ON THE ERGODICITY OF THE ADAPTIVE METROPOLIS ALGORITHM ON UNBOUNDED DOMAINS
ON THE ERGODICITY OF THE ADAPTIVE METROPOLIS ALGORITHM ON UNBOUNDED DOMAINS
复制标题
DOI：
10.1214/10-aap682
复制
发表时间：
2010-12-01
影响因子：
1.8
通讯作者：
Vihola, Matti
中科院分区：
文献类型：
--
作者：
Saksman, Eero;Vihola, Matti
本文介绍了足够的条件，以确保Haario，Saksman和Tamminen的自适应大都市（AM）算法的正确牙齿性[Bernoulli 7（2001）223-242]，以实现非竞争支持的目标分布。确保大数量法则的条件要求超出目标密度衰减的尾巴并具有常规轮廓。结果是基于辅助过程的终身性，该过程被依次限制为可行的适应集，对AM链的生长速率的独立估计以及相应的几何漂移常数。约束过程的终身性结果是通过安德烈（Andrieu）和莫林（Moulines）引起的方法来获得的[Ann。应用。概率。 16（2006）1462-1505]。
This paper describes sufficient conditions to ensure the correct ergodicity of the Adaptive Metropolis (AM) algorithm of Haario, Saksman and Tamminen [Bernoulli 7 (2001) 223-242] for target distributions with a noncompact support. The conditions ensuring a strong law of large numbers require that the tails of the target density decay super-exponentially and have regular contours. The result is based on the ergodicity of an auxiliary process that is sequentially constrained to feasible adaptation sets, independent estimates of the growth rate of the AM chain and the corresponding geometric drift constants. The ergodicity result of the constrained process is obtained through a modification of the approach due to Andrieu and Moulines [Ann. Appl. Probab. 16 (2006) 1462-1505].