| A. Wald. Sequential Analysis. Wiley, New York, 1947. |
....solved. Several researchers in the machine learning and the KDD communities have used heuristics based on stopping sampling when some conclusion seems very likely [13, 18, 19] On the other hand, statisticians have worked extensively on sequential sampling since the 40s (Wald s work is classical [23]; see, e.g. 10] for recent works) But they focused mostly on minimizing the number of experiments for hypothesis testing. Only very recently, some sequential sampling algorithms have been developed that (i) can be applied to current, general, KDD tasks and that (ii) have theoretical guarantees ....
A. Wald, Sequential Analysis, John Wiley & Sons, 1947.
....that do not cover the sequences used in practice [2,5,14] Also, sequences of increments that minimize the average running time of Shellsort were not known so far. 2 Sequential Analysis Sequential analysis is a method of verifying statistical hypotheses developed by Abraham Wald in the 1940s [13]. Whereas classical statistical criteria fix the R. Freivalds (Ed. FCT 2001, LNCS 2138, pp. 106 117, 2001. Springer Verlag Berlin Heidelberg 2001 size of the random sample before it is drawn, in sequential analysis its size is determined dynamically by analyzing a sequentially obtained ....
Wald, A.: Sequential Analysis. J. Wiley & Sons, New York, 1947.
....Watermark Detection In this section we describe the analysis involved in designing a sequential watermark detector as a binary hypothesis test and explain how some of the popular watermarking techniques can be detected by this method. Sequential hypothesis testing was pioneered by Wald [8]. The main feature of a sequential hypothesis test that di#erentiates it from a fixed sample size (FSS) hypothesis test is the number of observations (or samples) required by the sequential detector. Unlike a FSS detector, this number is not pre determined, but a random variable. It varies ....
....functions of conditioned on H 1 and H 0 be denoted by f 1 (y 1 , y 2 , y n ) and f 0 (y 1 , y 2 , y n ) n 1, respectively. Select two decision thresholds A and B such that #. Then the optimal detector based on the sequential probability ratio test (SPRT) is given by [8] (Ch. 3) 1 , y 2 , y n ) ln # # # # (3) 1 , y 2 , y n ) denotes the logarithm of the likelihood ratio of the first n observations. If the log likelihood ratio does not exceed one of two decision thresholds, one more observation is taken and the new log likelihood ....
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A. Wald, Sequential Analysis, NY, Wiley, 1947.
....patterns. For example, in the e commerce domain we found products that were much more likely to be visited when a combination of related products was visited than when only one of those products was visited. 6. RELATED WORK Our method falls in the general category of sequential analysis [17], which determines at runtime the number of examples needed to satisfy a given quality criterion. Other recent examples of this approach include Maron and Moore s racing algorithm for model selection [13] Greiner s PALO algorithm for probabilistic hill climbing [7] Sche#er and Wrobel s ....
A. Wald. Sequential analysis. Wiley, New York, 1947.
....exposition of significance tests and hypothesis tests proceeded on the assumption of a fixed sample size. We now relax this assumption and generalize the description to situations in which the sample size is not fixed beforehand. The following description of sequential tests is borrowed from Wald [102,22]. An essential feature of the sequential test, as distinguished from the [fixed sample size test] is that the number of observations required by the sequential test depends on the outcome of the observations and is therefore not predetermined but a random variable. The sequential method of ....
A. Wald, Sequential analysis, Wiley (
....the approximative test. The pair (r, s) is called the precision of the approximative test. To result in a good approximation, the values r, s should be small (e.g. r = s = 0.05) at any rate, we assume that r s # 1, so that 1 r # 1 s , which will be needed below. Using the Wald procedure [6], we define the likelihood ratio LQ(n) sup p#[0,#) p sup p#[#,1] p , 3.5) and we obtain the following approximative sequential testing scheme: then H a is true with probability at most s. r then H b is true with probability at most r. 3. Otherwise r # ....
Wald, A. (1947). Sequential Analysis. New York: Wiley. 5
....we start from a statistical representation, we are able to utilize the powerful tools that have been devel oped for stochastic measurement processes. Maximum likelihood estimation [Ljung, 1983] is used for extracting the feature parameters. Sequential hypothesis tests, originally developed by Wald [Wald, 1947], are used for on line segmentation of the measurement processes into a sequence of measurement models. The second important thread comes from dynamics in configuration space [LozanoPErez, 1983, Arnold, 1989] Cofi guratio space is the space of all possible generalized coordinates, or ....
....Benveniste ct at. 1987] These works have been applied to segmentation of EEG, ECG, speech, and geophysical signals. The best reference is the collection of papers in [Basseville and Benveniste, 1986] Their works are all related to the sequential likelihood ratio test, originally developed by [Wald, 1947], and the generalized likelihood ratio test (GLR) The GLR test was applied to changed failure detection for linear dynamic systems in [Willsky and Jones, 1976, Willsky, 1976, Chien and Adams, 1976, Tanaka and Muller, 1990] and to detection of incidents on freeways in [Willsky ct at. 1980] ....
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A. Wald. Sequential Analysis. John Wiley & Sons, 1947.
....Sequential Hypothesis Testing In order to develop algorithms for processing dynamic contact information, weintroduce a sequential hypothesis testing model of the sensing process. This area has been an active area of research in statistics and signal processing since its initial developmentbyWald [28]. A mathematical review is given by Siegmund [25] There havebeenanumber of important results during the last decade [3, 29] These methods are relevanttoany signal processing task which can be modeled as a stochastic measurement process on an underlying system which undergoes discontinuous ....
Abraham Wald. Sequential Analysis. John Wiley & Sons, Inc., 1947.
....to attributes of interest, and either the relations are of moderate size (10 records or less) or no indices are available for the relations. 2. 12.2 Sequential Sampling Lipton Naughton in [LNS90, LN90] revived the sequential sampling (which they called adaptive sampling) approach of Wald [Wal47] to selectivity estimation. Here sequentiality is statistical, i.e. one decides after each element sampled whether to continue sampling (in contrast to the usage in DBMS, where sequential algorithms usually refer to sequentially scanning the relation) It is well known that sequential sampling ....
Abraham Wald. Sequential Analysis. John Wiley & Sons, 1947.
....time spend estimating the underlying model dominates the overall time bound, this will lead us to reduce it from a polynomial of degree 4 to a polynomial of degree 2 in worst case, a signi cant reduction. Adaptive sampling has been studied since long time ago (see, for instance, the book by Walt [9]) and has also been recently used in the context of database query estimation [7] and knowledge discovery [1, 2] Furthermore, adaptivity is a very desirable property for an algorithm that is expected to be used in practical applications. See the discussion about the relevance of adaptivity in the ....
Abraham Wald. Sequential Analysis. Wiley Mathematical, Statistics Series, 1947.
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A. Wald. Sequential Analysis. Wiley, New York, 1947.
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A. Wald. Sequential Analysis. John Wiley and Sons, Inc., New York, 1947.
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Wald, A 1947, Sequential Analysis, John Wiley and Sons, New York.
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A. Wald. Sequential Analysis. Wiley, 1947.
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A. Wald. Sequential Analysis. Dover, New York, 1947.
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Abraham Wald. Sequential Analysis. John Wiley & Sons, 1947.
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A. Wald. Sequential Analysis. Wiley, 1947.
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A. Wald. Sequential Analysis. Wiley, 1947.
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Abraham Wald. Sequential Analysis. J. Wiley & Sons, New York, 1947.
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Abraham Wald. Sequential Analysis. J. Wiley & Sons, New York, 1947.
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A. Wald, Sequential Analysis, Wiley, New York, 1947.
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A. Wald. Sequential Analysis. J. Wiley & Sons, New York, 1947.
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Wald, A. Sequential Analysis. Wiley, New York (1947).
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A. Wald. Sequential Analysis. J. Wiley & Sons, New York, 1947.
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A. Wald. Sequential Analysis. Wiley, 1947.
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