Embedding Positive Process Models into Lognormal Bayesian State Space Frameworks using Moment Matching

In ecology it is common for processes to be bounded based on physical constraints of the system. One common example is the positivity constraint, which applies to phenomena such as duration times, population sizes, and total stock of a system's commodity. In this paper, we propose a novel method for embedding these dynamical systems into a lognormal state space model using an approach based on moment matching. Our method enforces the positivity constraint, allows for embedding of arbitrary mean evolution and variance structure, and has a closed-form Markov transition density which allows for more flexibility in fitting techniques. We discuss two existing lognormal state space models, and examine how they differ from the method presented here. We use 180 synthetic datasets to compare the forecasting performance under model misspecification and assess estimability of precision parameters between our method and existing methods. We find that our models well under misspecification, and that fixing the observation variance both helps to improve estimation of the process variance and improves forecast performance. To test our method on a difficult problem, we compare the predictive performance of two lognormal state space models in predicting Leaf Area Index over a 151 day horizon by embedding a process-based ecosystem model. We find that our moment matching model performs better than its competitor, and is better suited for long predictive horizons. Overall, our study helps to inform practitioners about the importance of embedding sensible dynamics when using models complex systems to predict out of sample.