Uncertainty Evaluation of Weibull Estimators through Monte Carlo Simulation: Applications for Crack Initiation Testing.
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ABSTRACT:
SUBMITTER: Park JP
PROVIDER: S-EPMC5456946 | biostudies-literature |
REPOSITORIES: biostudies-literature
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Project description:BackgroundPlotless density estimators are those that are based on distance measures rather than counts per unit area (quadrats or plots) to estimate the density of some usually stationary event, e.g. burrow openings, damage to plant stems, etc. These estimators typically use distance measures between events and from random points to events to derive an estimate of density. The error and bias of these estimators for the various spatial patterns found in nature have been examined using simulated populations only. In this study we investigated eight plotless density estimators to determine which were robust across a wide range of data sets from fully mapped field sites. They covered a wide range of situations including animal damage to rice and corn, nest locations, active rodent burrows and distribution of plants. Monte Carlo simulations were applied to sample the data sets, and in all cases the error of the estimate (measured as relative root mean square error) was reduced with increasing sample size. The method of calculation and ease of use in the field were also used to judge the usefulness of the estimator. Estimators were evaluated in their original published forms, although the variable area transect (VAT) and ordered distance methods have been the subjects of optimization studies.ResultsAn estimator that was a compound of three basic distance estimators was found to be robust across all spatial patterns for sample sizes of 25 or greater. The same field methodology can be used either with the basic distance formula or the formula used with the Kendall-Moran estimator in which case a reduction in error may be gained for sample sizes less than 25, however, there is no improvement for larger sample sizes. The variable area transect (VAT) method performed moderately well, is easy to use in the field, and its calculations easy to undertake.ConclusionPlotless density estimators can provide an estimate of density in situations where it would not be practical to layout a plot or quadrat and can in many cases reduce the workload in the field.
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Project description:MotivationIn molecular biology, as in many other scientific fields, the scale of analyses is ever increasing. Often, complex Monte Carlo simulation is required, sometimes within a large-scale multiple testing setting. The resulting computational costs may be prohibitively high.ResultsWe here present MCFDR, a simple, novel algorithm for false discovery rate (FDR) modulated sequential Monte Carlo (MC) multiple hypothesis testing. The algorithm iterates between adding MC samples across tests and calculating intermediate FDR values for the collection of tests. MC sampling is stopped either by sequential MC or based on a threshold on FDR. An essential property of the algorithm is that it limits the total number of MC samples whatever the number of true null hypotheses. We show on both real and simulated data that the proposed algorithm provides large gains in computational efficiency.AvailabilityMCFDR is implemented in the Genomic HyperBrowser (http://hyperbrowser.uio.no/mcfdr), a web-based system for genome analysis. All input data and results are available and can be reproduced through a Galaxy Pages document at: http://hyperbrowser.uio.no/mcfdr/u/sandve/p/mcfdr.Contactgeirksa@ifi.uio.no.
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Project description:The use of Monte-Carlo (MC) p$$ p $$ -values when testing the significance of a large number of hypotheses is now commonplace. In large-scale hypothesis testing, we will typically encounter at least some p$$ p $$ -values near the threshold of significance, which require a larger number of MC replicates than p$$ p $$ -values that are far from the threshold. As a result, some incorrect conclusions can be reached due to MC error alone; for hypotheses near the threshold, even a very large number (eg, 106$$ 1{0}^6 $$ ) of MC replicates may not be enough to guarantee conclusions reached using MC p$$ p $$ -values. Gandy and Hahn (GH)6-8 have developed the only method that directly addresses this problem. They defined a Monte-Carlo error rate (MCER) to be the probability that any decisions on accepting or rejecting a hypothesis based on MC p$$ p $$ -values are different from decisions based on ideal p$$ p $$ -values; their method then makes decisions by controlling the MCER. Unfortunately, the GH method is frequently very conservative, often making no rejections at all and leaving a large number of hypotheses "undecided". In this article, we propose MERIT, a method for large-scale MC hypothesis testing that also controls the MCER but is more statistically efficient than the GH method. Through extensive simulation studies, we demonstrate that MERIT controls the MCER while making more decisions that agree with the ideal p$$ p $$ -values than GH does. We also illustrate our method by an analysis of gene expression data from a prostate cancer study.
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