Dynamical System Identification, Model Selection and Model Uncertainty Quantification by Bayesian Inference. (arXiv:2401.16943v1 [stat.ME])

This study presents a Bayesian maximum \textit{a~posteriori} (MAP) framework
for dynamical system identification from time-series data. This is shown to be
equivalent to a generalized zeroth-order Tikhonov regularization, providing a
rational justification for the choice of the residual and regularization terms,
respectively, from the negative logarithms of the likelihood and prior
distributions. In addition to the estimation of model coefficients, the
Bayesian interpretation gives access to the full apparatus for Bayesian
inference, including the ranking of models, the quantification of …

arxiv bayesian bayesian inference data framework generalized identification inference map model selection negative quantification regularization residual series stat.me study terms uncertainty