This dissertation is about Bayesian learning from data. How can humans and computers learn from data? This question is at the core of both statistics and — as its name already suggests — machine... Show moreThis dissertation is about Bayesian learning from data. How can humans and computers learn from data? This question is at the core of both statistics and — as its name already suggests — machine learning. Bayesian methods are widely used in these fields, yet they have certain limitations and problems of interpretation. In two chapters of this dissertation, we examine such a limitation, and overcome it by extending the standard Bayesian framework. In two other chapters, we discuss how different philosophical interpretations of Bayesianism affect mathematical definitions and theorems about Bayesian methods and their use in practise. While some researchers see the Bayesian framework as normative (all statistics should be based on Bayesian methods), in the two remaining chapters, we apply Bayesian methods in a pragmatic way: merely as tool for interesting learning problems (that could also have been addressed by non-Bayesian methods). Show less
This thesis is composed of papers on four topics: Bayesian theory for the sparse normal means problem, specifically for the horseshoe prior (Chapters 1-3), Bayesian theory for community detection ... Show moreThis thesis is composed of papers on four topics: Bayesian theory for the sparse normal means problem, specifically for the horseshoe prior (Chapters 1-3), Bayesian theory for community detection (Chapter 4), nested model selection (Chapter 5), and the application of competing risk methods in the presence of time-dependent clustering (Chapter 6). Show less
