Towards an epistemic theory of probability.

The main concern of this thesis is to develop an epistemic conception of probability. In chapter one we look at Ramsey's work. In addition to his claim that the axioms of probability ace laws of consistency for partial beliefs, we focus attention on his view that the reasonableness of our probability statements does not consist merely in such coherence, but is to be assessed through the vindication of the habits which give rise to them. In chapter two we examine de Finetti's account, and compare it with Ramsey's. One significant point of divergence is de Finetti's claim that coherence is the only valid form of appraisal for probability statements. His arguments for this position depend heavily on the implementation of a Bayesian model for belief change; we argue that such an approach fails to give a satisfactory account of the relation between probabilities and objective facts. In chapter three we stake out the ground for oar own positive proposals - for an account which is non-objective in so far as it does not require the postulation of probabilistic facts, but non-subjective in the sense that probability statements are open to objective forms of appraisal. we suggest that a certain class of probability statements are best interpreted as recommendations of partial belief; these being measurable by the betting quotients that one judges to be fair. Moreover, we argue that these probability statements are open to three main forms of appraisal (each quantifiable through the use of proper scoring rules), namely: (i) Coherence (ii) Calibration (iii) Refinement. The latter two forms of appraisal are applicable both in an ex ante sense (relative to the information known by the forecaster) and an ex post one (relative to the results of the events forecast). In chapters four and five we consider certain problems which confront theories of partial belief; in particular, (1) difficulties surrounding the justification of the rule to maximise one's information, and (2) problems with the ascription of probabilities to mathematical propositions. Both of these issues seem resolvable; the first through the principle of maximising expected utility (SEU), and the second either by amending the axioms of probability, or by making use of the notion that probabilities are appraisable via scoring rules. There do remain, however, various difficulties with SEU, in particular with respect to its application in real-life situations. These are discussed, but no final conclusion reached, except that an epistemic theory such as ours is not undermined by the inapplicability of SEU in certain situations

Redressing the emperor in causal clothing

Over-flexibility in the definition of Friston blankets obscures a key distinction between observational and interventional inference. The latter requires cognizers form not just a causal representation of the world but also of their own boundary and relationship with it, in order to diagnose the consequences of their actions. We suggest this locates the blanket in the eye of the beholder

Modelling competing legal arguments using Bayesian model comparison and averaging

Bayesian models of legal arguments generally aim to produce a single integrated model, combining each of the legal arguments under consideration. This combined approach implicitly assumes that variables and their relationships can be represented without any contradiction or misalignment, and in a way that makes sense with respect to the competing argument narratives. This paper describes a novel approach to compare and ‘average’ Bayesian models of legal arguments that have been built independently and with no attempt to make them consistent in terms of variables, causal assumptions or parameterization. The approach involves assessing whether competing models of legal arguments are explained or predict facts uncovered before or during the trial process. Those models that are more heavily disconfirmed by the facts are given lower weight, as model plausibility measures, in the Bayesian model comparison and averaging framework adopted. In this way a plurality of arguments is allowed yet a single judgement based on all arguments is possible and rational

Time in causal structure learning

A large body of research has explored how the time between two events affects judgments of causal strength between them. In this article, we extend this work in 4 experiments that explore the role of temporal information in causal structure induction with multiple variables. We distinguish two qualitatively different types of information: The order in which events occur, and the temporal intervals between those events. We focus on one-shot learning in Experiment 1. In Experiment 2, we explore how people integrate evidence from multiple observations of the same causal device. Participants' judgments are well predicted by a Bayesian model that rules out causal structures that are inconsistent with the observed temporal order, and favors structures that imply similar intervals between causally connected components. In Experiments 3 and 4, we look more closely at participants' sensitivity to exact event timings. Participants see three events that always occur in the same order, but the variability and correlation between the timings of the events is either more consistent with a chain or a fork structure. We show, for the first time, that even when order cues do not differentiate, people can still make accurate causal structure judgments on the basis of interval variability alone

Causal superseding

When agents violate norms, they are typically judged to be more of a cause of resulting outcomes. In this paper, we suggest that norm violations also affect the causality attributed to other agents, a phenomenon we refer to as ‘‘causal superseding.’’ We propose and test a counterfactual reasoning model of this phenomenon in four experiments. Experiments 1 and 2 provide an initial demonstration of the causal superseding effect and distinguish it from previously studied effects. Experiment 3 shows that this causal superseding effect is dependent on a particular event structure, following a prediction of our counterfactual model. Experiment 4 demonstrates that causal superseding can occur with violations of non-moral norms. We propose a model of the superseding effect based on the idea of counterfactual sufficiency

Formalizing Neurath's ship:Approximate algorithms for online causal learning

Higher-level cognition depends on the ability to learn models of the world. We can characterize this at the computational level as a structure-learning problem with the goal of best identifying the prevailing causal relationships among a set of relata. However, the computational cost of performing exact Bayesian inference over causal models grows rapidly as the number of relata increases. This implies that the cognitive processes underlying causal learning must be substantially approximate. A powerful class of approximations that focuses on the sequential absorption of successive inputs is captured by the Neurath's ship metaphor in philosophy of science, where theory change is cast as a stochastic and gradual process shaped as much by people's limited willingness to abandon their current theory when considering alternatives as by the ground truth they hope to approach. Inspired by this metaphor and by algorithms for approximating Bayesian inference in machine learning, we propose an algorithmic-level model of causal structure learning under which learners represent only a single global hypothesis that they update locally as they gather evidence. We propose a related scheme for understanding how, under these limitations, learners choose informative interventions that manipulate the causal system to help elucidate its workings. We find support for our approach in the analysis of four experiments

A fluorescent approach for identifying P2X1 ligands.

There are no commercially available, small, receptor-specific P2X1 ligands. There are several synthetic derivatives of the natural agonist ATP and some structurally-complex antagonists including compounds such as PPADS, NTP-ATP, suramin and its derivatives (e.g. NF279, NF449). NF449 is the most potent and selective ligand, but potencies of many others are not particularly high and they can also act at other P2X, P2Y and non-purinergic receptors. While there is clearly scope for further work on P2X1 receptor pharmacology, screening can be difficult owing to rapid receptor desensitisation. To reduce desensitisation substitutions can be made within the N-terminus of the P2X1 receptor, but these could also affect ligand properties. An alternative is the use of fluorescent voltage-sensitive dyes that respond to membrane potential changes resulting from channel opening. Here we utilised this approach in conjunction with fragment-based drug-discovery. Using a single concentration (300 μM) we identified 46 novel leads from a library of 1443 fragments (hit rate = 3.2%). These hits were independently validated by measuring concentration-dependence with the same voltage-sensitive dye, and by visualising the competition of hits with an Alexa-647-ATP fluorophore using confocal microscopy; confocal yielded kon (1.142 × 10(6) M(-1) s(-1)) and koff (0.136 s(-1)) for Alexa-647-ATP (Kd = 119 nM). The identified hit fragments had promising structural diversity. In summary, the measurement of functional responses using voltage-sensitive dyes was flexible and cost-effective because labelled competitors were not needed, effects were independent of a specific binding site, and both agonist and antagonist actions were probed in a single assay. The method is widely applicable and could be applied to all P2X family members, as well as other voltage-gated and ligand-gated ion channels. This article is part of the Special Issue entitled 'Fluorescent Tools in Neuropharmacology'.Our thanks are given to Richard Evans for the P2X1 cDNA, and to Prof. Oliver Mühlemann for kindly providing lab space for M-DR. M-DR was supported by the HOLCIM Stiftung zur Förderung der wissenschaftlichen Fortbildung. The British Heart Foundation supported AJT (grant; PG/13/39/30293) and RWF (grant; RG/09/003/27122).This is the final version of the article. It first appeared from Elsevier via http://dx.doi.org/10.1016/j.neuropharm.2015.05.01