Jan-Willem Romeijn

We consider the use of interventions for resolving a problem of unidentified statistical models. The leading examples are from latent variable modelling, an influential statistical tool in the social sciences. We first explain the problem of statistical identifiability and contrast it with the identifiability of causal models. We then draw a parallel between the latent variable models and Bayesian networks with hidden nodes. This allows us to clarify the use of interventions for dealing with unidentified statistical models. We end by discussing the philosophical and methodological import of our result.

While probabilistic logics in principle might be applied to solve a range of problems, in practice they are rarely applied --- perhaps because they seem disparate, complicated, and computationally intractable. This programmatic book argues that several approaches to probabilistic logic fit into a simple unifying framework in which logically complex evidence is used to associate probability intervals or probabilities with sentences. Specifically, Part I shows that there is a natural way to present a question posed in probabilistic logic, and that various inferential procedures provide semantics for that question, while Part II shows that there is the potential to develop computationally feasible methods to mesh with this framework. The book is intended for researchers in philosophy, logic, computer science and statistics. A familiarity with mathematical concepts and notation is presumed, but no advanced knowledge of logic or probability theory is required.

I defend a threefold form of pluralism about chance, involving a tripartite distinction between propensities, probabilities, and frequencies. The argument has a negative and a positive part. Negatively, I argue against the identity thesis that informs current propensity theories, which already suggests the need for a tripartite distinction. Positively, I argue that that a tripartite distinction is implicit in much statistical practice. Finally, I apply a well-known framework in the modelling literature in order to characterize these three separate concepts functionally in terms of their roles in modelling practice.

Bayesian nested-model comparisons involve an assessment of the probabilities for a relatively simple model and a more general encompassing model. Since the simpler model can be viewed as a subset of the more complex model it is nested in, Popper has argued that the axioms of probability are violated when the simpler model is nonetheless assigned a higher prior probability. While Popper raised this objection in the context of assigning prior probabilities to models, we argue that Popper’s objection does not just concern the priors, but Bayesian model comparisons more generally. We term this ‘the subset problem’. A variety of solutions have been proposed in the literature. We discuss some of these solutions and combine them into a new Bayesian account, in which both the probability assignments and the algebra over which they are assigned receive a specific interpretation. Finally, we discuss a new non-Bayesian solution, in which nested models are assigned an attractiveness measure that need not be additive.

We present a conservative extension of a Bayesian account of confirmation that can deal with the problem of old evidence and new theories. So-called open-minded Bayesianism challenges the assumption—implicit in standard Bayesianism—that the correct empirical hypothesis is among the ones currently under consideration. It requires the inclusion of a catch-all hypothesis, which is characterized by means of sets of probability assignments. Upon the introduction of a new theory, the former catch-all is decomposed into a new empirical hypothesis and a new catch-all. As will be seen, this motivates a second update rule, besides Bayes’ rule, for updating probabilities in light of a new theory. This rule conserves probability ratios among the old hypotheses. This framework allows for old evidence to confirm a new hypothesis due to a shift in the theoretical context. The result is a version of Bayesianism that, in the words of Earman, “keep[s] an open mind, but not so open that your brain falls out”.

In psychiatry, many scientists desire to move from a classification system based on symptoms toward a system based on biological causes. The idea is that psychiatric diseases should be redefined such that each disease would be associated with specific biological causes. This desire is intelligible because causal disease models often facilitate understanding and identification of new ways to intervene in disease processes. In its attempt to move from syndromal to specific etiological definitions, psychiatry follows the trend of general medicine.Current psychiatric...

In groups where members deliberate with limited information, consensus can emerge where, under complete information, fundamental disagreement would prevail. Using an agent-based model, we explore the factors contributing to group consensus by comparing argumentation styles in two types of groups: agents in groups of advocates communicate arguments for options perceived as personally beneficial. Agents in groups of diplomats do the same but avoid disagreement in that they bring up arguments supporting a second-best option whenever their interaction partner perceives to benefit the least from what the sender finds best. Results show that consensus depends on argumentation style, but also on what members initially perceive as preferred. Diplomats are more likely to form consensus when initial perceptions accurately align with full information preferences, which diverge within the group. Conversely, and perhaps counterintuitively, in the presence of inaccurate initial perceptions, groups of advocates converge while diplomats part in disagreement. Our results imply that the ideal argumentation style must be considered carefully in light of both the desired outcome and the initial information distribution: when conflicting stakes produce a trade-off between consensus and truthful perceptions, polite versus selfish ways of deliberation may produce one or the other outcome, depending on the initial information members are equipped with.

While probabilistic logics in principle might be applied to solve a range of problems, in practice they are rarely applied --- perhaps because they seem disparate, complicated, and computationally intractable. This programmatic book argues that several approaches to probabilistic logic fit into a simple unifying framework in which logically complex evidence is used to associate probability intervals or probabilities with sentences. Specifically, Part I shows that there is a natural way to present a question posed in probabilistic logic, and that various inferential procedures provide semantics for that question, while Part II shows that there is the potential to develop computationally feasible methods to mesh with this framework. The book is intended for researchers in philosophy, logic, computer science and statistics. A familiarity with mathematical concepts and notation is presumed, but no advanced knowledge of logic or probability theory is required.

This paper presents the progicnet programme. It proposes a general framework for probabilistic logic that can guide inference based on both logical and probabilistic input. After an introduction to the framework as such, it is illustrated by means of a toy example from psychometrics. It is shown that the framework can accommodate a number of approaches to probabilistic reasoning: Bayesian statistical inference, evidential probability, probabilistic argumentation, and objective Bayesianism. The framework thus provides insight into the relations between these approaches, it illustrates how the results of different approaches can be combined, and it provides a basis for doing efficient inference in each of the approaches.

We consider the use of interventions for resolving a problem of unidentified statistical models. The leading examples are from latent variable modelling, an influential statistical tool in the social sciences. We first explain the problem of statistical identifiability and contrast it with the identifiability of causal models. We then draw a parallel between the latent variable models and Bayesian networks with hidden nodes. This allows us to clarify the use of interventions for dealing with unidentified statistical models. We end by discussing the philosophical and methodological import of our result.

Over the past decades or so the probabilistic model of rational belief has enjoyed increasing interest from researchers in epistemology and the philosophy of science. Of course, such probabilistic models were used for much longer in economics, in game theory, and in other disciplines concerned with decision making. Moreover, Carnap and co-workers used probability theory to explicate philosophical notions of confirmation and induction, thereby targeting epistemic rather than decision-theoretic aspects of rationality. However, following Carnap’s early applications, philosophy has more recently seen an increased popularity of probabilistic models in other areas concerned with the philosophical analysis of belief: there are models targeting coherence, informativeness, simplicity, and so on.In brief, the probabilistic model of belief comprises of a language, detailing the propositions about which an agent is supposed to have beliefs, and a function over the language that expresses beliefs: ..

We represent consensus formation processes based on iterated opinion pooling as a dynamic approach to common knowledge of posteriors :1236–1239, 1976; Geanakoplos and Polemarchakis in J Econ Theory 28:192–200, 1982). We thus provide a concrete and plausible Bayesian rationalization of consensus through iterated pooling. The link clarifies the conditions under which iterated pooling can be rationalized from a Bayesian perspective, and offers an understanding of iterated pooling in terms of higher-order beliefs.

This edited collection showcases some of the best recent research in the philosophy of science. It comprises of thematically arranged papers presented at the 5th conference of the European Philosophy of Science Association (EPSA15), covering a broad variety of topics within general philosophy of science, and philosophical issues pertaining to specific sciences. The collection will appeal to researchers with an interest in the philosophical underpinnings of their own discipline, and to philosophers who wish to study the latest work on the themes discussed.