Friday, 17 January 2014

Roving Researcher and the Great US Trip

Since January 5, I have been travelling in the USA. The trip started with the National Radio Science Meeting in Boulder, Colorado. After that I flew to Cleveland in order to visit the Mathematics Department of the Case Western Reserve University. We are trying to solve some high-dimensional inverse problems with around 1,000,000 unknowns. Add dynamic features to this and real-time requirement.... Well if you do it wisely, regular MacBook Pro can do the job!

Today I am giving a talk in the colloquium at the math dept for around 30 persons. Title and abstract below! I will be back in Sodankylä Jan 29 afternoon. Before the trans-Atlantic flight, I will stop in Boston for two nights and discuss our African affairs and upcoming projects!

Bayesian inversion with Gaussian stochastic difference equations

Linear stochastic difference equations provide a computationally efficient way to present certain Gaussian random processes. It is well-known that difference equations can be derived from stochastic differential equations via discretisation schemes. This makes them appealing for Bayesian statistical  inverse problems, because we can model a priori probability distributions with continuous-parameter models and make the practical computations in finite spaces. Hence we are interested for constructing stochastic difference approximations of certain Gaussian processes. We start by considering the stationary Gaussian Markov random fields and their fast approximations via systems of linear stochastic difference equations. We study discretisation schemes of the stochastic differential equations on different lattices and consider the continuous limits, i.e. the convergence of the discrete objects to the continuous objects. Then we extend the study to non-stationary random fields, i.e. anisotropic and inhomogeneous fields via numerical examples.

In the Rocky Mountains with the giant car. Note the Texas plates!!

The campus police car at the Case Western Reserve University.

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