Bayesian Principal Component Regression Model with Spatial Effects for Forest Inventory under Small Field Sample Size

Despite the fact that environmental variables often exhibit spatial correlation, this is not typically accounted in calibration models for remote sensed observations. Another feature in many remote sensing instruments is that the derived predictor variables are highly correlated. Both of these affect the prediction accuracy, especially when the training set for model calibration is small. We propose a general model calibration procedure for remote sensed data and demonstrate it with airborne laser scanning data for forest inventory. The model is a linear regression model that accounts for multicollinearity in the predictors by principal components and Bayesian regularization. It has a spatial random effect component to account for the spatial correlations not explained by a simple linear model. A very efficient Markov chain Monte Carlo sampling scheme is given that allows for full Bayesian uncertainty quantification of the model predictions. Our proposed model outperforms other linear calibration models tested, especially when there are spatial effects, multicollinearity and the training set size is small.