ALGEBRAIC METHODS FOR DATA ANALYSIS CHINE

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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.