We calibrate a mathematical model of renal tubulointerstitial fibrosis by Hao et al which is used to explore potential drugs for Lupus Nephritis, against a real data set of 84 patients. For this purpose, we present a general calibration procedure which can be used for the calibration analysis of other biological systems as well. Central to the procedure is the idea of designing a Bayesian Gaussian process (GP) emulator that can be used as a surrogate of the fibrosis mathematical model which is computationally expensive to run massively at every input value. The procedure relies on detecting influential model parameters by a GP‐based sensitivity analysis, and calibrating them by specifying a maximum likelihood criterion, tailored to the application, which is optimized via Bayesian global optimization.
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Abstract -
In this paper, the convergence of a homotopy method (1.1) for solving the steady state problem of Burgers’ equation is considered. When ν is fixed, we prove that the solution of (1.1) converges to the unique steady state solution as epsilon → 0, which is independent of the initial conditions. Numerical examples are presented to confirm this conclusion by using the continuous finite element method. In contrast, when ν = epsilon → 0, numerically we show that steady state solutions obtained by (1.1) indeed depend on initial conditions.more » « less
