MCMC and Multivariate Models

In this chapter, we focus on models with multivariate output. That includes most process-based models (PBMs). Models with multivariate output are not fundamentally different from the simpler models we studied in the previous chapters; we can still write them as functions f of their input consisting of covariates x and parameters \(\theta \) . But the output \(z=f(x,\theta )\) from the models will be multivariate, e.g. time series of different properties of an ecosystem. That does not affect the principles of Bayesian calibration in any way but may complicate its execution. In this chapter, we illustrate these issues with a quite simple PBM that as output produces two time series: the growth over time of the biomass and leaf area of vegetation.