Full Bayesian Inference in Hidden Markov Models of Plant Growth
Accurately modeling the growth process of plants in interaction with their environment is important for predicting their biophysical characteristics, referred to as phenotype prediction. Most models are described by discrete dynamic systems in general state-space representation with important domain-specific characteristics: First, plant model parameters have usually clear functional meanings and may be of genetic origins, thus necessitating a precise estimation. Second, critical growth variables, specifically biomass production and dynamic allocation to organs, are hidden variables not accessible to measure. Finally, the difficulty to assess the local plant environment may imply the introduction of process noises in models. Therefore, a precise understanding of the system’s behavior requires the joint estimation of functional parameters, hidden states, and noise parameters. In this paper we describe how a full Bayesian method of estimation can accurately estimate all these key model variables using Markov chain Monte Carlo (MCMC) techniques. In the presence of both process and observation noises, it requires to use adequate particle MCMC (PMCMC) algorithms to efficiently sample the hidden states which, consequently, allows for a precise estimation of all noise parameters involved. Thanks to the Bayesian framework, appropriate choices of prior distributions for the noise parameters have enabled analytical posterior distributions and only simple updates are required.
Furthermore, this estimation strategy can be easily generalized and adapted to different types of plant growth models, such as organ-scale or compartmental, provided that they are formulated as hidden Markov models. Our estimation method improves on those classically used in plant growth modeling in several aspects: First, by building upon a general probabilistic framework the estimation results allow proper statistical analyses. It is useful in prediction, no only for uncertainty and risk analysis (e.g., for crop yield prediction) but also to analyze the results of experimental trials, for example, to compare genotypes in breeding. Moreover, the care taken in the estimation of hidden variables opens new perspectives in the understanding of inner growth processes, notably the balance and interaction between biomass production and allocation (referred to as source-sink dynamics). Applications of this estimation procedure are demonstrated on the GreenLab model for Arabidopsis thaliana and the Log-Normal Allocation and Senescence (LNAS) model for sugar beet, on both synthetic and real data.