On Bayesian problem-solving: helping Bayesians solve simple Bayesian word problems

(2015) On Bayesian problem-solving: helping Bayesians solve simple Bayesian word problems. Resolving the " Bayesian Paradox " —Bayesians Who Failed to Solve Bayesian Problems A well-supported conclusion a reader would draw from the vast amount of research on Bayesian inference could be distilled into one sentence: " People are profoundly Bayesians, but they fail to solve Bayesian word problems. " Indeed, two strands of research tell different stories about our ability to make Bayesian inferences—our ability to infer posterior probability from prior probability and new evidence according to Bayes's theorem. People see, move, coordinate, remember, learn, reason and argue consistently with complex probabilistic Bayesian computations, but they fail to solve, computationally much simpler, Bayesian word problems. On the one hand, a first strand of research shows that people are profoundly Bayesians. Strong evidence indicates that the brain represents probability distributions and certain neural circuits perform Bayesian computations (Pouget et al., 2013). Bayesian computation models account for a wide range of observations on sensory perception, motoric behavior and sensorimotor coordination (see Chater et al., 2010; Pouget et al., 2013). Bayesian computations approximate observed patterns in inductive reasoning, memory, language production, and language comprehension (Chater et al., 2010). Even 12-month-old preverbal infants present behavior consistent with the behavior of a Bayesian ideal observer: infants integrate multiple sources of information to form rational expectations about situations they have never encountered before (Téglás et al., 2011). In everyday life, people form cognitive judgments predicting the occurrence of everyday events consistent with a Bayesian ideal observer (Griffiths and Tenenbaum, 2006). On the other hand, however, a second strand of research shows that people fail to make the simplest possible Bayesian inference once they are presented with Bayesian word problems. Indeed, people tend to largely ignore or neglect base-rate information in probability judgment tasks such as social judgment or textbook problem tasks (Kahneman and Tversky, 1973; Bar-Hillel, 1980) or they tend to fail to be Bayesians in a completely opposite way—by overweighting base-rate information (Teigen and Keren, 2007). In fact, people require costly and intense training with most statistical formats to achieve good performance with probabilistic inferences that deteriorates with time very quickly (Sedlmeier and Gigerenzer, 2001). So people are Bayesians who fail to solve simple Bayesian word problems. As with most paradoxes, a solution to this " Bayesian paradox " lies in taking closer look at conceptualizations: at what constitutes a Bayesian inference in these …