隨機時間針對馬可夫鏈之收斂

Abstract

在本論文中，我們提出一個隨機時間來當作在執行蒙地卡羅馬可夫鏈法時的停止時間。首先，證明基於一個假設條件下，當演算法停止時，其機率分布與穩定分布會很靠近。之後，利用厄任菲司特甕這例子來呈現此假設條件的重要性。

In this thesis, we propose a random time to stop the M.C.M.C algorithm for sampling. We prove that under the assumption, the total variation between the distribution of our algorithm and the stationary distribution tends to zero. Later, we provide an example based on Ehrenfest chain to emphasize the significance of the assumption.