Intuitive statistics
Intuitive statistics, or folk statistics, is the cognitive phenomenon where organisms use data to make generalizations and predictions about the world. This can be a small amount of sample data or training instances, which in turn contribute to inductive inferences about either population-level properties, future data, or both. Inferences can involve revising hypotheses, or beliefs, in light of probabilistic data that inform and motivate future predictions. The informal tendency for cognitive animals to intuitively generate statistical inferences, when formalized with certain axioms of probability theory, constitutes statistics as an academic discipline.
Because this capacity can accommodate a broad range of informational domains, the subject matter is similarly broad and overlaps substantially with other cognitive phenomena. Indeed, some have argued that "cognition as an intuitive statistician" is an apt companion metaphor to the computer metaphor of cognition. Others appeal to a variety of statistical and probabilistic mechanisms behind theory construction and category structuring. Research in this domain commonly focuses on generalizations relating to number, relative frequency, risk, and any systematic signatures in inferential capacity that an organism might have.
Background and theory
Intuitive inferences can involve generating hypotheses from incoming sense data, such as categorization and concept structuring. Data are typically probabilistic and uncertainty is the rule, rather than the exception, in learning, perception, language, and thought. Recently, researchers have drawn from ideas in probability theory, philosophy of mind, computer science, and psychology to model cognition as a predictive and generative system of probabilistic representations, allowing information structures to support multiple inferences in a variety of contexts and combinations. This approach has been called a probabilistic language of thought because it constructs representations probabilistically, from pre-existing concepts to predict a possible and likely state of the world.Probability
Statisticians and probability theorists have long debated about the use of various tools, assumptions, and problems relating to inductive inference in particular. David Hume famously considered the problem of induction, questioning the logical foundations of how and why people can arrive at conclusions that extend beyond past experiences - both spatiotemporally and epistemologically. More recently, theorists have considered the problem by emphasizing techniques for arriving from data to hypothesis using formal content-independent procedures, or in contrast, by considering informal, content-dependent tools for inductive inference. Searches for formal procedures have led to different developments in statistical inference and probability theory with different assumptions, including Fisherian frequentist statistics, Bayesian inference, and Neyman-Pearson statistics.Gerd Gigerenzer and David Murray argue that twentieth century psychology as a discipline adopted probabilistic inference as a unified set of ideas and ignored the controversies among probability theorists. They claim that a normative but incorrect view of how humans "ought to think rationally" follows from this acceptance. They also maintain, however, that the intuitive statistician metaphor of cognition is promising, and should consider different formal tools or heuristics as specialized for different problem domains, rather than a content- or context-free toolkit. Signal detection theorists and object detection models, for example, often use a Neyman-Pearson approach, whereas Fisherian frequentist statistics might aid cause-effect inferences.
Frequentist inference
focuses on the relative proportions or frequencies of occurrences to draw probabilistic conclusions. It is defined by its closely related concept, frequentist probability. This entails a view that "probability" is nonsensical in the absence of pre-existing data, because it is understood as a relative frequency that long-run samples would approach given large amounts of data. Leda Cosmides and John Tooby have argued that it is not possible to derive a probability without reference to some frequency of previous outcomes, and this likely has evolutionary origins: Single-event probabilities, they claim, are not observable because organisms evolved to intuitively understand and make statistical inferences from frequencies of prior events, rather than to "see" probability as an intrinsic property of an event.Bayesian inference
generally emphasizes the subjective probability of a hypothesis, which is computed as a posterior probability using Bayes' Theorem. It requires a "starting point" called a prior probability, which has been contentious for some frequentists who claim that frequency data are required to develop a prior probability, in contrast to taking a probability as an a priori assumption.Bayesian models have been quite popular among psychologists, particularly learning theorists, because they appear to emulate the iterative, predictive process by which people learn and develop expectations from new observations, while giving appropriate weight to previous observations. Andy Clark, a cognitive scientist and philosopher, recently wrote a detailed argument in support of understanding the brain as a constructive Bayesian engine that is fundamentally action-oriented and predictive, rather than passive or reactive. More classic lines of evidence cited among supporters of Bayesian inference include conservatism, or the phenomenon where people modify previous beliefs toward, but not all the way to, a conclusion implied by previous observations. This pattern of behavior is similar to the pattern of posterior probability distributions when a Bayesian model is conditioned on data, though critics argued that this evidence had been overstated and lacked mathematical rigor.
Alison Gopnik more recently tackled the problem by advocating the use of Bayesian networks, or directed graph representations of conditional dependencies. In a Bayesian network, edge weights are conditional dependency strengths that are updated in light of new data, and nodes are observed variables. The graphical representation itself constitutes a model, or hypothesis, about the world and is subject to change, given new data.
Error management theory
is an application of Neyman-Pearson statistics to cognitive and evolutionary psychology. It maintains that the possible fitness costs and benefits of type I and type II errors are relevant to adaptively rational inferences, toward which an organism is expected to be biased due to natural selection. EMT was originally developed by Martie Haselton and David Buss, with initial research focusing on its possible role in sexual overperception bias in men and sexual underperception bias in women.This is closely related to a concept called the "smoke detector principle" in evolutionary theory. It is defined by the tendency for immune, affective, and behavioral defenses to be hypersensitive and overreactive, rather than insensitive or weakly expressed. Randolph Nesse maintains that this is a consequence of a typical payoff structure in signal detection: In a system that is invariantly structured with a relatively low cost of false positives and high cost of false negatives, naturally selected defenses are expected to err on the side of hyperactivity in response to potential threat cues. This general idea has been applied to hypotheses about the apparent tendency for humans to apply agency to non-agents based on uncertain or agent-like cues. In particular, some claim that it is adaptive for potential prey to assume agency by default if it is even slightly suspected, because potential predator threats typically involve cheap false positives and lethal false negatives.
Heuristics and biases
are efficient rules, or computational shortcuts, for producing a judgment or decision. The intuitive statistician metaphor of cognition led to a shift in focus for many psychologists, away from emotional or motivational principles and toward computational or inferential principles. Empirical studies investigating these principles have led some to conclude that human cognition, for example, has built-in and systematic errors in inference, or cognitive biases. As a result, cognitive psychologists have largely adopted the view that intuitive judgments, generalizations, and numerical or probabilistic calculations are systematically biased. The result is commonly an error in judgment, including recurrent logical fallacies, innumeracy, and emotionally motivated shortcuts in reasoning. Social and cognitive psychologists have thus considered it "paradoxical" that humans can outperform powerful computers at complex tasks, yet be deeply flawed and error-prone in simple, everyday judgments.Much of this research was carried out by Amos Tversky and Daniel Kahneman as an expansion of work by Herbert Simon on bounded rationality and satisficing. Tversky and Kahneman argue that people are regularly biased in their judgments under uncertainty, because in a speed-accuracy tradeoff they often rely on fast and intuitive heuristics with wide margins of error rather than slow calculations from statistical principles. These errors are called "cognitive illusions" because they involve systematic divergences between judgments and accepted, normative rules in statistical prediction.
Gigerenzer has been critical of this view, arguing that it builds from a flawed assumption that a unified "normative theory" of statistical prediction and probability exists. His contention is that cognitive psychologists neglect the diversity of ideas and assumptions in probability theory, and in some cases, their mutual incompatibility. Consequently, Gigerenzer argues that many cognitive illusions are not violations of probability theory per se, but involve some kind of experimenter confusion between subjective probabilities with degrees of confidence and long-run outcome frequencies. Cosmides and Tooby similarly claim that different probabilistic assumptions can be more or less normative and rational in different types of situations, and that there is not general-purpose statistical toolkit for making inferences across all informational domains. In a review of several experiments they conclude, in support of Gigerenzer, that previous heuristics and biases experiments did not represent problems in an ecologically valid way, and that re-representing problems in terms of frequencies rather than single-event probabilities can make cognitive illusions largely vanish.
Tversky and Kahneman refuted this claim, arguing that making illusions disappear by manipulating them, whether they are cognitive or visual, does not undermine the initially discovered illusion. They also note that Gigerenzer ignores cognitive illusions resulting from frequency data, e.g., illusory correlations such as the hot hand in basketball. This, they note, is an example of an illusory positive autocorrelation that cannot be corrected by converted data to natural frequencies.
For adaptationists, EMT can be applied to inference under any informational domain, where risk or uncertainty are present, such as predator avoidance, agency detection, or foraging. Researchers advocating this adaptive rationality view argue that evolutionary theory casts heuristics and biases in a new light, namely, as computationally efficient and ecologically rational shortcuts, or instances of adaptive error management.