DUGi

Non-detect Bootstrap Method for Estimating Distributional Parameters of Compositional Samples Revisited: a Multivariate Approach

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Bootstrap resampling is an attractive, computationally-intensive approach for estimating populationparameters and their associated uncertainties. Values below detection limit—also referredto as non-detects—frequently arise particularly when dealing with multivariate geochemical concentrations,making the estimation of distributional parameters—mean, median, percentiles—adifficult challenge. The bootstrap method can be used repeatedly for analyzing resampled versionsof the original data set. This way it is possible to estimate univariate distributional parameterswhile also capturing the additional uncertainty due to missing information. Within this approach,a method must be chosen to substitute non-detects with appropriate values given the compositionalnature of the data. This idea was first introduced by Olea (2008) in the previous CoDaWork’08meeting. Making use of the isometric log-ratio transformation and analyzing one variable at a time,he proposed a univariate bootstrap procedure where the distributional parameters of geochemicalcomponents were modeled from bootstrap resamples considering different criteria to impute nondetects.After conducting a sensitivity analysis on both proportion of non-detects and sample size,the study concluded that when drawing randomly a value from the extrapolated tail below the detectionlimit of the distribution best fitting the complete data—usually the log-normal distributionfor geochemical data—the bootstrap estimates turned out to be more accurate than those obtainedusing simple imputation methods. Rather than analyzing each variable separately, here we makea step further to get the most of the covariance structure of the data set, extending the univariateapproach for replacing non-detects to a multivariate setting. As a test bench, a number of datasets containing non-detects are artificially generated from real geochemical data and used to evaluatethe performance of different replacement methods within the bootstrap process. First resultsshow improved results when non-detects are replaced by random values drawn from a conditionaltruncated additive logistic model

Universitat de Girona. Departament d’Informàtica i Matemàtica Aplicada