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

Frontiers in Psychology

Volumn 6, Issue , 2015, Pages

  Sirota, Miroslav ^a   Vallée Tourangeau, Gaëlle ^a   Vallée Tourangeau, Frédéric ^a   Juanchich, Marie ^a  

^a KINGSTON UNIVERSITY   (United Kingdom)

Author keywords

Bayesian problem solving; Bayesian reasoning; Bayesian research paradox; mathematical problem solving; natural frequencies

Indexed keywords

EID: 84947281006     PISSN: None     EISSN: 16641078     Source Type: Journal    
DOI: 10.3389/fpsyg.2015.01141     Document Type: Article

References (34)

1. Bar-Hillel M. (1980). The base-rate fallacy in probability judgments. Acta Psychol. 44, 211–233. 10.1016/0001-6918(80)90046-3
2. Barbey A. K. Sloman S. A. (2007). Base-rate respect: from ecological rationality to dual processes. Behav. Brain Sci. 30, 241–254. 10.1017/S0140525X0700165317963533
3. Barrett H. C. Frederick D. A. Haselton M. G. Kurzban R. (2006). Can manipulations of cognitive load be used to test evolutionary hypotheses? J. Pers. Soc. Psychol. 91, 513. 10.1037/0022-3514.91.3.51316938033
4. Chater N. Oaksford M. Hahn U. Heit E. (2010). Bayesian models of cognition. Wiley Interdiscipl. Rev. Cogn. Sci. 1, 811–823. 10.1002/wcs.79
5. Cosmides L. Tooby J. (1996). Are humans good intuitive statisticians after all? Rethinking some conclusions from the literature on judgment under uncertainty. Cognition 58, 1–73. 10.1016/0010-0277(95)00664-811018509
6. Geary D. C. (1995). Reflections of evolution and culture in children's cognition: implications for mathematical development and instruction. Am. Psychol. 50, 24. 10.1037/0003-066X.50.1.247872578
7. Gigerenzer G. Hoffrage U. (1995). How to improve Bayesian reasoning without instruction - Frequency formats. Psychol. Rev. 102, 684–704. 10.1037/0033-295X.102.4.68426030173
8. Gilhooly K. J. Murphy P. (2005). Differentiating insight from non-insight problems. Think. Reason. 11, 279–302. 10.1080/13546780442000187
9. Griffiths T. L. Tenenbaum J. B. (2006). Optimal predictions in everyday cognition. Psychol. Sci. 17, 767–773. 10.1111/j.1467-9280.2006.01780.x16984293
10. Hasher L. Zacks R. T. (1984). Automatic processing of fundamental information: the case of frequency of occurrence. Am. Psychol. 39, 1372. 10.1037/0003-066x.39.12.13726395744
11. Hertwig R. Barron G. Weber E. U. Erev I. (2004). Decisions from experience and the effect of rare events in risky choice. Psychol. Sci. 15, 534–539. 10.1111/j.0956-7976.2004.00715.x15270998
12. Johnson-Laird P. N. Legrenzi P. Girotto V. Legrenzi M. S. Caverni J. P. (1999). Naive probability: a mental model theory of extensional reasoning. Psychol. Rev. 106, 62–88. 10.1037/0033-295X.106.1.6210197363
13. Johnson E. D. Tubau E. (2015). Comprehension and computation in Bayesian problem solving. Front. Psychol. 6:938. 10.3389/fpsyg.2015.00938
14. Kahneman D. Tversky A. (1973). On the psychology of prediction. Psychol. Rev. 80, 237. 10.1037/h0034747
15. Kahneman D. Tversky A. (1974). Subjective probability: a judgment of representativeness, in The Concept of Probability in Psychological Experiments, ed Staël Von Holstein C.-A. S. (Dordrecht: Springer), 25–48.
16. Kintsch W. (1988). The role of knowledge in discourse comprehension: a construction-integration model. Psychol. Rev. 95, 163. 10.1037/0033-295X.95.2.1633375398
17. Kintsch W. Greeno J. G. (1985). Understanding and solving word arithmetic problems. Psychol. Rev. 92, 109. 10.1037/0033-295X.92.1.1093983303
18. Kleiter G. D. (1994). Natural sampling: rationality without base rates, in Contributions to Mathematical Psychology, Psychometrics, and Methodology, eds Fischer G. Laming D. (New York, NY: Springer), 375–388. 10.1007/978-1-4612-4308-3_27
19. Lesage E. Navarrete G. De Neys W. (2013). Evolutionary modules and Bayesian facilitation: the role of general cognitive resources. Think. Reason. 19, 27–53. 10.1080/13546783.2012.713177
20. Mandel D. R. (2008). Violations of coherence in subjective probability: a representational and assessment processes account. Cognition 106, 130–156. 10.1016/j.cognition.2007.01.00117300773
21. Mandel D. R. (2014). Visual representation of rational belief revision: another look at the Sleeping Beauty problem. Front. Psychol. 5:1232. 10.3389/fpsyg.2014.0123225400609
22. Mandel D. R. (2015). Instruction in information structuring improves Bayesian judgment in intelligence analysts. Front. Psychol. 6:387. 10.3389/fpsyg.2015.0038725904882
23. Metcalfe J. Wiebe D. (1987). Intuition in insight and noninsight problem solving. Mem. Cogn. 15, 238–246. 10.3758/BF031977223600264
24. Navarrete G. Correia R. Froimovitch D. (2014). Communicating risk in prenatal screening: the consequences of Bayesian misapprehension. Front. Psychol. 5:1272. 10.3389/fpsyg.2014.0127225414688
25. Pouget A. Beck J. M. Ma W. J. Latham P. E. (2013). Probabilistic brains: knowns and unknowns. Nat. Neurosci. 16, 1170–1178. 10.1038/nn.349523955561
26. Sedlmeier P. Gigerenzer G. (2001). Teaching Bayesian reasoning in less than two hours. J. Exp. Psychol. Gen. 130, 380–400. 10.1037/0096-3445.130.3.38011561916
27. Sirota M. Juanchich M. (2011). Role of numeracy and cognitive reflection in Bayesian reasoning with natural frequencies. Stud. Psychol. 53, 151–161.
28. Sirota M. Juanchich M. Hagmayer Y. (2014a). Ecological rationality or nested sets? Individual differences in cognitive processing predict Bayesian reasoning. Psychon. Bull. Rev. 21, 198–204. 10.3758/s13423-013-0464-623794254
29. Sirota M. Kostovičová L. Juanchich M. (2014b). The effect of iconicity of visual displays on statistical reasoning: evidence in favor of the null hypothesis. Psychon. Bull. Rev. 21, 961–968. 10.3758/s13423-013-0555-424307248
30. Sirota M. Kostovičová L. Vallee-Tourangeau F. (2015a). How to train your Bayesian: A problem-representation transfer rather than a format-representation shift explains training effects. Q. J. Exp. Psychol. 68, 1–9. 10.1080/17470218.2014.97242025283723
31. Sirota M. Kostovičová L. Vallée-Tourangeau F. (2015b). Now you Bayes, now you don't: effects of set-problem and frequency-format mental representations on statistical reasoning. Psychon. Bull. Rev. [Epub ahead of print]. 10.3758/s13423-015-0810-y25711182
32. Téglás E. Vul E. Girotto V. Gonzalez M. Tenenbaum J. B. Bonatti L. L. (2011). Pure reasoning in 12-month-old infants as probabilistic inference. Science 332, 1054–1059. 10.1126/science.119640421617069
33. Teigen K. H. Keren G. (2007). Waiting for the bus: when base-rates refuse to be neglected. Cognition 103, 337–357. 10.1016/j.cognition.2006.03.00716723123
34. Vallée-Tourangeau G. Sirota M. Juanchich M. Vallée-Tourangeau F. (2015). Beyond getting the numbers right: what does it mean to be a “successful” Bayesian reasoner? Front. Psychol. 6:712. 10.3389/fpsyg.2015.0071226082734