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:The purpose of this study is to show how Monte Carlo analysis of meta-analytic estimators can be used to select estimators for specific research situations. Our analysis conducts 1620 individual experiments, where each experiment is defined by a unique combination of sample size, effect size, effect size heterogeneity, publication selection mechanism, and other research characteristics. We compare 11 estimators commonly used in medicine, psychology, and the social sciences. These are evaluated on the basis of bias, mean squared error (MSE), and coverage rates. For our experimental design, we reproduce simulation environments from four recent studies. We demonstrate that relative estimator performance differs across performance measures. Estimator performance is a complex interaction of performance indicator and aspects of the application. An estimator that may be especially good with respect to MSE may perform relatively poorly with respect to coverage rates. We also show that the size of the meta-analyst's sample and effect heterogeneity are important determinants of relative estimator performance. We use these results to demonstrate how these observable characteristics can guide the meta-analyst to choose the most appropriate estimator for their research circumstances.
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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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Project description:BackgroundMonte Carlo simulation is considered as the most accurate method for dose calculation in radiotherapy. PRIMO is a Monte-Carlo program with a user-friendly graphical interface.Material and methodA VitalBeam with 6MV and 6MV flattening filter free (FFF), equipped with the 120 Millennium multileaf collimator was simulated by PRIMO. We adjusted initial energy, energy full width at half maximum (FWHM), focal spot FWHM, and beam divergence to match the measurements. The water tank and ion-chamber were used in the measurement. Percentage depth dose (PDD) and off axis ratio (OAR) were evaluated with gamma passing rates (GPRs) implemented in PRIMO. PDDs were matched at different widths of standard square fields. OARs were matched at five depths. Transmission factor and dose leaf gap (DLG) were simulated. DLG was measured by electronic portal imaging device using a sweeping gap method.ResultFor the criterion of 2%/2 mm, 1%/2 mm and 1%/1 mm, the GPRs of 6MV PDD were 99.33-100%, 99-100%, and 99-100%, respectively; the GPRs of 6MV FFF PDD were 99.33-100%, 98.99-99.66%, and 97.64-98.99%, respectively; the GPRs of 6MV OAR were 96.4-100%, 90.99-100%, and 85.12-98.62%, respectively; the GPRs of 6MV FFF OAR were 95.15-100%, 89.32-100%, and 87.02-99.74%, respectively. The calculated DLG matched well with the measurement (6MV: 1.36 mm vs. 1.41 mm; 6MV FFF: 1.07 mm vs. 1.03 mm, simulation vs measurement). The transmission factors were similar (6MV: 1.25% vs. 1.32%; 6MV FFF: 0.8% vs. 1.12%, simulation vs measurement).ConclusionThe calculated PDD, OAR, DLG and transmission factor were all in good agreement with measurements. PRIMO is an independent (with respect to analytical dose calculation algorithm) and accurate Monte Carlo tool.
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Project description:There is substantial evidence suggesting climate change is having an adverse impact on the world's water resources. One must remember, however, that climate change is beset by uncertainty. It is therefore meaningful for climate change impact assessments to be conducted with stochastic-based frameworks. The degree of uncertainty about the nature of a stochastic phenomenon may differ from one another. Deep uncertainty refers to a situation in which the parameters governing intervening probability distributions of the stochastic phenomenon are themselves subjected to some degree of uncertainty. In most climatic studies, however, the assessment of the role of deep-uncertain nature of climate change has been limited. This work contributes to fill this knowledge gap by developing a Markov Chain Monte Carlo (MCMC) analysis involving Bayes' theorem that merges the stochastic patterns of historical data (i.e., the prior distribution) and the regional climate models' (RCMs') generated climate scenarios (i.e., the likelihood function) to redefine the stochastic behavior of a non-conditional climatic variable under climate change conditions (i.e., the posterior distribution). This study accounts for the deep-uncertainty effect by evaluating the stochastic pattern of the central tendency measure of the posterior distributions through regenerating the MCMCs. The Karkheh River Basin, Iran, is chosen to evaluate the proposed method. The reason for selecting this case study was twofold. First, this basin has a central role in ensuring the region's water, food, and energy security. The other reason is the diverse topographic profile of the basin, which imposes predictive challenges for most RCMs. Our results indicate that, while in most seasons, with the notable exception of summer, one can expect a slight drop in the temperature in the near future, the average temperature would continue to rise until eventually surpassing the historically recorded values. The results also revealed that the 95% confidence interval of the central tendency measure of computed posterior probability distributions varies between 0.1 and 0.3 °C. The results suggest exercising caution when employing the RCMs' raw projections, especially in topographically diverse terrain.
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Project description:BACKGROUND: Exposure to air pollution is associated with a short-term increase in mortality, and this field has begun to focus on health impact assessment. OBJECTIVES: Our aim was to estimate the impact of PM10 on mortality within 2 days from the exposure in the Italian region of Lombardy for the year 2007, at the municipality level, examining exposure entailed by daily intermunicipality commuting and accounting for uncertainty propagation. METHODS: We combined data from different sources to derive probabilistic distributions for all input quantities used to calculate attributable deaths (mortality rates, PM10 concentrations, estimated PM10 effects, and commuting flows) and applied a Monte Carlo procedure to propagate uncertainty and sample the distribution of attributable deaths for each municipality. RESULTS: We estimated that annual average PM10 concentrations above the World Health Organization-recommended threshold of 20 ?g/m3 were responsible for 865 short-term deaths (80% credibility interval: 475, 1,401), 26% of which were attributable to PM10 above the European Union limit of 40 ?g/m3. Reducing annual average PM10 concentrations > 20 ?g/m3 by 20% would have reduced the number of attributable deaths by 36%. The largest estimated impacts were along the basin of the Po River and in the largest cities. Commuting contributed to the spatial distribution of the estimated impact. CONCLUSIONS: Our estimates, which incorporated uncertainty quantification, indicate that the short-term impact of PM10 on mortality in Lombardy in 2007 was notable, and that reduction in air pollution would have had a substantial beneficial effect on population health. Using commuting data helped to identify critical areas for prioritizing intervention.
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Project description:Conventional mammography can suffer from poor contrast between healthy and cancerous tissues due to the small difference in attenuation properties. Coherent scatter slot scan imaging is an imaging technique which provides additional information and is compatible with conventional mammography. A Monte Carlo simulation of coherent scatter slot scan imaging was performed to assess its performance and provide system optimization. Coherent scatter could be exploited using a system similar to conventional slot scan mammography system with antiscatter grids tilted at the characteristic angle of cancerous tissues. System optimization was performed across several parameters, including source voltage, tilt angle, grid distances, grid ratio, and shielding geometry. The simulated carcinomas were detectable for tumors as small as 5 mm in diameter, so coherent scatter analysis using a wide-slot setup could be promising as an enhancement for screening mammography. Employing coherent scatter information simultaneously with conventional mammography could yield a conventional high spatial resolution image with additional coherent scatter information.
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