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Scan Statistics for Detecting a Local Change in Model Parameters for Normal Data
In this chapter, we review the testing procedures that have been investigated in the scientific literature for detecting a local change in the...
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Designing Distributed Sensor Detection Systems Using the Scan Statistic
The scan statistic has been successfully used to detect anomalies in georeferenced data, making it a suitable candidate for fusing measurements in...
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Demimartingale Approaches for ScanStatistics
Scan statistics are defined as random variables enumerating the moving windows in a sequence of binary outcome trials which contain a prescribed...
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Generating Function Methods for Run and Scan Statistics
Runs and pattern statistics have found successful applications in various fields. Many classical results of distributions of runs were obtained by...
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Martingale Methods
We survey the ways that martingales and the method of gambling teams can be used to obtain otherwise hard-to-get information for the moments and...
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Adjusted Inference for the Spatial Scan Statistic
A modification is proposed to the usual inference test of the Kulldorff’s spatial scan statistic, incorporating additional information about the size...
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Approximations for Discrete Scan Statistics on i.i.d and Markov-Dependent Bernoulli Trials
In this short note, we examine some approximations for the distribution of the discrete scan statistic defined on i.i.d. and Markov-dependent...
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On Scan Statistics Through the Finite Markov Chain Imbedding Approach
This chapter provides a short review of the finite Markov chain imbedding approach for studying the distributions of discrete scan statistics,...
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Scan Statistics Applications in Genomics
The area of scan statistics encompasses a broad class of methods for detecting clusters of events. These methods have been applied to identify...
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Scan Statistics for Detecting a Local Change in Model Parameters for Normal Data
In this chapter, we review the testing procedures that have been investigated in the scientific literature for detecting a local change in the...
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Poisson Approximations for the Number of kl-Scans
Consider a lecture class with a population of N students. Suppose we keep track of the order of students called upon to answer a question. Each...
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The Role of Scan Statistics in High-Energy Astrophysics
Astronomers often face with the problem of recognizing activity periods of celestial sources. Once an activity period is found during the operations...
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Two-Dimensional Discrete Scan Statistics with Arbitrary Window Shape
The definition of the two-dimensional discrete scan statistic with rectangular window shape is extended to a more general framework. In particular,...
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Scan Statistics for Integer-Valued Random Variables: Conditional Case
In this chapter, we review approximations and inequalities for the distribution of conditional scan statistics for a sequence of independent and...
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Spatial Scan Statistics for Functional Data
In this chapter, we propose a review of spatial scan statistics methods for functional data. These are defined by spatial locations within which...
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Quality (Q) Measures
This chapter considers various “quality” measures of test outcome which can be derived from the 2 × 2 contingency tableContingency table, that is...
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Number Needed (Reciprocal) Measures and Their Combinations as Likelihoods
This chapter considers various “number needed” (reciprocal or multiplicative inverse) measures of test outcome which can be derived from the basic...
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Introduction
This chapter describes the basic fourfold, 2 × 2, contingency tableContingency table, cross-classifying actual and predicted classes, and introduces...
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Wilcoxon Rank Sum Scan Statistics for Continuous Data with Outliers
In this chapter, we investigate the performance of several Wilcoxon rank sum scan statistics in detecting a local change in population mean, in the...
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Calibrating the Scan Statistic with Size-Dependent Critical Values
It is known that the scan statistic with variable window size favors the detection of signals with small spatial extent and there is a corresponding...