Positivity of hit-and-run and related algorithms
Positivity of hit-and-run and related algorithms
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DOI：
10.1214/ecp.v18-2507
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发表时间：
2012-12
影响因子：
0.5
通讯作者：
Daniel Rudolf;Mario Ullrich
中科院分区：
文献类型：
--
作者：
Daniel Rudolf;Mario Ullrich
我们证明了与肇事逃逸算法、随机扫描Gibbs采样器、切片采样器和Metropolis算法相对应的马尔可夫算子的正性。特别是，结果表明，没有必要考虑这些马尔可夫链的懒惰版本。证明依赖于一个著名的引理，该引理将乘积$MTM^*$的正性(对于某些算子$M$和$T$)与$T$的正性联系起来。需要找到马尔可夫算子与正算子$T$的那种表示。
We prove positivity of the Markov operators that correspond to the hit-and-run algorithm, random scan Gibbs sampler, slice sampler and Metropolis algorithm with positive proposal. In particular, the results show that it is not necessary to consider the lazy versions of these Markov chains. The proof relies on a well known lemma which relates the positivity of the product $MTM^*$, for some operators $M$ and $T$, to the positivity of $T$. It remains to find that kind of representation of the Markov operator with a positive operator $T$.