1. Demonstration of the value of a Bayesian approach when interpreting a single experiment.
Demonstration of the value of a Bayesian approach when interpreting a single experiment. A, Consider the scientist facing the challenge of testing 1000 hypotheses, for example, in a proteomics or drug screening experiment, in which each protein measured or compound assayed tests the hypothesis that the protein expression is changed or the compound is active. Without knowledge of the target class only a small fraction of these hypotheses (say 10%) are true. If the power of the experiment is 80%, 80 hypotheses will be correctly identified as true (marked “true +”) and 20 will be false negatives (“false –”) as shown in the expected outcomes table. Of the 900 remaining false hypotheses, 45 will be incorrectly ascribed as being true (“false +” in the table) with α = 0.05, and 855 will be correctly ascertained as negatives (“true –”). Thus, the chance of correctly interpreting a positive outcome (equivalent to precision in a ROC analysis) is only 64% (=80/125). B, If the statistical power of the experiment is 30%, the chance of correctly interpreting a positive result drops to only 40% (=45/75). Blue in the outcomes table represent numbers that have changed from the previous panel. C, Now imagine that, with experience, one is working in a more restricted target space in which 40% of hypotheses are expected to be true: the chance of correctly interpreting a positive result jumps to 80% even when power = 30% (=120/150). D, A plot of these variables (plus the 10% power case) shows that the chance of correctly interpreting a single outcome depends on α, power, and the a priori probability that the hypothesis is true.
Ray Dingledine eNeuro 2018;5:ENEURO
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