Monte Carlo cross-validation methods

The story of the initial steps in the development of molecular simulation methods for the study of liquids at the molecular scale has been charmingly recounted hy Wood (1986 1996). By 1957, these simulation techniques had been firmly established the successful cross-checking of molecular dynamics calculations against Monte Carlo results was a crucial step in validating simulation methods for the broader scientific community. 

We still use the corn protein data described in Section 4.1. Here we do not consider all the variables but only the 28 wavelengths selected by CARS. For the proposed method, the number of Monte Carlo simulations is set to 1000. At each simulation 60% samples selected randomly are used as training samples and the remaining serve as test samples. The number of latent variables (LVs) for PCR, PLS and ECR (a = 0.5) is chosen using 5-fold cross validation. 

Using t-test, 13 out of the 21 variables are identified to be significant (P < 0.01). For SPA, we use the same setting as described in our previous work [14]. Three variables are selected with the aid of SPA. Let Vo, Vi and V2 denote the sets containing all the 21 variables, the 13 variables selected by t-test and the 3 variables selected by SPA, respectively. To run the proposed method, we set the number of Monte Carlo simulations to 1000. At each simulation 70% samples are randomly selected to build a PLS-LDA model with the number of latent variables optimized by 10-fold cross validation. The remaining 30% samples working as test sets on which the misclassification error is computed. 

The LLL version of the MORSE neutron Monte Carlo code was used to generate plutonium metal-array-criticality data. We used a 92-group neutron cross-section set derived from Howerton s compilation. Thermal data for water were derived by the FLANGE code. Validation of the computational methods was done by calculating (a) a single water-reflected metal sphere, (b) the limiting critical concentration of plutonium in water, (c) the arrays of 3- and 6-kg plutonium cylinders, and (d) the lattices of Pu-Al rods in water. ... 

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