In many learning or inference tasks human behavior approximates that of a Bayesian ideal observer, suggesting that, at some level, cognition can be described as Bayesian inference. However, a number of findings have highlighted an intriguing mismatch between human behavior and standard assumptions about optimality: People often appear to make decisions based on just one or a few samples from the appropriate posterior probability distribution, rather than using the full distribution. Although sampling-based approximations are a common way to implement Bayesian (...) inference, the very limited numbers of samples often used by humans seem insufficient to approximate the required probability distributions very accurately. Here, we consider this discrepancy in the broader framework of statistical decision theory, and ask: If people are making decisions based on samples—but as samples are costly—how many samples should people use to optimize their total expected or worst-case reward over a large number of decisions? We find that under reasonable assumptions about the time costs of sampling, making many quick but locally suboptimal decisions based on very few samples may be the globally optimal strategy over long periods. These results help to reconcile a large body of work showing sampling-based or probability matching behavior with the hypothesis that human cognition can be understood in Bayesian terms, and they suggest promising future directions for studies of resource-constrained cognition. (shrink)
Is language understanding a special case of social cognition? To help evaluate this view, we can formalize it as the rational speech-act theory: Listeners assume that speakers choose their utterances approximately optimally, and listeners interpret an utterance by using Bayesian inference to “invert” this model of the speaker. We apply this framework to model scalar implicature (“some” implies “not all,” and “N” implies “not more than N”). This model predicts an interaction between the speaker's knowledge state and the listener's interpretation. (...) We test these predictions in two experiments and find good fit between model predictions and human judgments. (shrink)
Hierarchical Bayesian models (HBMs) provide an account of Bayesian inference in a hierarchically structured hypothesis space. Scientific theories are plausibly regarded as organized into hierarchies in many cases, with higher levels sometimes called ‘paradigms’ and lower levels encoding more specific or concrete hypotheses. Therefore, HBMs provide a useful model for scientific theory change, showing how higher‐level theory change may be driven by the impact of evidence on lower levels. HBMs capture features described in the Kuhnian tradition, particularly the idea that (...) higher‐level theories guide learning at lower levels. In addition, they help resolve certain issues for Bayesians, such as scientific preference for simplicity and the problem of new theories. *Received July 2009; revised October 2009. †To contact the authors, please write to: Leah Henderson, Massachusetts Institute of Technology, 77 Massachusetts Avenue, 32D‐808, Cambridge, MA 02139; e‐mail: email@example.com. (shrink)
Marr's levels of analysis—computational, algorithmic, and implementation—have served cognitive science well over the last 30 years. But the recent increase in the popularity of the computational level raises a new challenge: How do we begin to relate models at different levels of analysis? We propose that it is possible to define levels of analysis that lie between the computational and the algorithmic, providing a way to build a bridge between computational- and algorithmic-level models. The key idea is to push the (...) notion of rationality, often used in defining computational-level models, deeper toward the algorithmic level. We offer a simple recipe for reverse-engineering the mind's cognitive strategies by deriving optimal algorithms for a series of increasingly more realistic abstract computational architectures, which we call “resource-rational analysis.”. (shrink)
Learning to understand a single causal system can be an achievement, but humans must learn about multiple causal systems over the course of a lifetime. We present a hierarchical Bayesian framework that helps to explain how learning about several causal systems can accelerate learning about systems that are subsequently encountered. Given experience with a set of objects, our framework learns a causal model for each object and a causal schema that captures commonalities among these causal models. The schema organizes the (...) objects into categories and specifies the causal powers and characteristic features of these categories and the characteristic causal interactions between categories. A schema of this kind allows causal models for subsequent objects to be rapidly learned, and we explore this accelerated learning in four experiments. Our results confirm that humans learn rapidly about the causal powers of novel objects, and we show that our framework accounts better for our data than alternative models of causal learning. (shrink)
We derive a probabilistic account of the vagueness and context-sensitivity of scalar adjectives from a Bayesian approach to communication and interpretation. We describe an iterated-reasoning architecture for pragmatic interpretation and illustrate it with a simple scalar implicature example. We then show how to enrich the apparatus to handle pragmatic reasoning about the values of free variables, explore its predictions about the interpretation of scalar adjectives, and show how this model implements Edgington’s Vagueness: a reader, 1997) account of the sorites paradox, (...) with variations. The Bayesian approach has a number of explanatory virtues: in particular, it does not require any special-purpose machinery for handling vagueness, and it is integrated with a promising new approach to pragmatics and other areas of cognitive science. (shrink)
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.
Predictions concerning the end of the world have proven less reliable than your broker’s recommendations or your fondest hopes. Whether you await the end fearfully or eagerly, you may rest assured that it will never come—not because the world is everlasting but because it has already ended, if indeed it ever began. But we need not mourn, for the world is indeed well lost, and with it the stultifying stereotypes of absolutism: the absurd notions of science as the effort to (...) discover a unique, prepackaged, but unfortunately undiscoverable reality, and of truth as agreement with that inaccessible reality. All notions of pure givenness and unconditional necessity and of a single correct perspective and system of categories are lost as well.If there is no such thing as the world, what are we living in? The answer might be “A world” or, better, “Several worlds.” For to deny that there is any such thing as the world is no more to deny that there are worlds than to deny that there is any such thing as the number between two and seven is to deny that there are numbers between two and seven. The task of describing the world is as futile as the task of describing the number between two and seven.The world is lost once we appreciate a curious feature of certain pairs of seemingly contradictory statements: if either is true, both are. Although “The earth is in motion” and “The earth is at rest” apparently contradict each other, both are true. But from a contradiction, every statement follows. So unless we are prepared to acknowledge the truth of every statement, the appearance of contradiction in cases like these must somehow be dispelled. Nelson Goodman is professor emeritus of philosophy at Harvard University. He has written Of Mind and Other Matters, Ways of Worldmaking, Problems and Projects, Languages of Art, The Structure of Appearance, and Fact, Fiction, and Forecast. His most recent contribution to Critical Inquiry is “How Buildings Mean” . Catherine Z. Elgin is associate professor of philosophy at the University of North Carolina, Chapel Hill. She is the author of With Reference to Reference and is currently writing a book entitled Philosophy without Foundations. (shrink)