Bayesian Measurement Error Correction in Structured Additive Distributional Regression with an Application to the Analysis of Sensor Data on Soil-Plant Variability

Abstract: The flexibility of the Bayesian approach to account for covariates with measurement error is combined with semiparametric regression models for a class of continuous, discrete and mixed univariate response distributions with potentially all parameters depending on a structured additive predictor. Markov chain Monte Carlo enables a modular and numerically efficient implementation of Bayesian measurement error correction based on the imputation of unobserved error-free covariate values. We allow for very general measurement errors, including correlated replicates with heterogeneous variances. The proposal is first assessed by a simulation trial, then it is applied to the assessment of a soil-plant relationship crucial for implementing efficient agricultural management practices. Observations on multi-depth soil information forage ground-cover for a seven hectares Alfalfa stand in South Italy were obtained using sensors with very refined spatial resolution. Estimating a functional relation between ground-cover and soil with these data involves addressing issues linked to the spatial and temporal misalignment and the large data size. We propose a preliminary spatial interpolation on a lattice covering the field and subsequent analysis by a structured additive distributional regression model accounting for measurement error in the soil covariate. Results are interpreted and commented in connection to possible Alfalfa management strategies.