Beliefs and Bayesian reasoning

Cohen, Andrew L.; Sidlowski, Sara; Staub, Adrian

doi:10.3758/s13423-016-1161-z

Cited by 17 publications

(26 citation statements)

References 23 publications

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“…Figure 12C, r = 0.78, p < .001), but this correlation is much lower in the unbelievable condition ( Figure 12D, r = 0.14, p = .06, comparative test: z = 2.64, p = .004). Our model therefore reproduces the belief bias effect reported by Cohen et al (2017).…”

Section: Belief Biassupporting

confidence: 84%

A theory of learning to infer

Dasgupta

Schulz

Tenenbaum

et al. 2019

Preprint

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Bayesian theories of cognition assume that people can integrate probabilities rationally.However, several empirical findings contradict this proposition: human probabilistic inferences are prone to systematic deviations from optimality. Puzzlingly, these deviations sometimes go in opposite directions. Whereas some studies suggest that people under-react to prior probabilities (base rate neglect), other studies find that people under-react to the likelihood of the data (conservatism). We argue that these deviations arise because the human brain does not rely solely on a general-purpose mechanism for approximating Bayesian inference that is invariant across queries. Instead, the brain is equipped with a recognition model that maps queries to probability distributions. The parameters of this recognition model are optimized to get the output as close as possible, on average, to the true posterior. Because of our limited computational resources, the recognition model will allocate its resources so as to be more accurate for high probability queries than for low probability queries. By adapting to the query distribution, the recognition model "learns to infer." We show that this theory can explain why and when people under-react to the data or the prior, and a new experiment demonstrates that these two forms of under-reaction can be systematically controlled by manipulating the query distribution. The theory also explains a range of related phenomena: memory effects, belief bias, and the structure of response variability in probabilistic reasoning. We also discuss how the theory can be integrated with prior sampling-based accounts of approximate inference.

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Section: Belief Biassupporting

confidence: 84%

A theory of learning to infer

Dasgupta

Schulz

Tenenbaum

et al. 2019

Preprint

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“…We developed a set of 26 Bayesian reasoning problems that reported the probabilities that people or objects had certain characteristics. The content of the problems was designed to be relatively arbitrary to encourage participants to rely on the reported probabilities instead of their background knowledge (Cohen et al, ). The stimuli followed the same format as the rollercoaster example from Section .…”

Section: Methodsmentioning

confidence: 99%

“…Participants were asked to base their answers only on the information given and not general knowledge, and they were warned that the probabilities provided in the problems may not be realistic. As this example shows, we tried to choose scenarios in which people would not have strong intuitions about what the probabilities should be (Cohen, Sidlowski, & Staub, ).…”

Section: Introductionmentioning

confidence: 99%

A visualization technique for Bayesian reasoning

Starns

Cohen

Bosco

et al. 2018

Applied Cognitive Psychology

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We tested a method for solving Bayesian reasoning problems in terms of spatial relations as opposed to mathematical equations. Participants completed Bayesian problems in which they were given a prior probability and two conditional probabilities and were asked to report the posterior odds. After a pretraining phase in which participants completed problems with no instruction or external support, participants watched a video describing a visualization technique that used the length of bars to represent the probabilities provided in the problem. Participants then completed more problems with a chance to implement the technique by clicking interactive bars on the computer screen. Performance improved dramatically from the pretraining phase to the interactive-bar phase. Participants maintained improved performance in transfer phases in which they were required to implement the visualization technique with either pencil-and-paper or no external medium. Accuracy levels for participants using the visualization technique were very similar to participants trained to solve the Bayes theorem equation. The results showed no evidence of learning across problems in the pretraining phase or for control participants who did not receive training, so the improved performance of participants using the visualization method could be uniquely attributed to the method itself. A classroom sample demonstrated that these benefits extend to instructional settings. The results show that people can quickly learn to perform Bayesian reasoning without using mathematical equations.We discuss ways that a spatial solution method can enhance classroom instruction on Bayesian inference and help students apply Bayesian reasoning in everyday settings.

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“…Sin embargo, una ventaja de este modelo es la posibilidad de con-trastar más de una hipótesis. 10,12,16,17 Una vez establecidas las hipótesis, asegurándose de ser mutuamente excluyentes y exhaustivas para las explicaciones plausibles, se determina su probabilidad bayesiana a priori (nivel de credibilidad). Esta probabilidad puede ser expresada como una razón (momios preresultados o momios a priori):…”

Section: Contrastación Por El Método Bayesianounclassified

“…2,12,16,20 Otra ventaja de esta perspectiva es que la credibilidad fi nal hacia una hipótesis depende también de nuestros conocimientos o expectativas antes de realizar un estudio, por ello, la necesidad de especifi cación previa. 17,21 Es lógico pensar que si la evidencia a priori ha sido muy sólida en su teoría o secundaria a observaciones empíricas, los nuevos datos aportarán poco a la credibilidad fi nal, pero si estas han sido muy pocas o mínimamente fundadas, aún con un FB tan grande (fuerza de la evidencia) como para aumentar o disminuir sustancialmente la credibilidad, es posible que no sea sufi ciente para cambiar la decisión en contra de la hipótesis que inicialmente se consideró. En esta postura es fundamental calcular la probabilidad posestudio o a posteriori como la credibilidad actualizada, es decir, la credibilidad que se obtiene tras la conjunción del nivel a priori más la evidencia obtenida del estudio.…”

Section: Contrastación Por El Método Bayesianounclassified

Análisis bayesiano. Conceptos básicos y prácticos para su interpretación y uso

Macías

Riojas-Garza

Contreras-Estrada

et al. 2018

RAM

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Bayesian statistics is based on subjective probability. It works with evidence updating considering the knowledge acquired prior to an investigation, plus the evidence obtained thereof. Results' interpretation requires for the hypotheses to be tested to be specified and their a priori probability to be estimated before the study. Study evidence is measured with the Bayes factor (compatibility ratio of the data under the proposed hypotheses). The conjunction of hypotheses a priori probabilities with the Bayes factor allows calculating the a posteriori probability of each one of them. The hypothesis with the highest degree of certainty at its update is the one that is accepted for decision making. In this review, three examples of hypothesis to be tested are shown: difference of means, correlation and association.

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Beliefs and Bayesian reasoning

Cited by 17 publications

References 23 publications

A theory of learning to infer

A theory of learning to infer

A visualization technique for Bayesian reasoning

Análisis bayesiano. Conceptos básicos y prácticos para su interpretación y uso

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