Controlled Discovery and Localization of Signals via Bayesian Linear Programming
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通过贝叶斯线性规划控制信号发现与定位
- 研究问题
- 当相关性等因素使信号位置难以精确确定时，如何输出尽可能多且尽可能小的互不重叠区域，同时控制错误发现？
- 方法与思路
- 作者提出贝叶斯线性规划 BLiP，以信号位置的后验分布为输入，在控制假阳性的要求下近似最大化期望检验力。
- 材料陈述的贡献
- 摘要称方法可接入多种贝叶斯模型，并报告在遗传精细定位和天文源检测中，额外计算使检验力提高百分之三十至一百二十。
- 阅读关注点
- 应核对检验力与错误发现的定义、近似最优保证的条件，以及后验可靠性、区域候选集合与优化结果之间的关系。
- 阅读边界
- 这是 arXiv 预印本，同行评审或期刊接收未经核实；摘要未说明错误控制的具体含义，报告的改善仅涉及所列应用比较。
原文摘要
Scientists often must simultaneously localize and discover signals. For instance, in genetic fine-mapping, high correlations between nearby genetic variants make it hard to identify the exact locations of causal variants. So the statistical task is to output as many disjoint regions containing a signal as possible, each as small as possible, while controlling false positives. Similar problems arise in any application where signals cannot be perfectly localized, such as locating stars in astronomical surveys and changepoint detection in sequential data. Common Bayesian approaches to these problems involve computing a posterior distribution over signal locations. However, existing procedures to translate these posteriors into actual credible regions for the signals fail to capture all the information in the posterior, leading to lower power and (sometimes) inflated false discoveries. With this motivation, we introduce Bayesian Linear Programming (BLiP). Given a posterior distribution over signals, BLiP outputs credible regions for signals which verifiably nearly maximize expected power while controlling false positives. BLiP overcomes an extremely high-dimensional and nonconvex problem to verifiably nearly maximize expected power while controlling false positives. BLiP is very computationally efficient compared to the cost of computing the posterior and can wrap around nearly any Bayesian model and algorithm. Applying BLiP to existing state-of-the-art analyses of UK Biobank data (for genetic fine-mapping) and the Sloan Digital Sky Survey (for astronomical point source detection) increased power by 30-120% in just a few minutes of additional computation. BLiP is implemented in pyblip (Python) and blipr (R).