Humphrey's paradox and the interpretation of inverse conditional propensities

The aim of this paper is to distinguish between, and examine, three issues surrounding Humphreys's paradox and interpretation of conditional propensities. The first issue involves the controversy over the interpretation of inverse conditional propensities — conditional propensities in which the conditioned event occurs before the conditioning event. The second issue is the consistency of the dispositional nature of the propensity interpretation and the inversion theorems of the probability calculus, where an inversion theorem is any theorem of probability that makes explicit (or implicit) appeal to a conditional probability and its corresponding inverse conditional probability. The third issue concerns the relationship between the notion of stochastic independence which is supported by the propensity interpretation, and various notions of causal independence. In examining each of these issues, it is argued that the dispositional character of the propensity interpretation provides a consistent and useful interpretation of the probability calculus.I would like to thank William L. Harper, Paul Humphreys, John Nicholas and Kathleen Okruhlik for helpful comments and advice on earlier drafts of this paper. Research for this paper was supported by a fellowship from the Social Sciences and Humanities Research Council of Canada (award number 452-90-2513).     

Intervention,determinism, and the causal minimality condition

We clarify the status of the so-called causal minimality condition in the theory of causal Bayesian networks, which has received much attention in the recent literature on the epistemology of causation. In doing so, we argue that the condition is well motivated in the interventionist (or manipulability) account of causation, assuming the causal Markov condition which is essential to the semantics of causal Bayesian networks. Our argument has two parts. First, we show that the causal minimality condition, rather than an add-on methodological assumption of simplicity, necessarily follows from the substantive interventionist theses, provided that the actual probability distribution is strictly positive. Second, we demonstrate that the causal minimality condition can fail when the actual probability distribution is not positive, as is the case in the presence of deterministic relationships. But we argue that the interventionist account still entails a pragmatic justification of the causal minimality condition. Our argument in the second part exemplifies a general perspective that we think commendable: when evaluating methods for inferring causal structures and their underlying assumptions, it is relevant to consider how the inferred causal structure will be subsequently used for counterfactual reasoning.     

Human causal induction: A glimpse at the whole picture

In the present work, most relevant evidence in causal learning literature is reviewed and a general cognitive architecture based on the available corpus of experimental data is proposed. However, contrary to algorithms formulated in the Bayesian nets framework, such architecture is not assumed to optimise the usefulness of the available information in order to induce the underlying causal structure as a whole. Instead, human reasoners seem to rely heavily on local clues and previous knowledge to discriminate between spurious and truly causal covariations, and piece those relations together only when they are demanded to do so. Bayesian networks and AI algorithms for causal inference are nonetheless considered valuable tools to identify the main computational goals of causal induction processes and to define the problems any intelligent causal inference system must solve.     

Bayes and blickets: effects of knowledge on causal induction in children and adults

People are adept at inferring novel causal relations, even from only a few observations. Prior knowledge about the probability of encountering causal relations of various types and the nature of the mechanisms relating causes and effects plays a crucial role in these inferences. We test a formal account of how this knowledge can be used and acquired, based on analyzing causal induction as Bayesian inference. Five studies explored the predictions of this account with adults and 4-year-olds, using tasks in which participants learned about the causal properties of a set of objects. The studies varied the two factors that our Bayesian approach predicted should be relevant to causal induction: the prior probability with which causal relations exist, and the assumption of a deterministic or a probabilistic relation between cause and effect. Adults' judgments (Experiments 1, 2, and 4) were in close correspondence with the quantitative predictions of the model, and children's judgments (Experiments 3 and 5) agreed qualitatively with this account.     

Children’s causal inferences from indirect evidence: Backwards blocking and Bayesian reasoning in preschoolers

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.     

Bayesian Model Averaging for Propensity Score Analysis

This article considers Bayesian model averaging as a means of addressing uncertainty in the selection of variables in the propensity score equation. We investigate an approximate Bayesian model averaging approach based on the model-averaged propensity score estimates produced by the R package BMA but that ignores uncertainty in the propensity score. We also provide a fully Bayesian model averaging approach via Markov chain Monte Carlo sampling (MCMC) to account for uncertainty in both parameters and models. A detailed study of our approach examines the differences in the causal estimate when incorporating noninformative versus informative priors in the model averaging stage. We examine these approaches under common methods of propensity score implementation. In addition, we evaluate the impact of changing the size of Occam’s window used to narrow down the range of possible models. We also assess the predictive performance of both Bayesian model averaging propensity score approaches and compare it with the case without Bayesian model averaging. Overall, results show that both Bayesian model averaging propensity score approaches recover the treatment effect estimates well and generally provide larger uncertainty estimates, as expected. Both Bayesian model averaging approaches offer slightly better prediction of the propensity score compared with the Bayesian approach with a single propensity score equation. Covariate balance checks for the case study show that both Bayesian model averaging approaches offer good balance. The fully Bayesian model averaging approach also provides posterior probability intervals of the balance indices.     

Correlation,partial correlation,and causation

Philosophers and scientists have maintained that causation, correlation, and “partial correlation” are essentially related. These views give rise to various rules of causal inference. This essay considers the claims of several philosophers and social scientists for causal systems with dichotomous variables. In section 2 important commonalities and differences are explicated among four major conceptions of correlation. In section 3 it is argued that whether correlation can serve as a measure of A's causal influence on B depends upon the conception of causation being used and upon certain background assumptions. In section 4 five major kinds of “partial correlation” are explicated, and some of the important relations are established among two conceptions of “partial correlation”, the conception of “screening off”, the conception of “partitioning”, and the measures of causal influence which have been suggested by advocates of path analysis or structural equation methods. In section 5 it is argued that whether any of these five conceptions of “partial correlation” can serve as a measure of causal influence depends upon the conception of causation being used and upon certain background assumptions. The important conclusion is that each of the approaches (considered here) to causal inference for causal systems with dichotomous variables stands in need of important qualifications and revisions if they are to be justified.     

Non-bayesian inference: causal structure trumps correlation

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.     

Interventionism and Causal Exclusion

A number of writers, myself included, have recently argued that an “interventionist” treatment of causation of the sort defended in Woodward, 2003 can be used to cast light on so‐called “causal exclusion” arguments. This interventionist treatment of causal exclusion has in turn been criticized by other philosophers. This paper responds to these criticisms. It describes an interventionist framework for thinking about causal relationships when supervenience relations are present. I contend that this framework helps us to see that standard arguments for causal exclusion involve mistaken assumptions about what it is appropriate to control for or hold fixed in assessing causal claims. The framework also provides a natural way of capturing the idea that properties that supervene on but that are not identical with realizing properties can be causally efficacious.     

A Two-Step Bayesian Approach for Propensity Score Analysis: Simulations and Case Study

A two-step Bayesian propensity score approach is introduced that incorporates prior information in the propensity score equation and outcome equation without the problems associated with simultaneous Bayesian propensity score approaches. The corresponding variance estimators are also provided. The two-step Bayesian propensity score is provided for three methods of implementation: propensity score stratification, weighting, and optimal full matching. Three simulation studies and one case study are presented to elaborate the proposed two-step Bayesian propensity score approach. Results of the simulation studies reveal that greater precision in the propensity score equation yields better recovery of the frequentist-based treatment effect. A slight advantage is shown for the Bayesian approach in small samples. Results also reveal that greater precision around the wrong treatment effect can lead to seriously distorted results. However, greater precision around the correct treatment effect parameter yields quite good results, with slight improvement seen with greater precision in the propensity score equation. A comparison of coverage rates for the conventional frequentist approach and proposed Bayesian approach is also provided. The case study reveals that credible intervals are wider than frequentist confidence intervals when priors are non-informative.     

因果信息和提示指导语对大学生贝叶斯推理的影响

基于三重加工心智模型,以大学生为被试,采用经典贝叶斯推理的文本范式,通过操纵自变量：因果信息（有或无）与提示指导语（提供或不提供）,试图探讨激发反省心智,消解理性障碍的情况下,因果贝叶斯框架的作用机制。估计正确率和准确性的结果都表明因果信息显著提高了贝叶斯推理成绩,准确性的结果也说明指导语可以提示被试放下既有观念,以无偏见的方式进行推理,从而有效促进了贝叶斯推理表现。而在提示条件下增加因果信息并没有促进作用,表明对于较高元认知的被试因果信息作用是有限的。     

What Fitness Can’t Be

Recently advocates of the propensity interpretation of fitness have turned critics. To accommodate examples from the population genetics literature they conclude that fitness is better defined broadly as a family of propensities rather than the propensity to contribute descendants to some future generation. We argue that the propensity theorists have misunderstood the deeper ramifications of the examples they cite. These examples demonstrate why there are factors outside of propensities that determine fitness. We go on to argue for the more general thesis that no account of fitness can satisfy the desiderata that have motivated the propensity account.     

因果信息和提示指导语对大学生贝叶斯推理的影响

基于三重加工心智模型，以大学生为被试，采用经典贝叶斯推理的文本范式，通过操纵自变量：因果信息（有或无）与提示指导语（提供或不提供），试图探讨激发反省心智，消解理性障碍的情况下，因果贝叶斯框架的作用机制。估计正确率和准确性的结果都表明因果信息显著提高了贝叶斯推理成绩，准确性的结果也说明指导语可以提示被试放下既有观念，以无偏见的方式进行推理，从而有效促进了贝叶斯推理表现。而在提示条件下增加因果信息并没有促进作用，表明对于较高元认知的被试因果信息作用是有限的。     

Rumination: Bridging a gap between forgivingness, vengefulness, and psychological health

It was argued in the present investigation that dispositional forgiveness and vengeance would be differentially related to components of rumination, and thus the mediating role of rumination in their relations with psychological health would also vary. Male and female undergraduates (N = 183) completed questionnaires assessing predispositions toward forgiveness, vengefulness, rumination, depressive affect, and life satisfaction. Regression analyses revealed that higher forgiveness and lower vengefulness were associated with greater psychological health (lower depressive affect; higher life satisfaction). Moreover, the relations between forgiveness (but not vengefulness) and psychological health were partially mediated by the decreased propensity of high forgivers to endorse ruminative brooding. These findings suggest that, although forgiveness and vengeance may be related, their impacts on psychological health reflect distinct ruminative tendencies.     

Feature inference and the causal structure of categories

The purpose of this article was to establish how theoretical category knowledge-specifically, knowledge of the causal relations that link the features of categories-supports the ability to infer the presence of unobserved features. Our experiments were designed to test proposals that causal knowledge is represented psychologically as Bayesian networks. In five experiments we found that Bayes' nets generally predicted participants' feature inferences quite well. However, we also observed a pervasive violation of one of the defining principles of Bayes' nets-the causal Markov condition-because the presence of characteristic features invariably led participants to infer yet another characteristic feature. We argue that this effect arises from a domain-general bias to assume the presence of underlying mechanisms associated with the category. Specifically, people take an exemplar to be a "well functioning" category member when it has most or all of the category's characteristic features, and thus are likely to infer a characteristic value on an unobserved dimension.     

Nomic Universals and Particular Causal Relations: Which are Basic and Which are Derived?

Armstrong holds that a law of nature is a certain sort of structural universal which, in turn, fixes causal relations between particular states of affairs. His claim that these nomic structural universals explain causal relations commits him to saying that such universals are irreducible, not supervenient upon the particular causal relations they fix. However, Armstrong also wants to avoid Plato’s view that a universal can exist without being instantiated, a view which he regards as incompatible with naturalism. This construal of naturalism forces Armstrong to say that universals are abstractions from a certain class of particulars; they are abstractions from first-order states of affairs, to be more precise. It is here argued that these two tendencies in Armstrong cannot be reconciled: To say that universals are abstractions from first-order states of affairs is not compatible with saying that universals fix causal relations between particulars. Causal relations are themselves states of affairs of a sort, and Armstrong’s claim that a law is a kind of structural universal is best understood as the view that any given law logically supervenes on its corresponding causal relations. The result is an inconsistency, Armstrong having to say that laws do not supervene on particular causal relations while also being committed to the view that they do so supervene. The inconsistency is perhaps best resolved by denying that universals are abstractions from states of affairs.

Mutability and propensity in causal selection

We examined differences in causal ratings of 1 factor depending on the mutability (defined as the ease with which a factor can be imagined to be different) and causal propensity (defined as the likelihood that the event would occur in the presence of a factor) of another factor that conjoined to produce the event. In 3 studies, causal ratings of the target factor depended on the interaction of mutability and propensity of the other factor. When the other factor was high in mutability, ratings of the target decreased as the propensity of the contributing factor increased, but when the other was low in mutability, ratings of the target increased as the propensity of the contributing factor increased. Mediation analysis indicated that mutability and propensity affected causal ratings by determining the comparison against which the event was considered. Comparison judgments also mediated beliefs about which factor should have adjusted to the other.     

Manipulation is key: on why non-mechanistic explanations in the cognitive sciences also describe relations of manipulation and control

A popular view presents explanations in the cognitive sciences as causal or mechanistic and argues that an important feature of such explanations is that they allow us to manipulate and control the explanandum phenomena. Nonetheless, whether there can be explanations in the cognitive sciences that are neither causal nor mechanistic is still under debate. Another prominent view suggests that both causal and non-causal relations of counterfactual dependence can be explanatory, but this view is open to the criticism that it is not clear how to distinguish explanatory from non-explanatory relations. In this paper, I draw from both views and suggest that, in the cognitive sciences, relations of counterfactual dependence that allow manipulation and control can be explanatory even when they are neither causal nor mechanistic. Furthermore, the ability to allow manipulation can determine whether non-causal counterfactual dependence relations are explanatory. I present a preliminary framework for manipulation relations that includes some non-causal relations and use two examples from the cognitive sciences to show how this framework distinguishes between explanatory and non-explanatory, non-causal relations. The proposed framework suggests that, in the cognitive sciences, causal and non-causal relations have the same criterion for explanatory value, namely, whether or not they allow manipulation and control.     

Causal relations in field research as a basis for practical control

The utility of causal relations in field research for practical control is critically examined. It is argued that generalizations involving hypothetical intervention or change, formulated in terms of the parameters of causal regression functions for natural variation, are incompatible with the formal selection requirements for use of these functions. Practical results may thus deviate markedly from those predicted by the functions. Consequently, the causal relations commonly measured in field research within psychology and related disciplines cannot be used in any strict sense for the purpose of practical control. This conclusion, however, applies to generalizations involving intervention which are based on natural variation, not necessarily to those based on manipulated variation. The account demonstrates the importance of adopting a concept of causality which makes a clear distinction between causal measurements, on the one hand, and generalizations from such results, on the other.     

Networks of Meaning: Intergroup Relations, Cultural Worldviews, and Knowledge Activation Principles

In this article, we bring advances in the fields of social cognition, personality, and culture to bear on the topic of intergroup relations. Specifically, principles of knowledge activation ( Higgins, 1996 ), and of the architecture of knowledge networks ( Cervone, 2005; Mischel & Shoda, 1995 ) are applied to understanding how cultural groups develop divergent worldviews. We discuss these principles within a recently proposed model of culture and person dynamics, the Cultural Cognitive-Affective Processing System ( Mendoza-Denton & Mischel, 2007 ). It is argued that the underlying psychological principles that govern knowledge acquisition and activation may be universal, but that the manifestations of these processes are culture specific. More precisely, culture impacts the availability, applicability, and accessibility of knowledge, as well as the organizational relationships among constructs. Together, these processes give rise to complex networks of meaning that, despite diverging across cultures, can nevertheless be communicated and understood by non-natives of that culture.