Ultrahigh Dimensional Variable Selection for Interpolation of Point Referenced Spatial Data: A Digital Soil Mapping Case Study.

Modern soil mapping is characterised by the need to interpolate point referenced (geostatistical) observations and the availability of large numbers of environmental characteristics for consideration as covariates to aid this interpolation. Modelling tasks of this nature also occur in other fields such as biogeography and environmental science. This analysis employs the Least Angle Regression (LAR) algorithm for fitting Least Absolute Shrinkage and Selection Operator (LASSO) penalized Multiple Linear Regressions models. This analysis demonstrates the efficiency of the LAR algorithm at selecting covariates to aid the interpolation of geostatistical soil carbon observations. Where an exhaustive search of the models that could be constructed from 800 potential covariate terms and 60 observations would be prohibitively demanding, LASSO variable selection is accomplished with trivial computational investment.

Similarities between line fishing and baited stereo-video estimations of length-frequency: novel application of Kernel Density Estimates.

Age structure data is essential for single species stock assessments but length-frequency data can provide complementary information. In south-western Australia, the majority of these data for exploited species are derived from line caught fish. However, baited remote underwater stereo-video systems (stereo-BRUVS) surveys have also been found to provide accurate length measurements. Given that line fishing tends to be biased towards larger fish, we predicted that, stereo-BRUVS would yield length-frequency data with a smaller mean length and skewed towards smaller fish than that collected by fisheries-independent line fishing. To assess the biases and selectivity of stereo-BRUVS and line fishing we compared the length-frequencies obtained for three commonly fished species, using a novel application of the Kernel Density Estimate (KDE) method and the established Kolmogorov-Smirnov (KS) test. The shape of the length-frequency distribution obtained for the labrid Choerodon rubescens by stereo-BRUVS and line fishing did not differ significantly, but, as predicted, the mean length estimated from stereo-BRUVS was 17% smaller. Contrary to our predictions, the mean length and shape of the length-frequency distribution for the epinephelid Epinephelides armatus did not differ significantly between line fishing and stereo-BRUVS. For the sparid Pagrus auratus, the length frequency distribution derived from the stereo-BRUVS method was bi-modal, while that from line fishing was uni-modal. However, the location of the first modal length class for P. auratus observed by each sampling method was similar. No differences were found between the results of the KS and KDE tests, however, KDE provided a data-driven method for approximating length-frequency data to a probability function and a useful way of describing and testing any differences between length-frequency samples. This study found the overall size selectivity of line fishing and stereo-BRUVS were unexpectedly similar.