ALGEBRAIC METHODS FOR DATA ANALYSIS CHINE

Gibbs Sampler算法基于一组小而强大的 概率和数理统计的结果。 这些结果 保证技术的严谨性和广泛的适用性， 法 然而，还有一些重要的问题， 一致性和执行情况，并对这些问题进行了审查。 我们已经在Intel iPSC/860上完全实现了Gibbs采样器 （Hypercube）在DCRT中。 提速近两个数量级 在一个问题中，需要100多个 参数，该算法花了大约5秒的时间来分析 超立方体，相比之下，近45分钟的凸 DCRT中的超级计算机。 这种计算效率的提高 允许生物医学界在一个非常困难的问题上工作， 实时交互的方式。 采样器因此大大扩展了传统的理解 合理和易于处理的生物模型，并允许非常 高维（多参数）数据分析。 它已被用于 真实的临床研究：参见Knebel等人（1992）， 机械通气与压力支持通气：比较 呼吸困难，焦虑和吸气努力，（提交给美国 呼吸系统疾病的回顾。） 在这项研究中，我们还比较了替代经典，仍然在技术上 非平凡方法，包括期望最大化方法。 的 真正经典的解决通风问题的方法要求 完全删除任何缺失点的情况 分析;吉布斯采样器，另一方面，平滑地允许 缺少数据。 此外，从几种方法（经典或吉布斯）的结果是 并不总是相同的，告诉我们，他们每个人都看到的数据在一个 不同的方式。 这些差异反过来会产生临床后果 并为研究人员提出新的问题和想法（例如， 解释性断奶的临床标准）。 我们注意到， 不同的统计方法经常会导致这种差异， 有时戏剧性地如此，从而导致研究人员要求更多 更精细，更集中的问题，以及可能导致 彻底改变目前被认为是最佳做法的做法。

The Gibbs Sampler algorithm is based on a small but powerful set of results in probability and mathematical statistics. These results guarantee both the technical rigor and the broad applicability of the method. There are, however, non-trivial issues concerned with convergence and implementation and these were examined. We have fully implemented the Gibbs Sampler on the Intel iPSC/860 (Hypercube) in DCRT. Speed-ups of nearly two orders of magnitude have been obtained: In one problem, requiring more than 100 parametthes, the algorithm took about 5 seconds to analyze on the Hypercube, as compared with nearly 45 minutes on the Convex Supercomputer in DCRT. Such increases in computational efficiency allow the biomedical community to work on very difficult problems in a real-time, interactive way. The Sampler thus greatly expands on the conventional understanding of reasonable and tractable biological models, and allows for very high-dimensional (many parameter) data analyses. It has been used by us for real clinical studies: see Knebel et al. (1992), Weaning from Mechanical Ventilation vs. Pressure Support Ventilation: Comparison of Dyspnea, Anxiety and Inspiratory Effort, (submitted to The American Review of Respiratory Diseases.) In this study, we also compared alternative classical, still technically non-trivial methods, including the Expectation-Maximization method. The truly classical methods for this ventilator problem require that every case having any missing points at all is entirely deleted from the analysis; the Gibbs Sampler, on the other hand, smoothly allows for missing data. Moreover, the results from the several methods (classical or Gibbs) are not always identical, telling us that they each see the data in a different way. These differences, in turn, have clinical consequences and suggest new questions and ideas for the researcher (e.g. better clinical criteria for ventilatory weaning). We note that advanced but distinct statistical methods can often result in such differences, sometimes dramatically so, and thus lead to the researcher to ask more refined, more focused questions, as well as possibly resulting in a complete change in what is considered current best practice.