Jon Williamson

Mechanistic philosophy of science views a large part of scientific activity as engaged in modelling mechanisms. While science textbooks tend to offer qualitative models of mechanisms, there is increasing demand for models from which one can draw quantitative predictions and explanations. Casini et al. (Theoria 26(1):5–33, 2011) put forward the Recursive Bayesian Networks (RBN) formalism as well suited to this end. The RBN formalism is an extension of the standard Bayesian net formalism, an extension that allows for modelling the hierarchical nature of mechanisms. Like the standard Bayesian net formalism, it models causal relationships using directed acyclic graphs. Given this appeal to acyclicity, causal cycles pose a prima facie problem for the RBN approach. This paper argues that the problem is a significant one given the ubiquity of causal cycles in mechanisms, but that the problem can be solved by combining two sorts of solution strategy in a judicious way.

The theory of belief revision and merging has recently been applied to judgement aggregation. In this paper I argue that judgements are best aggregated by merging the evidence on which they are based, rather than by directly merging the judgements themselves. This leads to a threestep strategy for judgement aggregation. First, merge the evidence bases of the various agents using some method of belief merging. Second, determine which degrees of belief one should adopt on the basis of this merged evidence base, by applying objective Bayesian theory. Third, determine which judgements are appropriate given these degrees of belief by applying a decision-theoretic account of rational judgement formation

Expert probability forecasts can be useful for decision making . But levels of uncertainty escalate: however the forecaster expresses the uncertainty that attaches to a forecast, there are good reasons for her to express a further level of uncertainty, in the shape of either imprecision or higher order uncertainty . Bayesian epistemology provides the means to halt this escalator, by tying expressions of uncertainty to the propositions expressible in an agent’s language . But Bayesian epistemology comes in three main varieties. Strictly subjective Bayesianism and empirically-based subjective Bayesianism have difficulty in justifying the use of a forecaster’s probabilities for decision making . On the other hand, objective Bayesianism can justify the use of these probabilities, at least when the probabilities are consistent with the agent’s evidence . Hence objective Bayesianism offers the most promise overall for explaining how testimony of uncertainty can be useful for decision making. Interestingly, the objective Bayesian analysis provided in Sect. 5 can also be used to justify a version of the Principle of Reflection.

Metabolism is a set of chemical reactions, used by living organisms to process chemical compounds in order to take energy and eliminate toxic compounds, for example. Its processes are referred as metabolic pathways. Understanding metabolism is imperative to biology, toxicology and medicine, but the number and complexity of metabolic pathways makes this a difficult task. In our paper, we investigate the use of causal Bayesian networks to model the pathways of yeast saccharomyces cerevisiae metabolism: such a network can be used to draw predictions about the levels of metabolites and enzymes in a particular specimen. We propose a two-stage methodology for causal networks, as follows. First construct a causal network from the network of metabolic pathways. The viability of this causal network depends on the validity of the causal Markov condition. If this condition fails, however, the principle of the common cause motivates the addition of a new causal arrow or a new `hidden' common cause to the network (stage 2 of the model formation process). Algorithms for adding arrows or hidden nodes have been developed separately in a number of papers, and in this paper we combine them, showing how the resulting procedure can be applied to the metabolic pathway problem. Our general approach was tested on neural cell morphology data and demonstrated noticeable improvements in both prediction and network accuracy.

Causal inference is perhaps the most important form of reasoning in the sciences. A panoply of disciplines, ranging from epidemiology to biology, from econometrics to physics, make use of probability and statistics to infer causal relationships. The social and health sciences analyse population-level data using statistical methods to infer average causal relations. In diagnosis of disease, probabilistic statements are based on population-level causal knowledge combined with knowledge of a particular person’s symptoms. For the physical sciences, the Salmon-Dowe account develops an analysis of causation based on the notion of process and interaction. In artificial intelligence, the development of graphical methods has leant impetus to a probabilistic analysis of causality. The biological sciences use probabilistic methods to look for evolutionary causes of the state of a current species and to look for genetic causal factors. This variegated situation raises at least two fundamental philosophical issues: about the relation between causality and probability, and about the interpretation of probability in causal analysis. In this book we bring philosophers and scientists together to discuss the relation between causality and probability, and the applications of these concepts within the sciences.

Objective Bayesianism says that the strengths of one’s beliefs ought to be probabilities, calibrated to physical probabilities insofar as one has evidence of them, and otherwise sufficiently equivocal. These norms of belief are often explicated using the maximum entropy principle. In this paper we investigate the extent to which one can provide a unified justification of the objective Bayesian norms in the case in which the background language is a first-order predicate language, with a view to applying the resulting formalism to inductive logic. We show that the maximum entropy principle can be motivated largely in terms of minimising worst-case expected loss.

We present a new framework for combining logic with probability, and demonstrate the application of this framework to breast cancer prognosis. Background knowledge concerning breast cancer prognosis is represented using logical arguments. This background knowledge and a database are used to build a Bayesian net that captures the probabilistic relationships amongst the variables. Causal hypotheses gleaned from the Bayesian net in turn generate new arguments. The Bayesian net can be queried to help decide when one argument attacks another. The Bayesian net is used to perform the prognosis, while the argumentation framework is used to provide a qualitative explanation of the prognosis.

Cancer treatment decisions should be based on all available evidence. But this evidence is complex and varied: it includes not only the patient’s symptoms and expert knowledge of the relevant causal processes, but also clinical databases relating to past patients, databases of observations made at the molecular level, and evidence encapsulated in scientific papers and medical informatics systems. Objective Bayesian nets offer a principled path to knowledge integration, and we show in this chapter how they can be applied to integrate various kinds of evidence in the cancer domain. This is important from the systems biology perspective, which needs to integrate data that concern different levels of analysis, and is also important from the point of view of medical informatics.

Mechanisms have become much-discussed, yet there is still no consensus on how to characterise them. In this paper, we start with something everyone is agreed on – that mechanisms explain – and investigate what constraints this imposes on our metaphysics of mechanisms. We examine two widely shared premises about how to understand mechanistic explanation: (1) that mechanistic explanation offers a welcome alternative to traditional laws-based explanation and (2) that there are two senses of mechanistic explanation that we call ‘epistemic explanation’ and ‘physical explanation’. We argue that mechanistic explanation requires that mechanisms are both real and local. We then go on to argue that real, local mechanisms require a broadly active metaphysics for mechanisms, such as a capacities metaphysics

According to objective Bayesianism, an agent’s degrees of belief should be determined by a probability function, out of all those that satisfy constraints imposed by background knowledge, that maximises entropy. A Bayesian net offers a way of efficiently representing a probability function and efficiently drawing inferences from that function. An objective Bayesian net is a Bayesian net representation of the maximum entropy probability function. In this paper we apply the machinery of objective Bayesian nets to breast cancer prognosis. Background knowledge is diverse and comes from several different sources: a database of clinical data, a database of molecular data, and quantitative data from the literature. We show how an objective Bayesian net can be constructed from this background knowledge and how it can be applied to yield prognoses and aid translation of clinical knowledge to genomics research