BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:David Bolin (King Abdullah University of Science and Technology) DTSTART:20230427T111500Z DTEND:20230427T120000Z DTSTAMP:20260422T155153Z UID:gbgstats/24 DESCRIPTION:Title: Gaussian Whittle-Matérn fields on metric graphs\nby David Bolin (Ki ng Abdullah University of Science and Technology) as part of Gothenburg st atistics seminar\n\nLecture held in MVL14.\n\nAbstract\nWe define a new cl ass of Gaussian processes on compact metric graphs such as street or river networks. The proposed models\, the Whittle-Matérn fields\, are defined via a fractional stochastic partial differential equation on the compact m etric graph and are a natural extension of Gaussian fields with Matérn co variance functions on Euclidean domains to the non-Euclidean metric graph setting. Existence of the processes\, as well as their sample path regular ity properties are derived. The model class in particular contains differe ntiable Gaussian processes. To the best of our knowledge\, this is the fir st construction of a valid differentiable Gaussian field on general compac t metric graphs.\nWe then focus on a model subclass which we show contains processes with Markov properties. For this case\, we show how to evaluate finite dimensional distributions of the process exactly and computational ly efficiently. This facilitates using the proposed models for statistical inference without the need for any approximations. Finally\, we derive so me of the main statistical properties of the model class\, such as consist ency of maximum likelihood estimators of model parameters and asymptotic o ptimality properties of linear prediction based on the model with misspeci fied parameters. \nThe usage of the model class is illustrated through an application to traffic data.\n LOCATION:https://researchseminars.org/talk/gbgstats/24/ END:VEVENT END:VCALENDAR