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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク SPRT ： ウィキペディア英語版 Sequential probability ratio test The sequential probability ratio test (SPRT) is a specific sequential hypothesis test, developed by Abraham Wald. Neyman and Pearson's 1933 result inspired Wald to reformulate it as a sequential analysis problem. The Neyman-Pearson lemma, by contrast, offers a rule of thumb for when all the data is collected (and its likelihood ratio known). While originally developed for use in quality control studies in the realm of manufacturing, SPRT has been formulated for use in the computerized testing of human examinees as a termination criterion.〔Ferguson, Richard L. (1969). (The development, implementation, and evaluation of a computer-assisted branched test for a program of individually prescribed instruction ). Unpublished doctoral dissertation, University of Pittsburgh.〕〔Reckase, M. D. (1983). A procedure for decision making using tailored testing. In D. J. Weiss (Ed.), New horizons in testing: Latent trait theory and computerized adaptive testing (pp. 237-254). New York: Academic Press.〕 ==Theory== As in classical hypothesis testing, SPRT starts with a pair of hypotheses, say $H\_0$ and $H\_1$ for the null hypothesis and alternative hypothesis respectively. They must be specified as follows: :$H\_0:\; p=p\_0$ :$H\_1:\; p=p\_1$ The next step is calculate the cumulative sum of the log-likelihood ratio, $\backslash log\; \backslash Lambda\_i$, as new data arrive: with $S\_0\; =\; 0$, then, for i=1,2,..., :$S\_i=S\_+\; \backslash log\; \backslash Lambda\_i$ The stopping rule is a simple thresholding scheme: * : continue monitoring (''critical inequality'') * $S\_i\; \backslash geq\; b$: Accept $H\_1$ * $S\_i\; \backslash leq\; a$: Accept $H\_0$ where a and b ( $a\; \backslash approx\; \backslash log\; \backslash frac$ and $b\; \backslash approx\; \backslash log\; \backslash frac$ In other words, $\backslash alpha$ and $\backslash beta$ must be decided beforehand in order to set the thresholds appropriately. The numerical value will depend on the application. The reason for using approximation signs is that, in the discrete case, the signal may cross the threshold between samples. Thus, depending on the penalty of making an error and the sampling frequency, one might set the thresholds more aggressively. Of course, the exact bounds may be used in the continuous case. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Sequential probability ratio test」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.