Training-Informed Differentiable Bayesian Inference with PROSPECT for Leaf Trait Retrieval and Uncertainty Analysis

Leaf radiative transfer models provide a physical basis for leaf trait retrieval, but compensating parameter effects and measurement discrepancies constrain estimation accuracy and uncertainty characterization. This study proposes Training-Informed Differentiable Bayesian Inference (TI-DBI). This method integrates training-derived joint lognormal priors, wavelength-specific spectral biases, and residual scales into a differentiable PROSPECT-D model, enabling joint parameter inference via the No-U-Turn Sampler (NUTS). Evaluated on multi-source datasets, TI-DBI yields relative root mean square errors (rRMSEs) of 27.31%, 33.72%, 16.22%, and 37.66% for chlorophyll (Cab), carotenoids (Car), equivalent water thickness (Cw), and leaf dry mass per area (Cm). Outperforming an uncalibrated Markov chain Monte Carlo (MCMC) baseline for all traits and partial least squares regression (PLSR) for Cab, Car, and Cw, these results confirm the specific value of the data-informed probabilistic framework. Beyond point-estimation, TI-DBI substantially improves uncertainty characterization. It yields narrower interval widths and lower interval scores than the uncalibrated baseline, with prediction interval coverage probability (PICP) of the 95% highest density intervals (HDIs) reaching 93.14%, 96.46%, 89.62%, and 86.22% for Cab, Car, Cw, and Cm, respectively. Ablation and sensitivity studies confirm that both the learned priors and spectral error calibration drive these performance gains across varying training fractions and spectral configurations. TI-DBI strictly preserves the forward model’s physical structure while providing a robust, practical framework for jointly evaluating trait estimation accuracy and posterior uncertainty.