Convergence rate of Markov chain methods for genomic motif discovery
Convergence rate of Markov chain methods for genomic motif discovery
复制标题
用于基因组基序发现的马尔可夫链方法的收敛率
DOI：
10.1214/12-aos1075
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发表时间：
2013
影响因子：
4.5
通讯作者：
J. Rosenthal
中科院分区：
文献类型：
--
作者：
D. Woodard;J. Rosenthal
我们分析了一个流行的吉布斯抽样方法用于统计发现的基因调控结合基序的DNA序列的收敛速度。这个采样器满足一个非常强的遍历形式（均匀）。然而，我们发现，由于后验分布的多峰性，收敛速度往往呈指数下降的DNA序列的长度的函数。具体来说，我们表明，每当有一个以上的真正的重复模式的数据。在实践中，生物数据中通常存在多个甚至大量的这种模式，目标是检测其中最保守和最频繁出现的模式。我们的研究结果与经验结果相匹配，其中基序发现吉布斯采样器表现出如此差的收敛性，以至于它仅用于寻找后验分布（候选基序）的模式，而不是从该分布中获取样本。我们的似乎是第一个有意义的边界上的马尔可夫链方法的收敛速度从一个多峰后验分布的采样，作为一个函数的统计量，如观察的数量。
We analyze the convergence rate of a popular Gibbs sampling method used for statistical discovery of gene regulatory binding motifs in DNA sequences. This sampler satisfies a very strong form of ergodicity (uniform). However, we show that, due to multimodality of the posterior distribution, the rate of convergence often decreases exponentially as a function of the length of the DNA sequence. Specifically, we show that this occurs whenever there is more than one true repeating pattern in the data. In practice there are typically multiple, even numerous, such patterns in biological data, the goal being to detect the most well-conserved and frequently-occurring of these. Our findings match empirical results, in which the motif-discovery Gibbs sampler has exhibited such poor convergence that it is used only for finding modes of the posterior distribution (candidate motifs) rather than for obtaining samples from that distribution. Ours appear to be the first meaningful bounds on the convergence rate of a Markov chain method for sampling from a multimodal posterior distribution, as a function of statistical quantities like the number of observations.
影响因子：
56.9
作者：
LAWRENCE, CE;ALTSCHUL, SF;WOOTTON, JC
通讯作者：
WOOTTON, JC