Bayesian Learning: Challenges, Limitations and Pragmatics

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 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).The author’s PhD position at the Mathematical Institute was supported by the Leiden IBM-SPSS Fund. The research was performed at the Centrum Wiskunde & Informatica (CWI). Part of the work was done while the author was visiting Inria Lille, partly funded by Leids Universiteits Fonds / Drs. J.R.D. Kuikenga Fonds voor Mathematici travel grant number W19204-1-35.Number theory, Algebra and Geometr

Optional Stopping with Bayes Factors: A categorization and extension of folklore results, with an application to invariant situations

It is often claimed that Bayesian methods, in particular Bayes factor methods for hypothesis testing, can deal with optional stopping. We first give an overview, using only most elementary probability theory, of three different mathematical meanings that various authors give to this claim: stopping rule independence, posterior calibration and (semi-) frequentist robustness to optional stopping. We then prove theorems to the effect that - while their practical implications are sometimes debatable - these claims do indeed hold in

Safe Testing

We present a new theory of hypothesis testing. The main concept is the S-value, a notion of evidence which, unlike p-values, allows for effortlessly combining evidence from several tests, even in the common scenario where the decision to perform a new test depends on the previous test outcome: safe tests based on S-values generally preserve Typ

How could the service delivery process of dynamic arm supports be optimized?

BACKGROUND: The service delivery process of dynamic arm support (DAS) is complex. Obtaining an optimal match between user and DAS depends on a variety of interrelated factors, different professionals are involved, and the market of available solutions is evolving. OBJECTIVE: To determine how the service delivery process of DAS could be optimized. METHODS: Interviews with DAS users that retrospectively focused on the experienced service delivery process, which was compared to the general Dutch prescription guideline. Results were presented in a focus group session to seven DAS consultants, and subsequently verified by a member-check. RESULTS: Sixteen people who considered the Gowing (a DAS new on the market) as a solution and seven DAS consultants participated. Aspects that can be optimized in the current service delivery process included an improved cooperation between clients, professionals and consultants, increased knowledge of DAS in professionals, an embedded user evaluation, and timely delivery. CONCLUSIONS: It is recommended that the service delivery process is optimized by developing a DAS specific prescription framework. The issues identified in this study should be addressed in this framework. For this additional knowledge on how to optimally match persons and DAS is needed

Why optional stopping can be a problem for Bayesians

Recently, optional stopping has been a subject of debate in the Bayesian psychology community. Rouder (Psychonomic Bulletin & Review21(2), 301–308, 2014) argues that optional stopping is no problem for Bayesians, and even recommends the use of optional stopping in practice, as do (Wagenmakers, Wetzels, Borsboom, van der Maas & Kievit, Perspectives on Psychological Science7, 627–633, 2012). This article addresses the question of whether optional stopping is problematic for Bayesian methods, and specifies under which circumstances and in which sense it is and is not. By slightly varying and extending Rouder’s (Psychonomic Bulletin & Review21(2), 301–308, 2014) experiments, we illustrate that, as soon as the parameters of interest are equipped with default or pragmatic priors—which means, in most practical applications of Bayes factor hypothesis testing—resilience to optional stopping can break down. We distinguish between three types of default priors, each having their own specific issues with optional stopping, ranging from no-problem-at-all (type 0 priors) to quite severe (type II priors)

On the truth-convergence of open-minded Bayesianism

Wenmackers and Romeijn [38] formalize ideas going back to Shimony [33] and Putnam [28] into an open-minded Bayesian inductive logic, that can dynamically incorporate statistical hypotheses proposed in the course of the learning process. In this paper, we show that Wenmackers and Romeijn’s proposal does not preserve the classical Bayesian consistency guarantee of merger with the true hypothesis. We diagnose the problem, and offer a forward-looking open-minded Bayesians that does preserve a version of this guarantee

All the world's a screen.

Charlotte Gould and Paul Sermon developed and presented this collaborative new artwork entitled 'All the World's a Screen', a live interactive telecommunications performance, to link public audiences in Manchester and Barcelona. On the evening of Saturday 28th May 2011 participants at MadLab in Manchester's Northern Quarter and Hangar Artist Studios in Poblenou, Barcelona were joined together on screen for the first time to create their very own interactive generative cinema experience, complete with sets, costumes and props. Employing the scenography techniques of Alfred Hitchcock the artists created a miniature film set in which the remote audiences acted and directed their own movie, transporting participants into animated environments and sets where they created unique personalised narratives

New order parameters in the Potts model on a Cayley tree

For the $q-$state Potts model new order parameters projecting on a group of spins instead of a single spin are introduced. On a Cayley tree this allows the physical interpretation of the Potts model at noninteger values q of the number of states. The model can be solved recursively. This recursion exhibits chaotic behaviour changing qualitatively at critical values of $q_0$ . Using an additional order parameter belonging to a group of zero extrapolated size the additional ordering is related to a percolation problem. This percolation distinguishes different phases and explains the critical indices of percolation class occuring at the Peierls temperature.Comment: 16 pages TeX, 5 figures PostScrip

God, the beautiful and mathematics: A response

Volker Kessler (‘God becomes beautiful … in mathematics’ - HTS 2018) argues two points to Rudolf Bohren’s list of four areas where (1) God becomes beautiful should be extended with a fifth one: mathematics and (2) mathematics can be argued as a place where God becomes beautiful. In this response, we would like to argue that (1) the extension of Bohren’s list that Kessler argues in favour of is superfluous and (2) that Kessler makes a number of questionable assumptions about (the philosophy of) mathematics. By arguing against Kessler, we intend to make an interdisciplinary contribution to the discussion about the relationship between mathematics and theology by pushing the debate into direction of a more careful consideration of mathematics as an area in which God’s beauty may become apparent. Contribution: Contributing to the interdisciplinary exploration of theology in HTS Teologiese Studies/Theological Studies, this article further develops the consideration of the fundamental theological topic of God, the beautiful and mathematics as it was proposed in this journal by Volker Kessler, by discussing it from a systematic theological and mathematical perspective

Validation of an AI-based algorithm for measurement of the thoracic aortic diameter in low-dose chest CT

OBJECTIVES: To evaluate the performance of artificial intelligence (AI) software for automatic thoracic aortic diameter assessment in a heterogeneous cohort with low-dose, non-contrast chest computed tomography (CT).MATERIALS AND METHODS: Participants of the Imaging in Lifelines (ImaLife) study who underwent low-dose, non-contrast chest CT (August 2017-May 2022) were included using random samples of 80 participants &lt;50y, ≥80y, and with thoracic aortic diameter ≥40 mm. AI-based aortic diameters at eight guideline compliant positions were compared with manual measurements. In 90 examinations (30 per group) diameters were reassessed for intra- and inter-reader variability, which was compared to discrepancy of the AI system using Bland-Altman analysis, paired samples t-testing and linear mixed models.RESULTS: We analyzed 240 participants (63 ± 16 years; 50 % men). AI evaluation failed in 11 cases due to incorrect segmentation (4.6 %), leaving 229 cases for analysis. No difference was found in aortic diameter between manual and automatic measurements (32.7 ± 6.4 mm vs 32.7 ± 6.0 mm, p = 0.70). Bland-Altman analysis yielded no systematic bias and a repeatability coefficient of 4.0 mm for AI. Mean discrepancy of AI (1.3 ± 1.6 mm) was comparable to inter-reader variability (1.4 ± 1.4 mm); only at the proximal aortic arch showed AI higher discrepancy (2.0 ± 1.8 mm vs 0.9 ± 0.9 mm, p &lt; 0.001). No difference between AI discrepancy and inter-reader variability was found for any subgroup (all: p &gt; 0.05).CONCLUSION: The AI software can accurately measure thoracic aortic diameters, with discrepancy to a human reader similar to inter-reader variability in a range from normal to dilated aortas.</p