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
- 当相关性使信号位置难以精确识别时，如何输出尽量多且尽量小的不相交信号区域，同时控制错误发现？
- 方法与思路
- 作者提出 BLiP，以已有信号位置后验为输入，通过贝叶斯线性规划选择可信区域，联合处理发现数量与定位精度。
- 材料陈述的贡献
- 摘要称，BLiP 可在控制错误发现时可验证地近似最大化期望功效，并报告遗传与天文应用中的功效提升及较低追加计算成本。
- 阅读关注点
- 应核对错误发现控制所处的概率框架、后验可靠性要求、近似最优性的保证，以及功效比较如何兼顾区域大小。
- 阅读边界
- 依据 arXiv 预印本版本摘要，不能据此声称已同行评审或期刊接收，也不推断刊本变化；具体保证条件和应用比较需核对全文。
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).