An autumn with Bayesian approaches in Vienna
14. December, 2017
Hi, my name is Aliaksandr Hubin and I am a PhD student at the department of Mathematics of the University of Oslo. In this report I would like to share my international exchange experience, which took place in Autumn 2017 and was funded by the NORBIS travel grant.
During my exchange I was staying in Vienna, Austria for a period of 3 months (from September to November 2017). There I was visiting Dr. Florian Frommlet, an assistant professor in statistics at the Center for Medical Statistics, Informatics and Intelligent Systems of Medical University of Vienna.
During the stay we have been working jointly on several projects. First of all we continued the collaboration and applied previously developed MJMCMC and GMJMCMC algorithms to GWAS studies. Performance of the algorithms was compared to other popular Bayesian approaches to GWAS such as MOSGWA and PiMass. The comparison was made on several simulation scenarios. Now the real data analysis is to be performed to finalize the paper. The results are to be published in the article entitled “A comprehensive study of Bayesian approaches to Genome-Wide Association Studies” written in collaboration with Michael Hagmann, Bernhard Bodenstorfer, Artur Gola, Małgorzata Bogdan, and Florian Frommlet.
Additionally we were finalizing the paper entitled “Deep nonlinear regression models in a Bayesian framework”, written together with Geir Storvik and Florian Frommlet. In this paper we have introduced the concept of a Deep Bayesian Regression model, which generalizes logic regressions, neural networks, fractional polynomials, and tree based regressions (and some other statistical learning approaches) into a flexible and general Bayesian framework. We then have suggested several algorithms for fitting DBR models. Several inference and prediction based examples were studied. In particular we have shown that the approach allows to recover highly nonlinear physical laws (like for example the 3rd Keppler’s law) in a closed form with a large power and low proportion of false positives. Additionally it showed good performance in asteroid and breast cancer classification problems. Finally some epigenetic study was performed with a goal to find optimal structure of dependence between the epigenetic observations and genetic factors in Arabidopsis thaliana.
Within the exchange duration I have given a talk entitled “Deep nonlinear regression models in a Bayesian framework” within Wiener Biometrische Sektion series of seminars. I have also had a chance to attend several other talks within Wiener Biometrische Sektion seminars and the as autumn seminar “Young Statisticians”, held at the Medical University of Vienna. Apart from that I attended the doctoral thesis defence of one of the fellow PhD students. This was an extremely interesting experience too, since the defense procedure was quite different from what I had seen in Norway.
The last but not least I met extremely interesting people carrying out advanced research in medical statistics ranging from clinical trials to survival analysis.
To conclude, I would like to thank NORBIS for an opportunity to spend these fantastic three months in beautiful Vienna, where not only I carried out some interesting research, but also had a chance to enjoy the imperial architecture and see numerous performances at the Opera House and Volksoper.
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