Modern methods in bayesian probabilistic modeling and their applications

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Abstract

A fundamental task in all fields of science is to learn from observations. However, undertaking this is usually hindered in two ways: first, the direct observation of the phenomenon may be challenging or impossible, requiring a model of the phenomenon and a statistical approach to separate desired from undesired information. Second, the number of observations may be small, so the resulting uncertainty must be taken into account. As a resort, the field of Bayesian modeling provides a canonical framework to perform statistical inference from data and prior knowledge in a way that allows to quantify the uncertainty of the results as well. In this approach, probability distributions are used as carriers of information and transformed accordingly. However, in most cases the required computations can only be performed numerically. In this work we contribute to Bayesian modeling in several ways: first, we present the paraNUTS algorithm for parallelized inference that is formulated in the map- reduce paradigm and achieves considerable speed-ups without significant loss of inference quality. Next, we present TuringOnline.jl, a software package for inference in online settings, that also achieves speed-ups while retaining inference quality to a high degree. Moreover, we present an application of Bayesian modeling to surface topography analysis that yielded action-guiding findings for the field to ensure reproducible results from future studies. Finally, we contribute to nowcasting of infection numbers with our CorCast system that provides the necessary unified treatment of data and models that is extremely important for practical application. Although targeted at the Sars-CoV-2 pandemic, the system is designed to be adopted to other epidemiological modeling easily. Additionally, the appendices cover research that was not related to Bayesian modeling: first, a scalable and flexible approach to signal classification in mass spectrometry raw data using locality-sensitive hashing and second, a machine learning approach to a classification task in the field of surface topography analysis.

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