In statistics, a scan statistic or window statistic is a problem relating to the clustering of randomly positioned points. An example of a typical problem is the maximum size of a cluster of points on a line or the longest series of successes recorded by a moving window of fixed length.[1]
Joseph Naus first published on the problem in the 1960s,[2] and has been called the "father of the scan statistic" in honour of his early contributions.[3] The results can be applied in epidemiology, public health and astronomy to find unusual clusters of events.[4]
It was extended by Martin Kulldorff to multidimensional settings and varying window sizes in a 1997 paper,[5] which is (as of 11 October 2015[update]) the most cited article in its journal, Communications in Statistics – Theory and Methods.[6] This work lead to the creation of the software SaTScan, a program trademarked by Martin Kulldorff that applies his methods to data.
Recent results have shown that using scale-dependent critical values for the scan statistic allows to attain asymptotically optimal detection simultaneously for all signal lengths, thereby improving on the traditional scan, but this procedure has been criticized for losing too much power for short signals. Walther and Perry (2022) considered the problem of detecting an elevated mean on an interval with unknown location and length in the univariate Gaussian sequence model.[7] They explain this discrepancy by showing that these asymptotic optimality results will necessarily be too imprecise to discern the performance of scan statistics in a practically relevant way, even in a large sample context. Instead, they propose to assess the performance with a new finite sample criterion. They presented three new calibration techniques for scan statistics that perform well across a range of relevant signal lengths to optimally increase performance of short signals.
The scan-statistic-based methods have been specifically developed to detect rare variant associations in the noncoding genome, especially for the intergenic region. Compared with fixed-size sliding window analysis, scan-statistic-based methods use data-adaptive size dynamic window to scan the genome continuously, and increase the analysis power by flexibly selecting the locations and sizes of the signal regions.[8] Some examples of these methods are Q-SCAN,[9] SCANG,[10]
WGScan.[11]
^Naus, J. I. (1982). "Approximations for Distributions of Scan Statistics". Journal of the American Statistical Association. 77 (377): 177–183. doi:10.1080/01621459.1982.10477783. JSTOR 2287786.
^Naus, Joseph Irwin (1964). Clustering of random points in line and plane (Ph. D.). Retrieved 6 January 2014.
^Wallenstein, S. (2009). "Joseph Naus: Father of the Scan Statistic". Scan Statistics. pp. 1–25. doi:10.1007/978-0-8176-4749-0_1. ISBN 978-0-8176-4748-3.
^Glaz, J.; Naus, J.; Wallenstein, S. (2001). "Introduction". Scan Statistics. Springer Series in Statistics. pp. 3–9. doi:10.1007/978-1-4757-3460-7_1. ISBN 978-1-4419-3167-2.
^Kulldorff, Martin (1997). "A spatial scan statistic" (PDF). Communications in Statistics – Theory and Methods. 26 (6): 1481–1496. doi:10.1080/03610929708831995.
^"Most Cited Articles". Communications in Statistics – Theory and Methods. Retrieved 11 October 2015.
^Walther, Guenther; Perry, Andrew (November 2022). "Calibrating the scan statistic: Finite sample performance versus asymptotics". Journal of the Royal Statistical Society, Series B (Statistical Methodology). 84 (5): 1608–1639. doi:10.1111/rssb.12549. ISSN 1369-7412. S2CID 221713232.
^Li, Zilin; Li, Xihao; Zhou, Hufeng; Gaynor, Sheila M.; Margaret, Sunitha Selvaraj; Arapoglou, Theodore; Qiuck, Corbin; Liu, Yaowu; Chen, Han; Sun, Ryan; Dey, Rounak; Arnett, Donna K.; Auer, Paul L.; Bielak, Lawrence F.; Bis, Joshua C.; Blackwell, Thomas W.; Blangero, John; Boerwinkle, Eric; Bowden, Donald W.; Brody, Jennifer A.; Cade, Brian E.; Conomos, Matthew P.; Correa, Adolfo; Cupples, L. Adrienne; Curran, Joanne E.; de Vries, Paul S.; Duggirala, Ravindranath; Franceschini, Nora; Freedman, Barry I.; Goring, Harald H.H.; Guo, Xiuqing; Kalyani, Rita R.; Kooperberg, Charles; Kral, Brian G.; Lange, Leslie A.; Lin, Bridget; Manichaikul, Ani; Martin, Lisa W.; Mathias, Rasika A.; Meigs, James B.; Mitchell, Braxton D.; Mitchell, Braxton D.; Montasser, May E.; Morrison, Alanna C.; Naseri, Take; O’Connell, Jeffrey R.; Palmer, Nicholette D.; Reupena, Muagututi’a Sefuiva; Rice, Kenneth M.; Rich, Stephen S.; Smith, Jennifer A.; Taylor, Kent D.; Taub, Margaret A.; Vasan, Ramachandran S.; Weeks, Daniel E.; Wilson, James G.; Yanek, Lisa R.; Zhao, Wei; NHLBI Trans-Omics for Precision Medicine (TOPMed) Consortium; TOPMed Lipids Working Group; Rotter, Jerome I.; Willer, Cristen; Natarajan, Pradeep; Peloso, Gina M.; Lin, Xihong (2022). "A framework for detecting noncoding rare-variant associations of large-scale whole-genome sequencing studies". Nature Methods. 19 (12): 1599–1611. doi:10.1038/s41592-022-01640-x. PMC 10008172. PMID 36303018. S2CID 243873361.
^Li, Zilin; Liu, Yaowu; Lin, Xihong (2022). "Simultaneous Detection of Signal Regions Using Quadratic Scan Statistics With Applications to Whole Genome Association Studies". Journal of the American Statistical Association. 117 (538): 823–834. doi:10.1080/01621459.2020.1822849. PMC 9285665. PMID 35845434.
^Li, Zilin; Li, Xihao; Liu, Yaowu; Shen, Jincheng; Chen, Han; Zhou, Hufeng; Morrison, Alanna C.; Boerwinkle, Eric; Lin, Xihong (2019). "Dynamic Scan Procedure for Detecting Rare-Variant Association Regions in Whole-Genome Sequencing Studies". American Journal of Human Genetics. 104 (5): 802–814. doi:10.1016/j.ajhg.2019.03.002. PMC 6507043. PMID 30982610.
^He, Zihuai; Xu, Bin; Buxbaum, Joseph; Ionita-Laza, Iuliana (2019). "A genome-wide scan statistic framework for whole-genome sequence data analysis". Nature Communications. 10 (1): 3018. doi:10.1038/s41467-019-11023-0. PMC 6616627. PMID 31289270.
In statistics, a scanstatistic or window statistic is a problem relating to the clustering of randomly positioned points. An example of a typical problem...
A computed tomography scan (CT scan; formerly called computed axial tomography scan or CAT scan) is a medical imaging technique used to obtain detailed...
after the fact Ramsey theory – Branch of mathematical combinatorics Scanstatistic Correlative-based fallacies – Informal fallacies based on correlative...
scanner (CT) and are known as PET-CT scanners. PET scan images can be reconstructed using a CT scan performed using one scanner during the same session...
SaTScan™. Retrieved 11 February 2023. Kulldorff, Martin (1997). "A spatial scanstatistic" (PDF). Communications in Statistics – Theory and Methods. 26 (6): 1481–1496...
A scanning electron microscope (SEM) is a type of electron microscope that produces images of a sample by scanning the surface with a focused beam of electrons...
An idle scan is a TCP port scan method for determining what services are open on a target computer without leaving traces pointing back at oneself. This...
Differential scanning calorimetry (DSC) is a thermoanalytical technique in which the difference in the amount of heat required to increase the temperature...
or telefax (short for telefacsimile), is the telephonic transmission of scanned printed material (both text and images), normally to a telephone number...
accomplished from even up to 10 meters away or in a live camera feed. Retinal scanning is a different, ocular-based biometric technology that uses the unique...
Statistical parametric mapping (SPM) is a statistical technique for examining differences in brain activity recorded during functional neuroimaging experiments...
tomography scan done at the ESRF (European synchrotron radiation facility) which had a resolution of about 25 microns the scan took about 22 hours.this scan was...
scan multiple directions, in which case it is known as lidar scanning or 3D laser scanning, a special combination of 3-D scanning and laser scanning....
other libraries whose collections Google scanned for Google Books and Google Scholar retained copies of the scans and have used them to create the HathiTrust...
the five most cited papers in the journal are: Kulldorff M. A spatial scanstatistic, 1997, 982 cites. Holland PW, Welsch RE. Robust regression using iteratively...
Press. pp. 448–9. ISBN 978-0-19-852783-1. Wood, Janice (May 11, 2012). "Scans Show Psychopaths Have Brain Abnormalities". Psych Central. Retrieved February...
scanners to calculate volumes and segmental volumes of an individual body scan. The aim is to establish whether the Body Volume Index has the potential...
forms of eye exam using ultrasound: A-scan ultrasound biometry, is commonly referred to as an A-scan (amplitude scan). A-mode provides data on the length...
highlight the need for more careful statistical analyses in fMRI research, given the large number of voxels in a typical fMRI scan and the multiple comparisons...
time, and is due to a bacterial infection. Diagnosis is typically by CT scan, though blood tests, colonoscopy, or a lower gastrointestinal series may...
astrocytes. The diagnosis typically is made by a combination of a CT scan, MRI scan, and tissue biopsy. There is no known method of preventing the cancer...
measure the similarity between two subjects' series of brain scans or between different scans of a same subject. The definition of the RV-coefficient makes...
Lens to improve the quality of visual and voice translation. It is able to scan text or a picture using the device and have it translated instantly. Moreover...
chapter 9 was added: The Principles of Statistical Estimation. The Design of Experiments Scanned version of Statistical Methods first edition Conniffe, Denis...