Two causal theories of counterfactual conditionals

Bayes nets are formal representations of causal systems that many psychologists have claimed as plausible mental representations. One purported advantage of Bayes nets is that they may provide a theory of counterfactual conditionals, such as If Calvin had been at the party, Miriam would have left early. This article compares two proposed Bayes net theories as models of people's understanding of counterfactuals. Experiments 1-3 show that neither theory makes correct predictions about backtracking counterfactuals (in which the event of the if-clause occurs after the event of the then-clause), and Experiment 4 shows the same is true of forward counterfactuals. An amended version of one of the approaches, however, can provide a more accurate account of these data.     

Agents and Causes: Dispositional Intuitions As a Guide to Causal Structure

Currently, two frameworks of causal reasoning compete: Whereas dependency theories focus on dependencies between causes and effects, dispositional theories model causation as an interaction between agents and patients endowed with intrinsic dispositions. One important finding providing a bridge between these two frameworks is that failures of causes to generate their effects tend to be differentially attributed to agents and patients regardless of their location on either the cause or the effect side. To model different types of error attribution, we augmented a causal Bayes net model with separate error sources for causes and effects. In several experiments, we tested this new model using the size of Markov violations as the empirical indicator of differential assumptions about the sources of error. As predicted by the model, the size of Markov violations was influenced by the location of the agents and was moderated by the causal structure and the type of causal variables.     

On the Stability of Psychological Hardiness: A Three-Year Longitudinal Study

More than 30 years of research has established psychological hardiness as an important individual resiliency resource. One important question still remaining is whether psychological hardiness can be trained. The present study explored this question longitudinally within the context of a 3-year military academy training program. Cadets from 3 different Norwegian military academies (N = 293) completed hardiness questionnaires during the first week of their training, and then again at the end of each year, resulting in a total of 4 waves of data. Using hierarchical linear modeling, no statistically significant effect of time on hardiness scores was found. The nonsignificant growth parameter was examined further using Bayesian statistics as an indicator of the relative evidence for the null hypothesis of no change over time versus the alternative hypothesis of change. The resulting Bayes factor provided substantial support in our data for the null hypothesis of no hardiness development during the 3-year officer training programs.     

Probing communication-induced memory biases in preverbal infants: Two replication attempts of Yoon,Johnson and Csibra (2008)

In a seminal study, Yoon, Johnson and Csibra [PNAS, 105, 36 (2008)] showed that nine-month-old infants retained qualitatively different information about novel objects in communicative and non-communicative contexts. In a communicative context, the infants encoded the identity of novel objects at the expense of encoding their location, which was preferentially retained in non-communicative contexts. This result had not yet been replicated. Here we attempted two replications, while also including a measure of eye-tracking to obtain more detail of infants’ attention allocation during stimulus presentation. Experiment 1 was designed following the methods described in the original paper. After discussion with one of the original authors, some key changes were made to the methodology in Experiment 2. Neither experiment replicated the results of the original study, with Bayes Factor Analysis suggesting moderate support for the null hypothesis. Both experiments found differential attention allocation in communicative and non-communicative contexts, with more looking to the face in communicative than non-communicative contexts, and more looking to the hand in non-communicative than communicative contexts. High and low level accounts of these attentional differences are discussed.     

Sufficiency and Necessity Assumptions in Causal Structure Induction

Research on human causal induction has shown that people have general prior assumptions about causal strength and about how causes interact with the background. We propose that these prior assumptions about the parameters of causal systems do not only manifest themselves in estimations of causal strength or the selection of causes but also when deciding between alternative causal structures. In three experiments, we requested subjects to choose which of two observable variables was the cause and which the effect. We found strong evidence that learners have interindividually variable but intraindividually stable priors about causal parameters that express a preference for causal determinism (sufficiency or necessity; Experiment 1). These priors predict which structure subjects preferentially select. The priors can be manipulated experimentally (Experiment 2) and appear to be domain‐general (Experiment 3). Heuristic strategies of structure induction are suggested that can be viewed as simplified implementations of the priors.     

Is Theism a Simple,and hence Probable,Explanation for the Universe?

Abstract

Richard Swinburne, in his The Existence of God (2004), presents a cosmological argument in defence of theism (Swinburne 1991: 119, 135). God, Swinburne argues, is more likely to bring about an ordered universe than other states (ibid.: 144, 299). To defend this view, Swinburne presents the following arguments: (1) That this ordered universe is a priori improbable (2004: 49, 150, 1991: 304 et seq.), given the stringent requirements for life (cf. also Leslie 2000: 12), and the Second Law of Thermodynamics (Giancoli 1990: 396); (2) That it seems as if this ordered universe can be explained by theism; (3) A theistic explanation for the universe is more probable because it is a simple explanation. To this end, Swinburne makes use of Bayes’ Theorem. Symbolically, this claim can be represented as (e) for the evidence of the existence of a complex universe, and (h) for a hypothesis. Swinburne’s argument is that theism has a higher prior probability, P(h_theism) > P(h_materialism), since theism is simpler than materialism. He concludes that P(e|h_theism) > P(e|h_materialism). In this paper I will address only this argument (3) above, and defend the view that it is false: theism is not simpler than materialism, nor it is more probably true. I conclude that theism is less probable than materialism, expressed by P(h_theism) < P(h_materialism) : 2/N(2n+1) < 1/n, where N is the number of possible universes and n the number of entities in existence.     

Approximated adjusted fractional Bayes factors: A general method for testing informative hypotheses

Informative hypotheses are increasingly being used in psychological sciences because they adequately capture researchers’ theories and expectations. In the Bayesian framework, the evaluation of informative hypotheses often makes use of default Bayes factors such as the fractional Bayes factor. This paper approximates and adjusts the fractional Bayes factor such that it can be used to evaluate informative hypotheses in general statistical models. In the fractional Bayes factor a fraction parameter must be specified which controls the amount of information in the data used for specifying an implicit prior. The remaining fraction is used for testing the informative hypotheses. We discuss different choices of this parameter and present a scheme for setting it. Furthermore, a software package is described which computes the approximated adjusted fractional Bayes factor. Using this software package, psychological researchers can evaluate informative hypotheses by means of Bayes factors in an easy manner. Two empirical examples are used to illustrate the procedure.     

Subliminal or not? Comparing null-hypothesis and Bayesian methods for testing subliminal priming

A difficulty for reports of subliminal priming is demonstrating that participants who actually perceived the prime are not driving the priming effects. There are two conventional methods for testing this. One is to test whether a direct measure of stimulus perception is not significantly above chance on a group level. The other is to use regression to test if an indirect measure of stimulus processing is significantly above zero when the direct measure is at chance. Here we simulated samples in which we assumed that only participants who perceived the primes were primed by it. Conventional analyses applied to these samples had a very large error rate of falsely supporting subliminal priming. Calculating a Bayes factor for the samples very seldom falsely supported subliminal priming. We conclude that conventional tests are not reliable diagnostics of subliminal priming. Instead, we recommend that experimenters calculate a Bayes factor when investigating subliminal priming.     

A tutorial on Bayes factor estimation with the product space method

The Bayes factor is an intuitive and principled model selection tool from Bayesian statistics. The Bayes factor quantifies the relative likelihood of the observed data under two competing models, and as such, it measures the evidence that the data provides for one model versus the other. Unfortunately, computation of the Bayes factor often requires sampling-based procedures that are not trivial to implement. In this tutorial, we explain and illustrate the use of one such procedure, known as the product space method (Carlin & Chib, 1995). This is a transdimensional Markov chain Monte Carlo method requiring the construction of a “supermodel” encompassing the models under consideration. A model index measures the proportion of times that either model is visited to account for the observed data. This proportion can then be transformed to yield a Bayes factor. We discuss the theory behind the product space method and illustrate, by means of applied examples from psychological research, how the method can be implemented in practice.