A Novel Solution to the Problem of Old Evidence

One of the most troubling and persistent challenges for Bayesian Confirmation Theory is the Problem of Old Evidence (POE, Glymour 1980). The problem arises for anyone who wants to model confirmation and theory appraisal in science by means of Bayesian Conditionalization. This paper addresses the problem as follows: First, I clarify the nature and the varieties of POE, following Eells (1985, 1990). Second, I analyze solution proposals where (i) confirmation is evaluated relative to a counterfactual credence function; (ii) confirmation occurs through learning the proposition that theory T accounts for evidence E (Garber 1983; Jeffrey 1983; Niiniluoto 1983). Third, I present a novel solution that improves upon the state of the art in terms of scope and plausibility of the underlying assumptions. Finally, I summarize my findings and put them into the context of the general debate about POE and Bayesianism

Foundations of a Probabilistic Theory of Causal Strength

This paper develops axiomatic foundations for a probabilistic theory of causal strength as difference-making. I proceed in three steps: First, I motivate the choice of causal Bayes nets as an adequate framework for defining and comparing measures of causal strength. Second, I prove several representation theorems for probabilistic measures of causal strength---that is, I demonstrate how these measures can be derived from a set of plausible adequacy conditions. Third, I use these results to argue for a specific measure of causal strength: the difference that interventions on the cause make for the probability of the effect. I conclude by discussing my results and outlining future research avenues

Conditional Degree of Belief

This paper articulates and defends a suppositional interpretation of conditional degree of belief. First, I focus on a type of probability that has a crucial role in Bayesian inference: conditional degrees of belief in an observation, given a statistical hypothesis. The suppositional analysis explains, unlike other accounts, why these degrees of belief track the corresponding probability density functions. Then, I extend the suppositional analysis and argue that all probabilities in Bayesian inference should be understood suppositionally and model-relative. This sheds a new and illuminating light on chance-credence coordination principles, the relationship between Bayesian models and their target system, and the epistemic significance of Bayes' Theorem

The Objectivity of Subjective Bayesianism

Subjective Bayesianism is a major school of uncertain reasoning and statistical inference. It is often criticized for a lack of objectivity: (i) it opens the door to the influence of values and biases, (ii) evidence judgments can vary substantially between scientists, (iii) it is not suited for informing policy decisions. My paper rebuts these concerns by bridging the debates on scientific objectivity and statistical method. First, I show that the above concerns arise equally for standard frequentist inference. Second, I argue that the involved senses of objectivity are epistemically inert. Third, I show that Subjective Bayesianism promotes other, epistemically relevant senses of scientific objectivity---most notably by increasing the transparency of scientific reasoning

The Objectivity of Subjective Bayesianism

Subjective Bayesianism is a major school of uncertain reasoning and statistical inference. It is often criticized for a lack of objectivity: (i) it opens the door to the influence of values and biases, (ii) evidence judgments can vary substantially between scientists, (iii) it is not suited for informing policy decisions. My paper rebuts these concerns by bridging the debates on scientific objectivity and statistical method. First, I show that the above concerns arise equally for standard frequentist inference. Second, I argue that the involved senses of objectivity are epistemically inert. Third, I show that Subjective Bayesianism promotes other, epistemically relevant senses of scientific objectivity---most notably by increasing the transparency of scientific reasoning

Degree of Corroboration: An Antidote to the Replication Crisis

The replication crisis poses an enormous challenge to the epistemic authority of science and the logic of statistical inference in particular. Two prominent features of Null Hypothesis Significance Testing (NHST) arguably contribute to the crisis: the lack of guidance for interpreting non-significant results and the impossibility of quantifying support for the null hypothesis. In this paper, I argue that also popular alternatives to NHST, such as confidence intervals and Bayesian inference, do not lead to a satisfactory logic of evaluating hypothesis tests. As an alternative, I motivate and explicate the concept of corroboration of the null hypothesis. Finally I show how degrees of corroboration give an interpretation to non-significant results, combat publication bias and mitigate the replication crisis