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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.

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

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• I work in Project Risk Management where we are continually eliciting subjective cost, delay and performance assessments from subject matter experts. My colleagues have never heard of Bayes.
Therefore, I found your slides very illuminating.
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### Teaching Bayesian Method

1. 1. Behavioral Economics – Decision Support Teaching Bayesian Reasoning Birte Gröger
2. 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. 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. 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. 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. 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. 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. 8. Teaching MethodsOverview• Teaching: showing people how to construct frequency representations• Mechanism: tutorial, practices, feedback Rule Training Frequency Grid Frequency Tree
9. 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. 10. Teaching MethodsRule Training
11. 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. 12. Teaching MethodsFrequency Grid
13. 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. 14. Teaching MethodsFrequency Tree
15. 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. 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. 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. 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. 19. Studies and ExperimentsResults – Studies 1b and 2 Study 1b Study 2
20. 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