Teaching Bayesian Method
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Transcript of Teaching Bayesian Method
Behavioral Economics – Decision Support
Teaching Bayesian Reasoning
Birte Gröger
Agenda
1. Bayesian Method/Inference2. Information Formats3. Teaching Methods4. Training Effectiveness5. Studies and Experiments6. Results and Conclusion
Teaching Bayesian Method in Less Than Two Hours
Bayesian Method/Inference
• 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
Bayes Rule in Theory
Bayesian Method/Inference
• 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
The Problems
Information Formats
• Cognitive algorithms work on information information needs representation format
• Mathematical probability and percentage = recent developments
• Input format for human minds: natural frequencies
Probability vs. Natural Frequencies
Information Formats
1. Bayesian computations = simpler, when information represented in natural frequencies
2. Natural frequencies = corresponding to the information format encountered throughout most of our evolutionary development
Crucial Theoretical Results
Ten of every 1,000 women who undergo a mammography have breast cancer.Eight of every 10 women with breast cancer who undergo a mammography will test positive. Ninety-nine of every 990 women without breast cancer who undergo a mammography will test positive.
The probability that a woman who undergoes a mammography will have breast cancer is 1%.If a woman undergoing a mammography has breast cancer, the probability that she will test positive is 80%.If a woman undergoing a mammography does not have cancer, the probability that she will test positive is 10%.
Information Formats
Example Comparison – Mammography Problem
Teaching Methods
• Teaching: showing people how to construct frequency representations
• Mechanism: tutorial, practices, feedback
Overview
Rule Training Frequency Grid Frequency Tree
Teaching Methods
• Explanation how to extract numerical information by computer system
• Translation of base-rate information in components of Bayes’ formula
• Insert probabilities• Calculation of result
Rule Training
Teaching Methods
Rule Training
Teaching Methods
• 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
Frequency Grid
Teaching Methods
Frequency Grid
Teaching Methods
• 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
Frequency Tree
Teaching Methods
Frequency Tree
Training Effectiveness
• Explanation of program and instructions• Answer format/solution as a formula• Systematically varied order of problems• Scoring criteria
Evaluation
strict
• Match exact value• Obscure fact that
participants created sound but inexact response
liberal
• Match value +/- 5%• Increased possibility
including non-Bayesian algorithms
At baseline (w/o training
– Test 1)
Immediately after training
(Test 2)
About a week after training
(Test 3)
1 to 3 months after training
(Test 4)
Training Effectiveness
Measures
• Comparing solution rates
• Traditional: steep decay curve• Expectation now: decay not as quick with
frequency training
Studies and Experiments
Study 1a
• 62 University of Chicago students
• 4 groups in 3 training methods and one w/o training as control
• All 4 tests with 10 problems each
• Old and new problems
• High attrition rates (increasing # of participants)
Study 1b
• 56 Free University of Berlin students
• Prevent high attrition rates with later payments and bonus based on results
• 2 groups with the different frequency trainings
• Reduced number of problems
• No attrition
Study 2
• 72 University of Munich students
• Issue of used graphical aids in frequency conditions
• Longer period of time between Test 3 and 4
• Use also graphical aid for rule training probability tree
Structure
Studies and Experiments
Results – 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
Studies and Experiments
Results – Studies 1b and 2
Study 1b Study 2
Conclusion
• 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
Teaching Bayesian Reasoning is possible