Intuitive statistics

[7][8] 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.

[1] 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.

[1] 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.

[14] 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.

[16] Alison Gopnik more recently tackled the problem by advocating the use of Bayesian networks, or directed graph representations of conditional dependencies.

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.

As a result, cognitive psychologists have largely adopted the view that intuitive judgments, generalizations, and numerical or probabilistic calculations are systematically biased.

[22][23][24][25] 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.

[27] 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.

[29] 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.

They also note that Gigerenzer ignores cognitive illusions resulting from frequency data, e.g., illusory correlations such as the hot hand in basketball.

[31] 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.

He and other researchers demonstrate that conclusions from the conjunction fallacy result from ambiguous language, rather than robust statistical errors or cognitive illusions.

Gary Marcus, for example, asserts that training data would have to be completely exhaustive for generalizations to occur in existing connectionist models, and that as a result, they do not handle novel observations well.

He further advocates an integrationist perspective between a language of thought, consisting of symbol representations and operations, and connectionist models than retain the distributed processing that is likely used by neural networks in the brain.

[15][43] Probabilistic inferences and generalization play central roles in concepts and categories and language learning,[44] and infant studies are commonly used to understand the developmental trajectory of humans' intuitive statistical toolkit(s).

For example, looking-time experiments using expected outcomes of red and white ping pong ball proportions found that 8-month-old infants appear to make inferences about population characteristics from which the sample came, and vice versa when given population-level data.

[51] The researchers involved in these findings have argued that humans possess some statistically structured, inferential system during preverbal stages of development and prior to formal education.

[47][50] It is less clear, however, how and why generalization is observed in infants: It might extend directly from detection and storage of similarities and differences in incoming data, or frequency representations.

Conversely, it might be produced by something like general-purpose Bayesian inference, starting with a knowledge base that is iteratively conditioned on data to update subjective probabilities, or beliefs.

Gopnik advocates the hypothesis that infant and childhood learning are examples of inductive inference, a general-purpose mechanism for generalization, acting upon specialized information structures ("theories") in the brain.

[54] On this view, infants and children are essentially proto-scientists because they regularly use a kind of scientific method, developing hypotheses, performing experiments via play, and updating models about the world based on their results.

[66] Specifically, infant categorization at as early as 4.5 months involves iterative and interdependent processes by which exemplars (data) and their similarities and differences are crucial for drawing boundaries around categories.

[76] For example, 9-month-old infants are capable of more quickly and dramatically updating their expectations when repeated syllable strings contain surprising features, such as rare phonemes.

[80][81] Multiple studies by Irene Pepperberg and her colleagues suggested that Grey parrots (Psittacus erithacus) have some capacity for recognizing numbers or number-like concepts, appearing to understand ordinality and cardinality of numerals.

[91][92] Such models serve as a starting point for intuitive generalizations to be made from a small number of cues, resulting in the physician's tradeoff between the "art and science" of medical judgement.

[93] This tradeoff was captured in an artificially intelligent (AI) program called MYCIN, which outperformed medical students, but not experienced physicians with extensive practice in symptom recognition.