Various indices for model selection and application to autocorrelation function for geotechnical property

Abstract

Evaluating multiple candidate models for prediction based on a large amount of accumulated data and selecting the appropriate model based on the criteria is an important task, which is called model selection. In this study, we have taken up Evidence, Laplace approximation, AIC, and BIC as indices for model selection, and conducted numerical experiments using 100 simulated data sets for polynomial and one-dimensional spatial distributions to investigate the rate at which the correct model is selected. The results showed that the model is selected correctly when the noise level or the second component of the random field is small, but when the noise level or the second component is large, the ratio of correct selection becomes small. Evidence is more stable than AIC and BIC in the numerical experiments. Furthermore, an example of model selection of autocorrelation function using Evidence, AIC and BIC is shown for measured data of geotechnical properties.