Pedretscher, B.; Kaltenbacher, B.; Pfeiler, O. Parameter identification and uncertainty quantification in stochastic state space models and its application to texture analysis. (English) Zbl 1480.60080 Appl. Numer. Math. 146, 38-54 (2019). Summary: In this paper, a computational framework, which enables efficient and robust parameter identification, as well as uncertainty quantification in state space models based on Itô stochastic processes, is presented. For optimization, a Maximum Likelihood approach based on the system’s corresponding Fokker-Planck equation is followed. Gradient information is included by means of an adjoint approach, which is based on the Lagrangian of the optimization problem. To quantify the uncertainty of the Maximum-A-Posteriori estimates of the model parameters, a Bayesian inference approach based on Markov Chain Monte Carlo simulations, as well as profile likelihoods are implemented and compared in terms of runtime and accuracy. The framework is applied to experimental electron backscatter diffraction data of a fatigued metal film, where the aim is to develop a model, which consistently and physically meaningfully captures the metal’s microstructural changes that are caused by external loading. MSC: 60G07 General theory of stochastic processes 62F15 Bayesian inference 35Q84 Fokker-Planck equations Keywords:stochastic state space model; parameter identification; uncertainty quantification; profile likelihood; adjoint approach; Fokker-Planck equation; thermo-mechanical fatigue; texture analysis Software:MTEX; AMICI; PESTO PDFBibTeX XMLCite \textit{B. Pedretscher} et al., Appl. Numer. Math. 146, 38--54 (2019; Zbl 1480.60080) Full Text: DOI References: [1] Alili, L.; Patie, P.; Pedersen, J. L., Representations of the first hitting time density of an Ornstein-Uhlenbeck process, Stoch. Models, 21, 967-980 (2005) · Zbl 1083.60064 [2] Amann, H.; Escher, J., Analysis II. 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