Assessing the accuracy of predictive models is critical because predictive models have been increasingly used across various disciplines and predictive accuracy determines the quality of resultant predictions. Pearson product-moment correlation coefficient (r) and the coefficient of determination (r²) are among the most widely used measures for assessing predictive models for numerical data, although they are argued to be biased, insufficient and misleading. In this study, geometrical graphs were used to illustrate what were used in the calculation of r and r² and simulations were used to demonstrate the behaviour of r and r² and to compare three accuracy measures under various scenarios. Relevant confusions about r and r², has been clarified. The calculation of r and r² is not based on the differences between the predicted and observed values. The existing error measures suffer various limitations and are unable to tell the accuracy. Variance explained by predictive models based on cross-validation (VEcv) is free of these limitations and is a reliable accuracy measure. Legates and McCabe’s efficiency (E₁) is also an alternative accuracy measure. The r and r² do not measure the accuracy and are incorrect accuracy measures. The existing error measures suffer limitations. VEcv and E₁ are recommended for assessing the accuracy. The applications of these accuracy measures would encourage accuracy-improved predictive models to be developed to generate predictions for evidence-informed decision-making.

Spatially continuous predictions of seabed hardness are important baseline environmental information for sustainable management of Australia’s marine jurisdiction. Seabed hardness is often inferred from multibeam backscatter data with unknown accuracy and can be inferred from underwater video footage at limited locations. In this study, we classified the seabed into four classes based on two new seabed hardness classification schemes (i.e., hard90 and hard70). We developed optimal predictive models to predict seabed hardness using random forest (RF) based on the point data of hardness classes and spatially continuous multibeam data. Five feature selection (FS) methods that are variable importance (VI), averaged variable importance (AVI), knowledge informed AVI (KIAVI), Boruta and regularized RF (RRF) were tested based on predictive accuracy. Effects of highly correlated, important and unimportant predictors on the accuracy of RF predictive models were examined. Finally, spatial predictions generated using the most accurate models were visually examined and analysed. This study confirmed that: 1) hard90 and hard70 are effective seabed hardness classification schemes; 2) seabed hardness of four classes can be predicted with a high degree of accuracy; 3) the typical approach used to pre-select predictive variables by excluding highly correlated variables needs to be re-examined; 4) the identification of the important and unimportant predictors provides useful guidelines for further improving predictive models; 5) FS methods select the most accurate predictive model(s) instead of the most parsimonious ones, and AVI and Boruta are recommended for future studies; and 6) RF is an effective modelling method with high predictive accuracy for multi-level categorical data and can be applied to ‘small p and large n’ problems in environmental sciences. Additionally, automated computational programs for AVI need to be developed to increase its computational efficiency and caution should be taken when applying filter FS methods in selecting predictive models.

Wavelet analysis, as a promising technique, has been used to approach numerous problems in science and engineering. Recent years have witnessed its novel application in economic and finance. This paper is to investigate whether features (or indicators) extracted using the wavelet analysis technique could improve financial forecasting by means of Financial Genetic Programming (FGP), a genetic programming-based forecasting tool. More specifically, to predict whether the Dow Jones Industrial Average (DJIA) Index will rise by 2.2% or more within the next 21 trading days, we first extract some indicators based on wavelet coefficients of the DJIA time series using a discrete wavelet transform; we then feed FGP with those wavelet-based indicators to generate decision trees and make predictions. By comparison with the prediction performance of our previous study, it is suggested that wavelet analysis be capable of bringing in promising indicators, and improving the forecasting performance of FGP.