Niklas Linde - Inverse Problems: a Bayesian Perspective (Perspective) скачать в хорошем качестве

Niklas Linde - Inverse Problems: a Bayesian Perspective (Perspective)

This presentation was presented during the 4th Cargèse Summer School on Flow and Transport in Porous and Fractured Media in 2018. Don’t hesitate to have a look on other lectures of the summer school on our channel! More information on the Summer School on https://cargese2018.sciencesconf.org/ ** Indirect data (e.g., drawdown data, tracer breakthrough curves, electrical resistances or seismic traces) acquired at a given site are best combined within a formal framework to provide subsurface models or process descriptions that honour known physics and prior knowledge while acknowledging non-linearity as well as experimental and modelling uncertainties. Bayes theorem offers a general framework to achieve this. As soon as the physical response is responding non-linearly to model parameter values (i.e., most physics of interest), then a general solution to the inverse problem must be sought using computationally expensive global search algorithms (e.g., Monte Carlo, Markov chain Monte Carlo). This lecture introduces basic theory and algorithms used to sample from posterior density functions. After this, case studies with focus on complex spatial priors are presented. Finally, I share my experience on how to make this beautiful theory work in practice when confronted with discontinuous spatial fields and large data sets with high signal-to-noise ratios. Find the slide presentation on https://perso.univ-rennes1.fr/joris.h... #InverseTheory #BayesianApproach #Stochastic #NonLinearProblems #Geophysics