A poor understanding of probability may lead people to misinterpret every day coincidences and form anomalistic beliefs. We investigated the relationship between anomalistic beli...

We were encouraged by the broad enthusiasm for building machines that learn and think in more human-like ways. Many commentators saw our set of key ingredients as helpful, but there was disagreement regarding the origin and structure of those ingredients. Our response covers three main dimensions of this disagreement: nature versus nurture, coherent theories versus theory fragments, and symbolic versus sub-symbolic representations. These dimensions align with classic debates in artificial intelligence and cognitive science, although, rather than embracing these debates, we (...) emphasize ways of moving beyond them. Several commentators saw our set of key ingredients as incomplete and offered a wide range of additions. We agree that these additional ingredients are important in the long run and discuss prospects for incorporating them. Finally, we consider some of the ethical questions raised regarding the research program as a whole. (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.

It is important to reveal how humans evaluate an explanation of the recent development of explainable artificial intelligence. So, what makes people feel that one explanation is more likely than another? In the present study, we examine how explanatory virtues affect the process of estimating subjective posterior probability. Through systematically manipulating two virtues, Simplicity—the number of causes used to explain effects—and Scope—the number of effects predicted by causes—in three different conditions, we clarified two points in Experiment 1: that Scope's effect (...) is greater than Simplicity's; and that these virtues affect the outcome independently. In Experiment 2, we found that instruction about the explanatory structure increased the impact of both virtues' effects but especially that of Simplicity. These results suggest that Scope predominantly affects the estimation of subjective posterior probability, but that, if perspective on the explanatory structure is provided, Simplicity can also affect probability estimation. (shrink)

Real causal systems are complicated. Despite this, causal learning research has traditionally emphasized how causal relations can be induced on the basis of idealized events, i.e. those that have been mapped to binary variables and abstracted from time. For example, participants may be asked to assess the efficacy of a headache-relief pill on the basis of multiple patients who take the pill (or not) and find their headache relieved (or not). In contrast, the current study examines learning via interactions with (...) continuous dynamic systems, systems that include continuous variables that interact over time (and that can be continuously observed in real time by the learner). To explore such systems, we develop a new framework that represents a causal system as a network of stationary Gauss--Markov (``\OU'') processes and show how such \textit{OU networks} can express complex dynamic phenomena such as feedback loops and oscillations. To assess adult's abilities to learn such systems, we conducted an experiment in which participants were asked to identify the causal relationships of a number of OU networks, potentially carrying out multiple, temporally-extended interventions. We compared their judgments to a normative model for learning OU networks as well as a range of alternative and heuristic learning models from the literature. We found that, although participants exhibited substantial learning of such systems, they committed certain systematic errors. These successes and failures were best accounted for by a model that describes people as focusing on pairs of variables, rather than evaluating the evidence with respect to the full space of possible structural models. We argue that our approach provides both a principled framework for exploring the space of dynamic learning environments as well as new algorithmic insights into how people interact successfully with a continuous causal world. (shrink)

The field of causal learning and reasoning (largely overlooked in the target article) provides an illuminating case study of how the modern Bayesian framework has deepened theoretical understanding, resolved long-standing controversies, and guided development of new and more principled algorithmic models. This progress was guided in large part by the systematic formulation and empirical comparison of multiple alternative Bayesian models.

If Bayesian Fundamentalism existed, Jones & Love's (J&L's) arguments would provide a necessary corrective. But it does not. Bayesian cognitive science is deeply concerned with characterizing algorithms and representations, and, ultimately, implementations in neural circuits; it pays close attention to environmental structure and the constraints of behavioral data, when available; and it rigorously compares multiple models, both within and across papers. J&L's recommendation of Bayesian Enlightenment corresponds to past, present, and, we hope, future practice in Bayesian cognitive science.