The information matrix of model (21) is singular under the null hypothesis (H_{0}:psi _{x}=0).
Let us now consider the calculation of the matrix of model coefficients, that is, the matrix of general term, given that is known.
a V s models produced by linearized inversion at two grid points shown in c Error bars are calculated from a posteriori covariance matrix of model parameters.
We analyze the stability of the disease-free equilibrium by investigating the eigenvalues of the Jacobian matrix of model (2.2) at (P_{0}).
The combined variance-covariance matrix of model parameters including both measurement error and a priori error is given as {boldsymbol{S}}_c={boldsymbol{S}}_m+{boldsymbol{S}}_s.
The (psi _{x}psi _{x}) element of the information matrix of model (21) reparametrised in terms of (gamma _{yy}(0),gamma _{yy}(1),alpha ) and (psi _{x}) is zero under the null hypothesis ( H_{0}:psi _{x}=0).
end{aligned} (27)In this context, we can prove the following proposition: The nullity of the information matrix of model (27) is one under the joint null hypothesis (H_{0}:psi _{x}=psi _{u}=0).
It depends on the most likely solution misfit ( {mathcal{L}}_{i} ) and the determinant of the posterior covariance matrix of model parameters ( {tilde{mathbf{C}}}_{i}^{{mathbf{M}}} ), in particular space time grid point.
end{aligned}Given (8), this result implies that the information matrix of model (21) will only have rank 3 under the null when the true value of (alpha ) is not zero.(square ).
The Jacobian matrix of model (3) at any state variable is given by J x,y)= begin{pmatrix} -bmathrm{e}^{- x+y)}y+alpha& bmathrm{e}^{- x+y)}y+alpha<a& bmathrm{epmatrix}.
