b) For individuals who reported having been told they had HBP (SR = 1), we estimate the probability of having clinically measured HBP using the sensitivity estimate described in Equation (2).
In this paper, we present an alternative approach using the PDE sensitivity equation to develop algorithms for computing gradients.
The rate of changes of eigenvectors and a subset of measured natural frequencies are used to assemble the sensitivity equation of the strain-based transfer function.
Three different numerical techniques were used to solve the sensitivity equations to control for possible numerical artifacts.
From the sensitivity equation along with the equations of motion, the time responses for the sensitivity analysis were obtained by using the Newmark time integration method.
A pseudo code description of the method can be found in Appendix C. The PCA based method differs from the other methods described here in that it does not use the sensitivity matrix S as defined in equation (7) but a truncated matrix which we refer to by.
The Gaussian proposal distribution for the MCMC was based on an approximation to the Hessian computed using a Jacobian obtained by simulating the sensitivity equations.
We solved the sensitivity equations for each parameter using three different numerical methods to control for possible artifacts; a 3-order Backward Difference (BDF3) method was compared with forward Finite Difference (FD), and the fifth-order variable step-size ODE15s routine of Matlab (The Mathworks, Natick MA).
Integration of the sensitivity equations was performed by using the staggered-direct method from the CVODES integrator.
The prediction accuracy for each subcellular location was evaluated using prediction sensitivity (Equation 1), specificity (Equation 2) and Matthews Correlation Coefficient (MCC) (Equation 3) (33).
