Robust estimation of parameters in nonlinear ordinary differential equation models

Identification of parameters in systems biology

“…where x d N is the solution of ( 1),( 2) with u = u N −1 , v = v d as it is constructed in (3). Finding x d N , U d N from (3), ( 4), (7) form the method of staggered corrector [17].…”

“…(2) Set x d N,0 (t) and find x d N (t, u N −1 ) via quasilinearization from (3),(4). (3) Having x d N (•, u N −1 ) find sensitivity matrices U d N by solving linear ODE systems (7). (4) Find ∆u by solving linear algebraic equations system (9) and update the new value u N of the parameter using (5).…”

“…Identification of parameters through noisy measurements is an ill-posed inverse problem and it requires the development of delicate regularization techniques [1]. Solving inverse problems in systems biology is an actively growing research field [2,3,4,5,6,7,8,9,10]. We refer to the survey article [6] for references.…”

Differential equations in data analysis

“…Analyzing the asymptotic properties of such an estimator, in the context of ODEs defined on a finite interval [0, T ], is referred to in the literature as infill asymptotics. Qiu, Hu, Liang, and Cui (2016) developed a robust estimation technique for ODE models that can cope with outliers by using an appropriate loss function in Equation ). An estimation methodology designed for data coming from the exponential family was developed in Miao, Wu, and Xue (2014).…”

Robust parameter estimation for dynamical systems from outlier-corrupted data

“…noise levels, outlier generating mechanisms, and mathematical models which influence the performance. For dynamical models of biological systems, the Huber M-estimator was already successfully applied, yielding more reliable parameter estimates (Cao et al, 2011;Qiu et al, 2016). A comprehensive evaluation of different methods in the field of quantitative biology is, however, missing.…”