2.3.3 Methods of combining likelihood values
To calibrate crop model parameters with multivariate observations, the Bayes’ multiplication method was applied here (He et al., 2010). The combined log-likelihood \(\mathcal{l}_{\text{combined}}\) can be written as:
\(\mathcal{l}_{\text{combined}}\left(\theta,\mathbf{\lambda},\mathbf{\sigma}_{1},\mathbf{\xi}\right)=\sum_{m=1}^{M}{\mathcal{l}\left(\theta,\lambda_{m},{\sigma_{1}}_{m},\xi_{m}|{\overset{\overline{}}{Y}}_{m}\right)}\)(11)
where \(\mathbf{\lambda}\), \(\mathbf{\sigma}_{1}\)and \(\mathbf{\xi}\)denote the parameter sets of the residual error model for the multivariate observations. \(M\) represents the number of observation types. For the particular observation type \(m\), \(\lambda_{m}\),\({\sigma_{1}}_{m}\), \(\xi_{m}\) denote its residual error parameters, and \({\overset{\overline{}}{Y}}_{m}\) represents its averaged field destructive sampling data.