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Remote sensing observations are extensively used for analysis ofenvironmental variables. These variables often exhibit spatial correlation,which has to be accounted for in the calibration models used in predictions,either by direct modelling of the dependencies or by allowing for spatiallycorrelated stochastic effects. Another feature in many remote sensinginstruments is that the derived predictor variables are highly correlated,which can lead to unnecessary model over-training and at worst, singularitiesin the estimates. Both of these affect the prediction accuracy, especially whenthe training set for model calibration is small. To overcome these modellingchallenges, we present a general model calibration procedure for remotelysensed data and apply it to airborne laser scanning data for forest inventory.We use a linear regression model that accounts for multicollinearity in thepredictors by principal components and Bayesian regularization. It has aspatial random effect component for the spatial correlations that are notexplained by a simple linear model. An efficient Markov chain Monte Carlosampling scheme is used to account for the uncertainty in all the modelparameters. We tested the proposed model against several alternatives and itoutperformed the other linear calibration models, especially when there werespatial effects, multicollinearity and the training set size was small.

Bayesian Principal Component Regression model with spatial effects for forest inventory under small field sample size