded Functionals For Adaptive MCMC
نویسنده
چکیده
We present counter-examples to demonstrate that when g is unbounded the conditions of Simultaneous Uniform Ergodicity and Diminishing Adaptation are not enough to guarantee that the the weak law of large numbers (WLLN) holds, although from the results of Roberts and Rosenthal [4] we know that WLLN holds under these conditions when g is bounded. Then we show various theoretical results of the WLLN for the adaptive MCMC and unbounded measurable function g. Finally we apply our results to the Adaptive Metropolis algorithm proposed by Haario et al. [7] (2001).
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