Center for Data-Driven Discovery (C3D)

Bayesian inference provides a consistent method for the extraction of information from physics experiments even in ill-conditioned circumstances. The approach provides a unified rationale for data analysis, which both justifies many of the commonly used analysis procedures and reveals some of the implicit underlying assumptions. The presentation introduces the general ideas of the Bayesian probability theory with emphasis on the application to the evaluation of experimental data in plasma-wall interaction experiments. As case studies for Bayesian parameter estimation techniques examples ranging from the deconvolution of apparatus functions for improved energy resolution to change point estimation in time series are discussed. Key numerical techniques suited for Bayesian analysis are presented with a focus on recent developments of Markov Chain Monte Carlo (MCMC) algorithms for high-dimensional integration problems. Bayesian model comparison, the quantitative ranking of models for the explanation of a given data set, is illustrated with examples collected from mass spectroscopy and surface analysis, covering problems like background subtraction and automated outlier detection. Additionally the Bayesian inference techniques for the design and optimization of future experiments are introduced: Experiments, instead of being merely passive recording devices, can now be designed to adapt to measured data and to change the measurement strategy on the fly to maximize the information of an experiment. The applied key concepts and necessary numerical tools which provide the means of designing such inference chains and the crucial aspects of data fusion are presented and areas of ongoing research are highlighted.