vignettes/Available_parameter_estimation_algorithms.Rmd
Available_parameter_estimation_algorithms.RmdFor the moment, CroptimizR includes two parameter estimation algorithms:
a Frequentist one: the Nelder-Mead Simplex (Nelder and Mead 1965),
a Bayesian one: DREAM-zs (Vrugt 2016).
Frequentist methods involve minimizing a goodness-of-fit criterion. Crop models often have discontinuities that make it difficult to use gradient-based minimization methods such as Gauss–Newton or Levenberg–Marquardt. A common approach, adopted in CroptimizR, is thus to use the Nelder–Mead simplex algorithm, which is adapted to non-smooth functions because the search of the optimum is not based on the computation of the function’s gradient. Although few theoretical results are available (Lagarias et al. 1998), this algorithm is very popular because it can be used for multidimensional minimization for essentially any function.
The simplex algorithm used in CroptimizR is interfaced from the nloptr package (Johnson) but a multi-start feature has been implemented in addition. Indeed, as it is a local optimization method, CroptimizR proposes to repeat automatically the minimization from different starting parameter values to minimize the risk of converging to a local minimum. The user specifies the number of repetitions and possibly the starting parameter values (if not provided, they are sampled within the parameters’ bounds. To help analyze the behavior of the algorithm, CroptimizR generates plots of final estimated parameter values versus initial values.
A simple example of application of the method is provided in this vignette.
In a Bayesian approach estimated parameters are treated as random variables and one seeks to determine their joint probability distribution, called the posterior distribution. The uncertainty in the estimated parameters are thus central in this approach. An advantage of the Bayesian approach is that it uses prior information about the parameters values.
The DREAM-zs algorithm is a multi-chain MCMC method which is recognized has an efficient method for complex, high-dimensional and multi-modal target distributions. It is extensively described in (Vrugt 2016). In CroptimizR, it is interfaced from the BayesianTools package (Hartig, Minunno, and Paul).
It provides different types of plots and results including plots of prior and posterior densities, correlation plots, Gelman diagnostic plot, sample of posterior distribution and associated statistics.
An example of application of the method is provided in this vignette.
For both method, multiple criteria to minimize (for frequentist methods) and likelihoods (for Bayesian methods) are provided in CroptimizR.