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Teaching Bayesian Method

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Made and presented for the course Behavioral Economics at the Viadrina University, winter term 2012/2013. …

Made and presented for the course Behavioral Economics at the Viadrina University, winter term 2012/2013.

Paper presented: Teaching Bayesian Reasoning in Less Than Two Hours by Peter Sedlmeier and Gerd Gigerenzer

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Transcript

  • 1. Behavioral Economics – Decision Support Teaching Bayesian Reasoning Birte Gröger
  • 2. AgendaTeaching Bayesian Method in Less Than Two Hours1. Bayesian Method/Inference2. Information Formats3. Teaching Methods4. Training Effectiveness5. Studies and Experiments6. Results and Conclusion
  • 3. Bayesian Method/InferenceBayes Rule in Theory• Named after Thomas Bayes, published 1763• Describing conditional probabilities (A|B) given another event (B)• Update beliefs in light of new evidence• Transfer prior probability P(A) into posterior probability
  • 4. Bayesian Method/InferenceThe Problems• Studies show: Bayesian inference is alien to human inference – Neglect or overweighing of base rates (conservatism) – Cognitive illusions = systematic deviations• Studies attempting to teach Bayesian reasoning with no success
  • 5. Information FormatsProbability vs. Natural Frequencies• Cognitive algorithms work on information  information needs representation format• Mathematical probability and percentage = recent developments• Input format for human minds: natural frequencies
  • 6. Information FormatsCrucial Theoretical Results1. Bayesian computations = simpler, when information represented in natural frequencies2. Natural frequencies = corresponding to the information format encountered throughout most of our evolutionary development
  • 7. Information FormatsExample Comparison – Mammography Problem The probability that a woman Ten of every 1,000 women who who undergoes a undergo a mammography have mammography will have breast breast cancer. cancer is 1%. Eight of every 10 women with If a woman undergoing a breast cancer who undergo a mammography has breast mammography will test cancer, the probability that she positive. will test positive is 80%. Ninety-nine of every 990 If a woman undergoing a women without breast cancer mammography does not have who undergo a mammography cancer, the probability that she will test positive. will test positive is 10%.
  • 8. Teaching MethodsOverview• Teaching: showing people how to construct frequency representations• Mechanism: tutorial, practices, feedback Rule Training Frequency Grid Frequency Tree
  • 9. Teaching MethodsRule Training• Explanation how to extract numerical information by computer system• Translation of base-rate information in components of Bayes’ formula• Insert probabilities• Calculation of result
  • 10. Teaching MethodsRule Training
  • 11. Teaching MethodsFrequency Grid• Representation cases by squares• Indicate squares according to base rates – Shaded percentage of population – Circled pluses (+) for hit rate on shaded squares – Circled pluses for false alarm rate on non-shaded squares• Calculate ratio: pluses in shaded squares divided by all circled pluses
  • 12. Teaching MethodsFrequency Grid
  • 13. Teaching MethodsFrequency Tree• Constructing reference class and breaking-down into four subclasses• System: explanation how to obtain frequencies• Inserting into corresponding nodes• Calculation by dividing number of true positive by sum of all positives
  • 14. Teaching MethodsFrequency Tree
  • 15. Training EffectivenessEvaluation• Explanation of program and instructions• Answer format/solution as a formula• Systematically varied order of problems• Scoring criteria strict liberal • Match exact value • Match value +/- 5% • Obscure fact that • Increased participants created possibility including sound but inexact non-Bayesian response algorithms
  • 16. Training EffectivenessMeasures• Comparing solution rates At baseline Immediately About a week 1 to 3 months (w/o training after training after training after training – Test 1) (Test 2) (Test 3) (Test 4)• Traditional: steep decay curve• Expectation now: decay not as quick with frequency training
  • 17. Studies and ExperimentsStructure Study 1a Study 1b Study 2• 62 University of • 56 Free University of • 72 University of Chicago students Berlin students Munich students• 4 groups in 3 training • Prevent high attrition • Issue of used graphical methods and one w/o rates with later aids in frequency training as control payments and bonus conditions• All 4 tests with 10 based on results • Longer period of time problems each • 2 groups with the between Test 3 and 4• Old and new problems different frequency • Use also graphical aid• High attrition rates trainings for rule training  (increasing # of • Reduced number of probability tree participants) problems • No attrition
  • 18. Studies and ExperimentsResults – Study 1a • Substantial improvement in Bayesian reasoning • High level of transfers: average performance in new problems almost as god as in old problems • Increase in median number of inferences in the frequency grid condition
  • 19. Studies and ExperimentsResults – Studies 1b and 2 Study 1b Study 2
  • 20. ConclusionTeaching Bayesian Reasoning is possible• Prove that Bayesian computations are simpler using natural frequencies• Environmental change  illusions• Idea: teach people to represent information according to cognitive algorithms• Translation in representation format = major tool for helping to attain insight• High immediate effects, better transfer to other problems and long-term stability