Efficient strategies for leave-one-out cross validation for genomic best linear unbiased prediction

Background： A random multiple-regression model that simultaneously fit all allele substitution effects for additive markers or haplotypes as uncorrelated random effects was proposed for Best Linear Unbiased Prediction, using whole-genome data. Leave-one-out cross validation can be used to quantify the predictive ability of a statistical model.Methods： Naive application of Leave-one-out cross validation is computationally intensive because the training and validation analyses need to be repeated n times, once for each observation. Efficient Leave-one-out cross validation strategies are presented here, requiring little more effort than a single analysis.Results： Efficient Leave-one-out cross validation strategies is 786 times faster than the naive application for a simulated dataset with 1,000 observations and 10,000 markers and 99 times faster with 1,000 observations and 100 markers. These efficiencies relative to the naive approach using the same model will increase with increases in the number of observations.Conclusions： Efficient Leave-one-out cross validation strategies are presented here, requiring little more effort than a single analysis.

Optimization of Shanghai marine environment monitoring sites by integrating spatial correlation and stratified heterogeneity

The water quality grades of phosphate（PO4-P） and dissolved inorganic nitrogen（DIN） are integrated by spatial partitioning to fit the global and local semi-variograms of these nutrients. Leave-one-out cross validation is used to determine the statistical inference method. To minimize absolute average errors and error mean squares,stratified Kriging（SK） interpolation is applied to DIN and ordinary Kriging（OK） interpolation is applied to PO4-P.Ten percent of the sites is adjusted by considering their impact on the change in deviations in DIN and PO4-P interpolation and the resultant effect on areas with different water quality grades. Thus, seven redundant historical sites are removed. Seven historical sites are distributed in areas with water quality poorer than Grade IV at the north and south branches of the Changjiang（Yangtze River） Estuary and at the coastal region north of the Hangzhou Bay. Numerous sites are installed in these regions. The contents of various elements in the waters are not remarkably changed, and the waters are mixed well. Seven sites that have been optimized and removed are set to water with quality Grades III and IV. Optimization and adjustment of unrestricted areas show that the optimized and adjusted sites are mainly distributed in regions where the water quality grade undergoes transition.Therefore, key sites for adjustment and optimization are located at the boundaries of areas with different water quality grades and seawater.

Discrimination between Dementia Groups and Healthy Elderlies Using Scalp-Recorded-EEG-Based Brain Functional Connectivity Networks

Objective: To establish a practical method for discriminating dementia groups and healthy elderlies, by using scalp-recorded electroencephalograms (EEGs). Methods: 16-ch EEGs were recorded during resting state for 39 dementia groups and 11 healthy elderlies. The connectivity between any two electrodes was estimated by synchronization likelihood (SL). The brain networks were constructed by normalized SL values. The present leave-one-out cross validation (LOOCV) required the Euclidean distance between any two subjects having 120-dimensional vectors concerned with the SL values for six frequency bands. In order to investigate factors which would affect the LOOCV results, principal component analysis (PCA) was applied to all the subjects. Results: The accuracy for the upper alpha yielded more than 80% and 70% in the dementia groups and the healthy elderlies, respectively. The LOOCV result could be explained in terms of brain networks such as executive control network (ECN) and default mode network (DMN) characterized by factor loadings of principal components. Conclusions: Dementia groups and healthy elderlies could be characterized by principal components of SL values between all the electrode pairs, even less connections, which revealed disruption and preservation of DMN and ECN. Significance: This study will provide a simple and practical method for discriminating dementia groups from healthy elderlies by scalp-recorded EEGs.