2014/09/05 by Serafim Kalliadasis, Kalliadasis, Serafim, Sebastian Krumscheid +3 · 2 citations
Mathematics · Medicine · Neuroscience · Physics and Astronomy · #Advanced Neuroimaging Techniques and Applications #FOS: Mathematics #Functional Brain Connectivity Studies #Markov Chains and Monte Carlo Methods #Statistics Theory (math.ST) #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.1409.1787
openalex publication_date 2014/09/05 · openalex created_date 2022/10/06 · openalex updated_date 2026/07/28
In many applications it is desirable to infer coarse-grained models from\nobservational data. The observed process often corresponds only to a few\nselected degrees of freedom of a high-dimensional dynamical system with\nmultiple time scales. In this work we consider the inference problem of\nidentifying an appropriate coarse-grained model from a single time series of a\nmultiscale system. It is known that estimators such as the maximum likelihood\nestimator or the quadratic variation of the path estimator can be strongly\nbiased in this setting. Here we present a novel parametric inference\nmethodology for problems with linear parameter dependency that does not suffer\nfrom this drawback. Furthermore, we demonstrate through a wide spectrum of\nexamples that our methodology can be used to derive appropriate coarse-grained\nmodels from time series of partial observations of a multiscale system in an\neffective and systematic fashion.\n