I argue that one central aspect of the epistemology of causation, the use of causes as evidence for their effects, is largely independent of the metaphysics of causation. In particular, I use the formalism of Bayesian causal graphs to factor the incremental evidential impact of a cause for its effect into a direct cause-to-effect component and a backtracking component. While the “backtracking” evidence that causes provide about earlier events often obscures things, once we our restrict attention to the (...) cause-to-effect component it is true to say promoting (inhibiting) causes raise (lower) the probabilities of their effects. This factoring assumes the same form whether causation is given an interventionist, counterfactual or probabilistic interpretation. Whether we think about causation in terms of interventions and causal graphs, counterfactuals and imaging functions, or probability raising against the background of causally homogenous partitions, if we describe the essential features of a situation correctly then the incremental evidence that a cause provides for its effect in virtue of being its cause will be the same. (shrink)

The paper displays the similarity between the theory of probabilistic causation developed by Glymour et al. since 1983 and mine developed since 1976: the core of both is that causal graphs are Bayesian nets. The similarity extends to the treatment of actions or interventions in the two theories. But there is also a crucial difference. Glymour et al. take causal dependencies as primitive and argue them to behave like Bayesian nets under wide circumstances. By contrast, I (...) argue the behavior of Bayesian nets to be ultimately the defining characteristic of causal dependence. (shrink)

Bayesian networks are computer programs which represent probabilitistic relationships graphically as directed acyclic graphs, and which can use those graphs to reason probabilistically , often at relatively low computational cost. Almost every expert system in the past tried to support probabilistic reasoning, but because of the computational difficulties they took approximating short-cuts, such as those afforded by MYCIN's certainty factors. That all changed with the publication of Judea Pearl's Probabilistic Reasoning in Intelligent Systems, in 1988, which synthesized a decade (...) of research making accurate graphical probabilistic reasoning computationally achievable.Bayesian network technology is now one of the fastest growing fields of research in artificial intelligence. That it has become a publication industry in its own right is shown by a search on Google scholar :This development, together with a parallel related growth in the use of causal discovery algorithms which automate the learning of Bayesian networks from sample data, has generated considerable interest, and controversy, within the philosophy-of-science community.Three central questions bringing together AI researchers and philosophers of science are: Are Bayesian networks Bayesian? What is the relation between probability and causality? Are the assumptions behind causal discovery of Bayesian networks realistic or fantastical?Jon Williamson, as a philosopher of science with a keen interest in the technology, asks and answers these questions in his new book. Although it is self-contained, his book is not very likely as an introduction to the technology , nor is it optimal even as an introduction to the philosophical problems in interpreting Bayesian networks . Rather Williamson's book is an attempt to move the debate forward by solving the central problems of the …. (shrink)

Independence of Conditionals (IC) has recently been proposed as a basic rule for causal structure learning. If a Bayesian network represents the causal structure, its Conditional Probability Distributions (CPDs) should be algorithmically independent. In this paper we compare IC with causal faithfulness (FF), stating that only those conditional independences that are implied by the causal Markov condition hold true. The latter is a basic postulate in common approaches to causal structure learning. The common spirit (...) of FF and IC is to reject causal graphs for which the joint distribution looks ‘non-generic’. The difference lies in the notion of genericity: FF sometimes rejects models just because one of the CPDs is simple, for instance if the CPD describes a deterministic relation. IC does not behave in this undesirable way. It only rejects a model when there is a non-generic relation between different CPDs although each CPD looks generic when considered separately. Moreover, it detects relations between CPDs that cannot be captured by conditional independences. IC therefore helps in distinguishing causal graphs that induce the same conditional independences (i.e., they belong to the same Markov equivalence class). The usual justification for FF implicitly assumes a prior that is a probability density on the parameter space. IC can be justified by Solomonoff’s universal prior, assigning non-zero probability to those points in parameter space that have a finite description. In this way, it favours simple CPDs, and therefore respects Occam’s razor. Since Kolmogorov complexity is uncomputable, IC is not directly applicable in practice. We argue that it is nevertheless helpful, since it has already served as inspiration and justification for novel causal inference algorithms. (shrink)

This paper has two main parts. In the first part, we motivate a kind of indeterminate, suppositional credences by discussing the prospect for a subjective interpretation of a causal Bayesian network, an important tool for causal reasoning in artificial intelligence. A CBN consists of a causal graph and a collection of interventional probabilities. The subjective interpretation in question would take the causal graph in a CBN to represent the causal structure that is (...) believed by an agent, and interventional probabilities in a CBN to represent suppositional credences. We review a difficulty noted in the literature with such an interpretation, and suggest that a natural way to address the challenge is to go for a generalization of CBN that allows indeterminate credences. In the second part, we develop a decision-theoretic foundation for such indeterminate suppositional credences, by generalizing a theory of coherent choice functions to accommodate some form of act-state dependence. The upshot is a decision-theoretic framework that is not only rich enough to, so to speak, ground the probabilities in a subjectively interpreted causal network, but also interesting in its own right, in that it accommodates both act-state dependence and imprecise probabilities. (shrink)

Causal reasoning is primarily concerned with what would happen to a system under external interventions. In particular, we are often interested in predicting the probability distribution of some random variables that would result if some other variables were forced to take certain values. One prominent approach to tackling this problem is based on causal Bayesian networks, using directed acyclic graphs as causal diagrams to relate post-intervention probabilities to pre-intervention probabilities that are estimable from observational data. However, (...) such causal diagrams are seldom fully testable given observational data. In consequence, many causal discovery algorithms based on data-mining can only output an equivalence class of causal diagrams. This paper is concerned with causal reasoning given an equivalence class of causal diagrams, represented by a ancestral graph. We present two main results. The first result extends Pearl 's celebrated do-calculus to the context of ancestral graphs. In the second result, we focus on a key component of Pearl's calculus---the property of invariance under interventions, and give stronger graphical conditions for this property than those implied by the first result. The second result also improves the earlier, similar results due to Spirtes et al. (shrink)

As a compact representation of joint probability distributions over a dependence graph of random variables, and a tool for modelling and reasoning in the presence of uncertainty, Bayesian networks are of great importance for artificial intelligence to combine domain knowledge, capture causal relationships, or learn from incomplete datasets. Known as a NP-hard problem in a classical setting, Bayesian inference pops up as a class of algorithms worth to explore in a quantum framework. This paper explores such (...) a research direction and improves on previous proposals by a judicious use of the utility function in an entangled configuration. It proposes a completely quantum mechanical decision-making process with a proven computational advantage. A prototype implementation in Qiskit (a Python-based program development kit for the IBM Q machine) is discussed as a proof-of-concept. (shrink)

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. (shrink)

This article assesses how people reason with categories whose features are related in causal cycles. Whereas models based on causal graphical models have enjoyed success modeling category-based judgments as well as a number of other cognitive phenomena, CGMs are only able to represent causal structures that are acyclic. A number of new formalisms that allow cycles are introduced and evaluated. Dynamic Bayesian networks represent cycles by unfolding them over time. Chain graphs augment CGMs by allowing the (...) presence of undirected links that model feedback relations between variables. Unfolded chain graphs are chain graphs that unfold over time. An existing model of causal cycles is also evaluated. Four experiments in which subjects reason about categories with cyclically related features provided evidence against DBNs and alpha centrality and for the two types of chain graphs. Chain graphs—a mechanism for representing the equilibrium distribution of a dynamic system—may thus be good candidates for modeling how people reason causally with complex systems. Applications of chain graphs to areas of cognition other than category-based judgments are discussed. (shrink)

Through their transcript products genes regulate the rates at which an immense variety of transcripts and subsequent proteins occur. Understanding the mechanisms that determine which genes are expressed, and when they are expressed, is one of the keys to genetic manipulation for many purposes, including the development of new treatments for disease. Viewing each gene in a genome as a distinct variable that is either on or off, or more realistically as a continuous variable, the values of some of these (...) variables influence the values of others through the regulatory proteins they express, including, of course, the possibility that the rate of expression of a gene at one time may, in various circumstances, influence the rate of expression of that same gene at a later time. If we imagine an arrow drawn from each gene expression variable at a given time to a gene variable whose expression it influences a short while after, the result is a network, technically a directed acyclic graph. For example, the DAG in Figure 1 is a representation of a system in which the expression level of gene G1 at time 1 ) causes the expression level of G2, which in turn causes the expression level of G3. The arrows in Figure 1 which do not have a variable at their tails are “error terms” which represent all of the causes of a variable other than the ones explicitly represented in the DAG. The DAG describes more than associations—it describes causal connections among gene expression rates. A shock to a cell—by mutation, heating, chemical treatment, etc. may alter the DAG describing the relations among gene expressions, for example by activating a gene that was otherwise not expressed, producing a cascade of new expression effects. Although “knockout” experiments can reveal some of the underlying causal network of gene expression levels, unless guided by information from other sources, such experiments are limited in how much of the network structure they can reveal, due to the sheer number of possible combinations of experimental manipulations of genes necessary to reveal the complete causal network. Recent developments have made it possible to compare quantitatively the expression of tens of thousands of genes in cells from different sources in a single experiment, and to trace gene expression over time in thousands of genes simultaneously. cDNA microarrays are already producing extensive data, much of it available on the web. Thus there are calls for analytic software that can be applied to microarray and other data to help infer regulatory networks. In this paper we will review current techniques that are available for searching for the causal relations between variables, describe algorithmic and data gathering obstacles to applying these techniques to gene expression levels, and describe the prospects for overcoming these obstacles. (shrink)

Modeling mechanisms is central to the biological sciences – for purposes of explanation, prediction, extrapolation, and manipulation. A closer look at the philosophical literature reveals that mechanisms are predominantly modeled in a purely qualitative way. That is, mechanistic models are conceived of as representing how certain entities and activities are spatially and temporally organized so that they bring about the behavior of the mechanism in question. Although this adequately characterizes how mechanisms are represented in biology textbooks, contemporary biological research practice (...) shows the need for quantitative, probabilistic models of mechanisms, too. In this paper we argue that the formal framework of causal graph theory is well-suited to provide us with models of biological mechanisms that incorporate quantitative and probabilistic information. On the ba-sis of an example from contemporary biological practice, namely feedback regulation of fatty acid biosynthesis in Brassica napus, we show that causal graph theoretical models can account for feedback as well as for the multi-level character of mechanisms. However, we do not claim that causal graph theoretical representations of mechanisms are advantageous in all respects and should replace common qualitative models. Rather, we endorse the more balanced view that causal graph theoretical models of mechanisms are useful for some purposes, while being insufficient for others. (shrink)

We examine possible causal structures of experiments with entangled quantum objects. Previously, these structures have been obscured by assuming a misleading probabilistic analysis of quantum non locality as 'Outcome Dependence or Parameter Dependence' and by directly associating these correlations with influences. Here we try to overcome these shortcomings: we proceed from a recent stronger Bell argument, which provides an appropriate probabilistic description, and apply the rigorous methods of causal graph theory. Against the standard view that there is (...) only an influence between the measurement outcomes, we show that there must be an influence from one setting to its distant outcome: EPR correlations can only come about if one of the outcomes is a common effect of both settings. Our discussion makes explicit under which assumptions similar conclusions from information theoretic considerations can be interpreted causally. (shrink)

The causal view of categories assumes that categories are represented by features and their causal relations. To study the effect of causal knowledge on categorization, researchers have used Bayesian causal models. Within that framework, categorization may be viewed as dependent on a likelihood computation (i.e., the likelihood of an exemplar with a certain combination of features, given the category's causal model) or as a posterior computation (i.e., the probability that the exemplar belongs to the (...) category, given its features). Across three experiments, in combination with computational modeling, we offer evidence that categorization is better accounted for by assuming that people compute posteriors and not likelihoods, though both probabilities are closely related. This result contrasts with existing analyses of causal-based categorization, which assume that likelihood computations give a good approximation of human judgments. We also find that people are able to compute likelihoods in a closely related task that elicits judgments of consistency rather than category membership judgments. Our analyses show that people do use causal probabilistic information as prescribed by a Bayesian model but that they flexibly compute likelihoods or posteriors depending on the task. We discuss our results in relation to the relevant literature on the topic. (shrink)

In this article I tackle the question of how the hierarchical order of mechanisms can be represented within a causal graph framework. I illustrate an answer to this question proposed by Casini, Illari, Russo, and Williamson and provide an example that their formalism does not support two important features of nested mechanisms: (i) a mechanism’s submechanisms are typically causally interacting with other parts of said mechanism, and (ii) intervening in some of a mechanism’s parts should have some influence (...) on the phenomena the mechanism brings about. Finally, I sketch an alternative approach taking (i) and (ii) into account. (shrink)

Young children spend a large portion of their time pretending about non-real situations. Why? We answer this question by using the framework of Bayesian causal models to argue that pretending and counterfactual reasoning engage the same component cognitive abilities: disengaging with current reality, making inferences about an alternative representation of reality, and keeping this representation separate from reality. In turn, according to causal models accounts, counterfactual reasoning is a crucial tool that children need to plan for the (...) future and learn about the world. Both planning with causal models and learning about them require the ability to create false premises and generate conclusions from these premises. We argue that pretending allows children to practice these important cognitive skills. We also consider the prevalence of unrealistic scenarios in children's play and explain how they can be useful in learning, despite appearances to the contrary. (shrink)

Peter Spirtes. Building Causal Graphs from Statistical Data in the Presence of Latent Variables.

Kin selection and multilevel selection are alternative approaches for studying the evolution of social behaviour, the relation between which has long been a source of controversy. Many recent theorists regard the two approaches as ultimately equivalent, on the grounds that gene frequency change can be correctly expressed using either. However, this shows only that the two are formally equivalent, not that they offer equally good causal representations of the evolutionary process. This article articulates the notion of an ‘adequate (...) class='Hi'>causal representation’ using causal graphs, and then seeks to identify circumstances under which kin and multilevel selection do and do not satisfy the test of causal adequacy. 1 Introduction2 The KS and MLS Approaches2.1 The MLS decomposition2.2 The KS decomposition3 Equivalence and Causality4 Two Problem Cases4.1 The non-social trait case4.2 Genotypic selection with meiotic drive5 Casual Adequacy: A Graphical Approach5.1 The basic idea5.2 Graphs with individual and group variables5.3 Cases where KS is causally adequate5.4 Cases where MLS is causally adequate6 Discussion6.1 Relation to previous work. (shrink)

In criminal trials, evidence often involves a degree of uncertainty and decision-making includes moving from the initial presumption of innocence to inference about guilt based on that evidence. The jurors’ ability to combine evidence and make accurate intuitive probabilistic judgments underpins this process. Previous research has shown that errors in probabilistic reasoning can be explained by a misalignment of the evidence presented with the intuitive causal models that people construct. This has been explored in abstract and context-free situations. However, (...) less is known about how people interpret evidence in context-rich situations such as legal cases. The present study examined participants’ intuitive probabilistic reasoning in legal contexts and assessed how people’s causal models underlie the process of belief updating in the light of new evidence. The study assessed whether participants update beliefs in line with Bayesian norms and if errors in belief updating can be explained by the causal structures underpinning the evidence integration process. The study was based on a recent case in England where a couple was accused of intentionally harming their baby but was eventually exonerated because the child’s symptoms were found to be caused by a rare blood disorder. Participants were presented with a range of evidence, one piece at a time, including physical evidence and reports from experts. Participants made probability judgments about the abuse and disorder as causes of the child’s symptoms. Subjective probability judgments were compared against Bayesian norms. The causal models constructed by participants were also elicited. Results showed that overall participants revised their beliefs appropriately in the right direction based on evidence. However, this revision was done without exact Bayesian computation and errors were observed in estimating the weight of evidence. Errors in probabilistic judgments were partly accounted for, by differences in the causal models representing the evidence. Our findings suggest that understanding causal models that guide people’s judgments may help shed light on errors made in evidence integration and potentially identify ways to address accuracy in judgment. (shrink)

A Bayesian network consists of two distinct parts: a directed acyclic graph (DAG or belief-network structure) and a set of parameters for the DAG. The DAG in a Bayesian network can be used to represent both causal hypotheses and sets of probability distributions. Under the causal interpretation, a DAG represents the causal relations in a given population with a set of vertices V when there is an edge from A to B if and only (...) if A is a direct cause of B relative to V. (We adopt the convention that sets of variables are capitalized and boldfaced, and individual variables are capitalized and italicized.) Under the statistical interpretation a DAG G can be taken to represent a set of all distributions all of which share a set of conditional independence relations that are entailed by satisfying a local directed Markov property (defined below). (shrink)

Curie’s Principle says that any symmetry property of a cause must be found in its effect. In this article, I consider Curie’s Principle from the point of view of graphical causal models, and demonstrate that, under one definition of a symmetry transformation, the causal modeling framework does not require anything like Curie’s Principle to be true. On another definition of a symmetry transformation, the graphical causal modeling formalism does imply a version of Curie’s Principle. These results yield (...) a better understanding of the logical landscape with respect to the relationship between Curie’s Principle and graphical causal modeling. (shrink)

I examine the adequacy of the causal graph-structural equations approach to causation for modeling biological mechanisms. I focus in particular on mechanisms with complex dynamics such as the PER biological clock mechanism in Drosophila. I show that a quantitative model of this mechanism that uses coupled differential equations – the well-known Goldbeter model – cannot be adequately represented in the standard causal graph framework, even though this framework does permit causal cycles. The reason is that (...) the model contains dynamical information about the mechanism that concerns causal properties but that does not correspond to variables that could be subject to independent interventions. Thus, a representation of the mechanisms as a causal structural model necessarily suppresses causally relevant information. (shrink)

Even though potential impacts of political and legal environments of business on ethical behavior of firms (EBOF) have been conceptually recognized, not much evidence (i.e., empirical work) has been produced to clarify their role. In this paper, using Bayesian causal maps (BCMs) methodology, relationships between legal and political environments of business and EBOF are investigated. The unique design of our study allows us to analyze these relationships based on the stages of development in 92 countries around the world. (...) The EBOF models structured through BCMs are used to explain how EBOF in a given country group are shaped by how managers perceive political, legislative, and protective environments of business in these countries. The results suggest that irregular payments and bribes are the most influential factors affecting managers’ perceptions of business ethics in relatively more advanced economies, whereas intellectual property protection is the most influential factor affecting managers’ perceptions of business ethics in less-advanced economies. The results also suggest that regardless of where the business is conducted in the world, judicial independence is the driving force behind managers’ perceptions of business ethics. In addition, the results of this study provide further support for scholars who argue that business ethics is likely to vary among countries based on their socio-economic factors. In addition to its managerial implications, the study provides directions for policy makers to improve the ethical conduct of businesses in their respective countries. (shrink)

A general principle for good pedagogic strategy is this: other things equal, make the essential principles of the subject explicit rather than tacit. We think that this principle is routinely violated in conventional instruction in statistics. Even though most of the early history of probability theory has been driven by causal considerations, the terms “cause” and “causation” have practically disappeared from statistics textbooks. Statistics curricula guide students away from the concept of causality, into remembering perhaps the cliche disclaimer “correlation (...) does not mean causation,” but rarely thinking about what correlation does mean. The treatment of causality is a serious handicap to later studies of such topics as experimental design, where often the main goal is to establish (or disprove) causation. Much of the technical vocabulary of the language used in research design textbooks consists in euphemisms for specific causal relations, e.g, “latent variable,” “intervening variable,” “confounding factor,” etc. The multiplicity of terms used to refer to causation results in confusion and, in effect, may hinder understanding of the basic principles of research design. (shrink)

I examine to what extent accounts of mechanisms based on formal interventionist theories of causality can adequately represent biological mechanisms with complex dynamics. Using a differential equation model for a circadian clock mechanism as an example, I first show that there exists an iterative solution that can be interpreted as a structural causal model. Thus, in principle, it is possible to integrate causal difference-making information with dynamical information. However, the differential equation model itself lacks the right modularity properties (...) for a full integration. A formal mechanistic model will therefore have to leave out either noncausal or causal explanatory relations. (shrink)

Previous asymptotically correct algorithms for recovering causal structure from sample probabilities have been limited even in sparse graphs to a few variables. We describe an asymptotically correct algorithm whose complexity for fixed graph connectivity increases polynomially in the number of vertices, and may in practice recover sparse graphs with several hundred variables. From..

Bayesian nets are widely used in artificial intelligence as a calculus for causal reasoning, enabling machines to make predictions, perform diagnoses, take decisions and even to discover causal relationships. This book, aimed at researchers and graduate students in computer science, mathematics and philosophy, brings together two important research topics: how to automate reasoning in artificial intelligence, and the nature of causality and probability in philosophy.

Evidential reasoning is hard, and errors can lead to miscarriages of justice with serious consequences. Analytic methods for the correct handling of evidence come in different styles, typically focusing on one of three tools: arguments, scenarios or probabilities. Recent research used Bayesian networks for connecting arguments, scenarios, and probabilities. Well-known issues with Bayesian networks were encountered: More numbers are needed than are available, and there is a risk of misinterpretation of the graph underlying the Bayesian network, (...) for instance as a causal model. The formalism presented here models presumptive arguments about coherent hypotheses that are compared in terms of their strength. No choice is needed between qualitative or quantitative analytic styles, since the formalism can be interpreted with and without numbers. The formalism is applied to key concepts in argumentative, scenario and probabilistic analyses of evidential reasoning, and is illustrated with a fictional crime investigation example based on Alfred Hitchcock’s film ‘To Catch A Thief’. (shrink)

Two key research issues in the field of causal learning are how people acquire causal knowledge when observing data that are presented sequentially, and the level of abstraction at which learning takes place. Does sequential causal learning solely involve the acquisition of specific cause-effect links, or do learners also acquire knowledge about abstract causal constraints? Recent empirical studies have revealed that experience with one set of causal cues can dramatically alter subsequent learning and performance with (...) entirely different cues, suggesting that learning involves abstract transfer, and such transfer effects involve sequential presentation of distinct sets of causal cues. It has been demonstrated that pre-training can modulate classic causal learning phenomena such as forward and backward blocking. To account for these effects, we propose a Bayesian theory of sequential causal learning. The theory assumes that humans are able to consider and use several alternative causal generative models, each instantiating a different causal integration rule. Model selection is used to decide which integration rule to use in a given learning environment in order to infer causal knowledge from sequential data. Detailed computer simulations demonstrate that humans rely on the abstract characteristics of outcome variables to select a causal integration rule, which in turn alters causal learning in a variety of blocking and overshadowing paradigms. When the nature of the outcome variable is ambiguous, humans select the model that yields the best fit with the recent environment, and then apply it to subsequent learning tasks. Based on sequential patterns of cue-outcome co-occurrence, the theory can account for a range of phenomena in sequential causal learning, including various blocking effects, primacy effects in some experimental conditions, and apparently abstract transfer of causal knowledge. (shrink)

Chronic myeloid leukemia (CML) is a cancer of the hematopoietic system initiated by a single genetic mutation which results in the oncogenic fusion protein Bcr-Abl. Untreated, patients pass through different phases of the disease beginning with the rather asymptomatic chronic phase and ultimately culminating into blast crisis, an acute leukemia resembling phase with a very high mortality. Although many processes underlying the chronic phase are well understood, the exact mechanisms of disease progression to blast crisis are not yet revealed. In (...) this paper we develop a mathematical model of CML based on causal Bayesian networks in order to study possible disease progression mechanisms. Our results indicate that an increase of Bcr-Abl levels alone is not sufficient to explain the phenotype of blast crisis and that secondary changes such as additional mutations are necessary to explain disease progression and the poor therapy response of patients in blast crisis. (shrink)

The study tests the hypothesis that conditional probability judgments can be influenced by causal links between the target event and the evidence even when the statistical relations among variables are held constant. Three experiments varied the causal structure relating three variables and found that (a) the target event was perceived as more probable when it was linked to evidence by a causal chain than when both variables shared a common cause; (b) predictive chains in which evidence is (...) a cause of the hypothesis gave rise to higher judgments than diagnostic chains in which evidence is an effect of the hypothesis; and (c) direct chains gave rise to higher judgments than indirect chains. A Bayesian learning model was applied to our data but failed to explain them. An explanation-based hypothesis stating that statistical information will affect judgments only to the extent that it changes beliefs about causal structure is consistent with the results. (shrink)

Previous research suggests that children can infer causal relations from patterns of events. However, what appear to be cases of causal inference may simply reduce to children recognizing relevant associations among events, and responding based on those associations. To examine this claim, in Experiments 1 and 2, children were introduced to a “blicket detector,” a machine that lit up and played music when certain objects were placed upon it. Children observed patterns of contingency between objects and the machine's (...) activation that required them to use indirect evidence to make causal inferences. Critically, associative models either made no predictions, or made incorrect predictions about these inferences. In general, children were able to make these inferences, but some developmental differences between 3- and 4-year-olds were found. We suggest that children's causal inferences are not based on recognizing associations, but rather that children develop a mechanism for Bayesian structure learning. Experiment 3 explicitly tests a prediction of this account. Children were asked to make an inference about ambiguous data based on the base rate of certain events occurring. Four-year-olds, but not 3-year-olds were able to make this inference. (shrink)

This article considers the extent to which Bayesian networks with imprecise probabilities, which are used in statistics and computer science for predictive purposes, can be used to represent causal structure. It is argued that the adequacy conditions for causal representation in the precise context—the Causal Markov Condition and Minimality—do not readily translate into the imprecise context. Crucial to this argument is the fact that the independence relation between random variables can be understood in several different ways (...) when the joint probability distribution over those variables is imprecise, none of which provides a compelling basis for the causal interpretation of imprecise Bayes nets. I conclude that there are serious limits to the use of imprecise Bayesian networks to represent causal structure. (shrink)

How should we reason with causal relationships? Much recent work on this question has been devoted to the theses (i) that Bayesian nets provide a calculus for causal reasoning and (ii) that we can learn causal relationships by the automated learning of Bayesian nets from observational data. The aim of this book is to..

Proponents of various causal exclusion arguments claim that for any given event, there is often a unique level of granularity at which that event is caused. Against these causal exclusion arguments, causal ecumenists argue that the same event or phenomenon can be caused at multiple levels of granularity. This paper argues that the Bayesian network approach to representing the causal structure of target systems is consistent with causal ecumenism. Given the ubiquity of Bayesian (...) networks as a tool for representing causal structure in both philosophy of science and science itself, this result speaks in favor of the ecumenical view, and against rival exclusionary accounts. Gebharter’s (Philos Phenomenol Res 95(2):353–375, 2017) argument that the Bayes nets formalism is consistent with causal exclusion is considered and rebutted. (shrink)

In this paper we compare causal models with reason models in the construction of Bayesian networks for legal evidence. In causal models, arrows in the network are drawn from causes to effects. In a reason model, the arrows are instead drawn towards the evidence, from factum probandum to factum probans. We explore the differences between causal models and reason models and observe several distinct advantages with reason models. Reason models are better aligned with the philosophy of (...) Bayesian inference, as they model reasons for up-dating beliefs. Reason models are better suited for measuring the combined support of the evidence, and a prior probability of guilt that reflects the number of possible perpetrators is accommodated more easily with reason models. (shrink)

Background: Evidence suggesting adverse drug reactions often emerges unsystematically and unpredictably in form of anecdotal reports, case series and survey data. Safety trials and observational studies also provide crucial information regarding the (un-)safety of drugs. Hence, integrating multiple types of pharmacovigilance evidence is key to minimising the risks of harm. Methods: In previous work, we began the development of a Bayesian framework for aggregating multiple types of evidence to assess the probability of a putative causal link between drugs (...) and side effects. This framework arose out of a philosophical analysis of the Bradford Hill Guidelines. In this article, we expand the Bayesian framework and add “evidential modulators,” which bear on the assessment of the reliability of incoming study results. The overall framework for evidence synthesis, “E-Synthesis”, is then applied to a case study. Results: Theoretically and computationally, E-Synthesis exploits coherence of partly or fully independent evidence converging towards the hypothesis of interest (or of conflicting evidence with respect to it), in order to update its posterior probability. With respect to other frameworks for evidence synthesis, our Bayesian model has the unique feature of grounding its inferential machinery on a consolidated theory of hypothesis confirmation (Bayesian epistemology), and in allowing any data from heterogeneous sources (cell-data, clinical trials, epidemiological studies), and methods (e.g., frequentist hypothesis testing, Bayesian adaptive trials, etc.) to be quantitatively integrated into the same inferential framework. Conclusions: E-Synthesis is highly flexible concerning the allowed input, while at the same time relying on a consistent computational system, that is philosophically and statistically grounded. Furthermore, by introducing evidential modulators, and thereby breaking up the different dimensions of evidence (strength, relevance, reliability), E-Synthesis allows them to be explicitly tracked in updating causal hypotheses. (shrink)

Previous research suggests that children can infer causal relations from patterns of events. However, what appear to be cases of causal inference may simply reduce to children recognizing relevant associations among events, and responding based on those associations. To examine this claim, in Experiments 1 and 2, children were introduced to a “blicket detector”, a machine that lit up and played music when certain objects were placed upon it. Children observed patterns of contingency between objects and the machine’s (...) activation that required them to use indirect evidence to make causal inferences. Critically, associative models either made no predictions, or made incorrect predictions about these inferences. In general, children were able to make these inferences, but some developmental differences between 3- and 4- year-olds were found. We suggest that children’s causal inferences are not based on recognizing associations, but rather that children develop a mechanism for Bayesian structure learning. Experiment 3 explicitly tests a prediction of this account. Children were asked to make an inference about ambiguous data based on the base-rate of certain events occurring. Fouryear-olds, but not 3-year-olds were able to make this inference. (shrink)

(2013). Hierarchical Bayesian models as formal models of causal reasoning. Argument & Computation: Vol. 4, Formal Models of Reasoning in Cognitive Psychology, pp. 36-45. doi: 10.1080/19462166.2012.700321.

Analysts often use data-driven approaches to supplement their knowledge when selecting covariates for effect estimation. Multiple variable selection procedures for causal effect estimation have been devised in recent years, but additional developments are still required to adequately address the needs of analysts. We propose a generalized Bayesian causal effect estimation algorithm to perform variable selection and produce double robust estimates of causal effects for binary or continuous exposures and outcomes. GBCEE employs a prior distribution that targets (...) the selection of true confounders and predictors of the outcome for the unbiased estimation of causal effects with reduced standard errors. The Bayesian machinery allows GBCEE to directly produce inferences for its estimate. In simulations, GBCEE was observed to perform similarly or to outperform DR alternatives. Its ability to directly produce inferences is also an important advantage from a computational perspective. The method is finally illustrated for the estimation of the effect of meeting physical activity recommendations on the risk of hip or upper-leg fractures among older women in the study of osteoporotic fractures. The 95% confidence interval produced by GBCEE is 61% narrower than that of a DR estimator adjusting for all potential confounders in this illustration. (shrink)

This paper investigates the relations between causality and propensity. Aparticular version of the propensity theory of probability is introduced, and it is argued that propensities in this sense are not causes. Some conclusions regarding propensities can, however, be inferred from causal statements, but these hold only under restrictive conditions which prevent cause being defined in terms of propensity. The notion of a Bayesian propensity network is introduced, and the relations between such networks and causal networks is investigated. (...) It is argued that causal networks cannot be identified with Bayesian propensity networks, but that causal networks can be a valuable heuristic guide for the construction of Bayesian propensity networks. (shrink)

Bayesian reasoning has been applied formally to statistical inference, machine learning and analysing scientific method. Here I apply it informally to more common forms of inference, namely natural language arguments. I analyse a variety of traditional fallacies, deductive, inductive and causal, and find more merit in them than is generally acknowledged. Bayesian principles provide a framework for understanding ordinary arguments which is well worth developing.

Artificial Intelligence (AI) and Philosophy of Science share a fundamental problem—that of understanding causality. Bayesian network techniques have recently been used by Judea Pearl in a new approach to understanding causality and causal processes (Pearl, 2000). Pearl’s approach has great promise, but needs to be supplemented with an explicit account of causal interaction. Thus far, despite considerable interest, philosophy has provided no useful account of causal interaction. Here we provide one, employing the concepts of Bayesian (...) networks. With it we demonstrate the failure of one of philosophy’s more sophisticated attempts to deal with the concept of causal interaction, that of Ellery Eells’ Probabilistic Causality (1991). (shrink)

Artificial Intelligence (AI) and Philosophy of Science share a fundamental problem—understanding causality. Bayesian networks have recently been used by Judea Pearl in a new approach to understanding causality (Pearl, 2000). Part of understanding causality is understanding causal interaction. Bayes nets can represent any degree of causal interaction, and researchers normally try to limit interactions, usually by replacing the full CPT with a noisy-OR function. But we show that noisy-OR and another common model are merely special cases of (...) the general linear systems definition of noninteraction. However, they apply in different situations, and we can measure the degree of causal interaction relative to any such model. (shrink)