Bayesian measurement error correction in structured additive distributional regression with an application to the analysis of sensor data on soil–plant variability
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The flexibility of the Bayesian approach to account for covariates with measurement error is combined with semiparametric regression models. We consider 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 and 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 aggregation 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.
KeywordsStructured additive distributional regression Agricultural management Bayesian semiparametric regression Measurement error
Alessio Pollice and Giovanna Jona Lasinio were partially supported by the PRIN2015 project “Environmental processes and human activities: capturing their interactions via statistical methods (EPHASTAT)” funded by MIUR - Italian Ministry of University and Research.
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