Transcript cog2005 5288

A Generative Model of Human
Performance on an Optimal Stopping
Problem
Michael Lee
Department of Psychology
University of Adelaide
with thanks to Peter Grünwald, Dan Navarro, Josh Tenenbaum, Chloë
Mount, Jay Myung, Woojae Kim, Doug Vickers, Matt Welsh, Tess
Gregory, Robyn Whibley, Gary Ewing & Michael Paradowski
79.69
[1/5]
34.40
[2/5]
72.55
[3/5]
95.77
[4/5]
24.26
[5/5]
Why Study This
Problem?
More Controlled than Knowledge-Rich
More Realistic than Knowledge-Lean
Complements other Optimisation Problems
Three Optimal Decisions
Empirical Data
50 Subjects on 40 Five-Point Problems
Individual Diffs in Accuracy & Confidence
No Evidence of Learning
Other Values Don’t Seem to Matter
Value in Position Matters
Being Currently Maximal Really Matters
A Generative
Model
A Generative Process for Threshold Models
Fix
Fix
Down
Same
Start
Down
Down
New
Two Regularities Generate 14 Models
FFF DDD FFD
FDF
DFF FDD FDN
DFD DFN DDF DNF DND DDN DNN
Parameter Variation Distributes over Decisions
Problem 20
FFF
80 Decision Sequences Indexed by FFF Model
Generative Framework
N
Generative
Process


F
D
pM  
Model
Family
Indexed
Sequences
pI M , 
0
Indexed Sequences
3121
Indexed Decision Sequences and Data
Indexed
Sequences
Data
Sequences
pI M , 
0
Indexed Sequences
0
Data Sequences
3121
pD M , 
540
Making Inferences About Generative Process
N
Generative
Process
p D 

F
D
pD M 
Model
Family
Data
Sequences
D
0
Data Sequences
540
Five Fun Steps to Entropification
One
Two
Three
Four
Five
pD M , I , w 
e  wf 0 / 1  D , I 

k
x1 1
 x 1 e
k
 wf 0 / 1  D , x1 ,, xn 
n  40
n
e  wm
pD M , I , w 
n n
x  wx




k

1
e
 x 0  x 
 
p*  max ( I ,w) pD M , I , w
MDL   ln p*  ln I
pD M   e MDL
k 5
f 0 /1 D, Y   m
The Rest of the Inference
N
p D  pD   p 
p   1
pD    x1 pD M x , pM x  

14
pM FFD     F2 D


F
D

Entropification
p DM
   F , D , N 
D
0
Data Sequences
540
Individual Results
for 4 Subjects
Subject 18: Generative Process Level
Subject 18 Model Family Level
Building Predictive Models
pM i D  
pD M i  pM i 

14
j 1


p D M j pM j 
Average All
Best All
Best Single
Subject 18: Posterior Predictive
Subject 18: Data & Predictive Model Summary
Subject 21: Generative Process Level
Subject 21: Model Family Level
Subject 21: Posterior Predictive
Subject 21: Data & Predictive Model Summary
Subject 11: Generative Process Level
Subject 11: Model Family Level
Subject 11: Posterior Predictive
Subject 11: Data & Predictive Model Summary
Subject 1: Generative Process Level
Subject 1 Model Family Level
Subject 1: Posterior Predictive
Subject 1: Data & Predictive Model Summary
Overall
Evaluation
Individual Differences at Generative Level
Cross Validation
Individual Differences in Predictive Models
Current Work
Same 50 Subjects on 40 Ten-Point Problems
Same 50 Subjects on 40 Twenty-Point Problems
Individuals Choose Early
Group Decision-Making
Questions?