Last Friday, Zhe Sha gave a talk on Bayesian Hierarchical modelling for large-scale geophysical inverse problems at one of the regular Statistics seminars organised by the University of Bristol’s Institute for Statistical Science.
In her talk, Zhe explained how a model-data synthesis framework, based on Bayesian hierarchical modelling, can be used improve our understanding and predictions of large-scale geophysical processes. Gaussian Markov random fields (GMRF) are used to approximate the spatial process to reduce the computational cost, and Bayesian inference is performed using the INLA (integrated nested Laplace approximations) method. For non-stationary global processes (i.e. processes with time-varying mean and/or variance), two general models are proposed and the GMRF approximation and INLA implementation are applied to both.
Finally, Zhe showed an example application of the framework: improving estimates of global(GIA) by using GPS measurements.