Power of the Sequential Monte Carlo Test

Silva, I.; Assunção, Renato M.; Costa, Marcelo Azevedo

doi:10.1080/07474940902816601

Cited by 37 publications

(30 citation statements)

References 13 publications

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“…where g is the number of simulated values greater than u , and h is the sequential parameter, Silva, Assunção and Costa [21] proved that for h = 50 , there is no loss in power when compared to the exact test. Furthermore, in this situation, the expected number of simulations under the null hypothesis is equal to 115 [22].…”

Section: Methodsmentioning

confidence: 99%

Maximum linkage space-time permutation scan statistics for disease outbreak detection

Costa

Kulldorff

2014

International Journal of Health Geographics

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BackgroundIn disease surveillance, the prospective space-time permutation scan statistic is commonly used for the early detection of disease outbreaks. The scanning window that defines potential clusters of diseases is cylindrical in shape, which does not allow incorporating into the cluster shape potential factors that can contribute to the spread of the disease, such as information about roads, landscape, among others. Furthermore, the cylinder scanning window assumes that the spatial extent of the cluster does not change in time. Alternatively, a dynamic space-time cluster may indicate the potential spread of the disease through time. For instance, the cluster may decrease over time indicating that the spread of the disease is vanishing.MethodsThis paper proposes two irregularly shaped space-time permutation scan statistics. The cluster geometry is dynamically created using a graph structure. The graph can be created to include nearest-neighbor structures, geographical adjacency information or any relevant prior information regarding the contagious behavior of the event under surveillance.ResultsThe new methods are illustrated using influenza cases in three New England states, and compared with the cylindrical version. A simulation study is provided to investigate some properties of the proposed arbitrary cluster detection techniques.ConclusionWe have successfully developed two new space-time permutation scan statistics methods with irregular shapes and improved computational performance. The results demonstrate the potential of these methods to quickly detect disease outbreaks with irregular geometries. Future work aims at performing intensive simulation studies to evaluate the proposed methods using different scenarios, number of cases, and graph structures.

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Section: Methodsmentioning

confidence: 99%

Maximum linkage space-time permutation scan statistics for disease outbreak detection

Costa

Kulldorff

2014

International Journal of Health Geographics

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“…Note that complete shrinkage to target ‫܂‬ ଶ (δ ୭୮୲ ଶ = 1) gives the same model as the traditional ASCA model applied to data that was scaled by the "variances" in ‫܂‬ ଶ , i.e. that was scaled by the diagonal elements with the within-group scatter matrix W. As mentioned in section 2.3 [20,21]. Sequential tests give similar results as conventional tests, but are computationally less demanding because permutation is stopped when there seems to be little evidence against the null hypothesis.…”

Section: Regularized Manovamentioning

confidence: 99%

“…A C C E P T E D ACCEPTED MANUSCRIPT 21 In this so-called Lower study, the metabolic response and loss of body fat due to four diets was studied in individuals suffering from metabolic syndrome [24]. (d) 60 : 5 : 35).…”

Section: A N U S C R I P Tmentioning

confidence: 99%

Regularized MANOVA (rMANOVA) in untargeted metabolomics

Engel

Blanchet

Bloemen

et al. 2015

Analytica Chimica Acta

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“…An important property is that \documentclass{article}\usepackage{amsmath}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{amsfonts}\pagestyle{empty}\begin{document}$MC_m$ \end{document} is a level \documentclass{article}\usepackage{amsmath}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{amsfonts}\pagestyle{empty}\begin{document}$\alpha$ \end{document} test. When \documentclass{article}\usepackage{amsmath}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{amsfonts}\pagestyle{empty}\begin{document}$U$ \end{document} has a continuous distribution, and \documentclass{article}\usepackage{amsmath}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{amsfonts}\pagestyle{empty}\begin{document}$m$ \end{document} is a multiple of \documentclass{article}\usepackage{amsmath}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{amsfonts}\pagestyle{empty}\begin{document}$\left\lfloor 1/\alpha\right\rfloor$ \end{document}, the probability of type I error is equal to \documentclass{article}\usepackage{amsmath}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{amsfonts}\pagestyle{empty}\begin{document}$\alpha$ \end{document}, and if the distribution of \documentclass{article}\usepackage{amsmath}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{amsfonts}\pagestyle{empty}\begin{document}$U$ \end{document} is discrete, then the size of the MC test is at most \documentclass{article}\usepackage{amsmath}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{amsfonts}\pagestyle{empty}\begin{document}$\alpha$ \end{document} [27]. Additionally, Jockel [28] has proved for a large class of test statistics that, if we choose \documentclass{article}\usepackage{amsmath}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{amsfonts}\pagestyle{empty}\begin{document}$m$ \end{document} large enough such as \documentclass{article}\usepackage{amsmath}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{amsfonts}\pagestyle{empty}\begin{document}$m=10000$ \end{document}, for example, the power loss of the MC test, with respect to the exact test, is less than \documentclass{article}\usepackage{amsmath}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{amsfonts}\pagestyle{empty}\begin{document}$2\%$ \end{document}.…”

Section: Constructing \Documentclass{article}\usepackage{amsmath}\usementioning

confidence: 99%

Tests for mean vectors in high dimension

Maboudou-Tchao

Silva

2013

Statistical Analysis

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Traditional multivariate tests, Hotelling's \documentclass{article}\usepackage{amsmath}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{amsfonts}\pagestyle{empty}\begin{document}$T^2$ \end{document} or Wilks \documentclass{article}\usepackage{amsmath}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{amsfonts}\pagestyle{empty}\begin{document}$\Lambda$ \end{document}, are designed for a test of the mean vector under the condition that the number of observations is larger than the number of variables. For high‐dimensional data, where the number of features is nearly as large as or larger than the number of observations, the existing tests do not provide a satisfactory solution because of the singularity of the estimated covariance matrix. In this article, we consider a test for the mean vector of independent and identically distributed multivariate normal random vectors where the dimension is larger than or equal to the number of observations. To solve this problem, we propose a modified Hotelling statistic. Simulation results show that the proposed test is superior to other tests available in the literature. However, because we do not know the theoretical distribution of this modified statistic, Monte Carlo methods were used to reach this conclusion. Instead of using conventional Monte Carlo methods, which perform a fixed‐number of simulations, we suggest using the sequential Monte Carlo test in order to decrease the number of simulations needed to reach a decision. Simulation results show that the sequential Monte Carlo test is preferable to a fixed‐sample test, especially when using computationally intensive statistical methods. © 2013 Wiley Periodicals, Inc. Statistical Analysis and Data Mining, 2013

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Power of the Sequential Monte Carlo Test

Cited by 37 publications

References 13 publications

Maximum linkage space-time permutation scan statistics for disease outbreak detection

Maximum linkage space-time permutation scan statistics for disease outbreak detection

Regularized MANOVA (rMANOVA) in untargeted metabolomics

Tests for mean vectors in high dimension

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