1. Change Detection in Dynamic Environments Mark Steyvers Scott Brown UC Irvine This work is supported by a grant from the US Air Force Office of Scientific Research (AFOSR grant number FA9550-04-1-0317)

2. Overview Experiments with dynamically changing environments Task: Given a sequence of random numbers, predict the next one Questions: –How do observers detect changes? –What are the individual differences?  “Jumpiness” Bayesian models + simple process models

3. = observed data = prediction Two-dimensional prediction task 11 x 11 button grid Touch screen monitor 1500 trials Self-paced Same sequence for all subjects

4. Sequence Generation (x,y) locations are drawn from two binomial distributions of size 10, and parameters θ At every time step, probability 0.1 of changing θ to a new random value in [0,1] Example sequence: Time θ=.12θ=.95θ=.46θ=.42θ=.92θ=.36

5. Example Sequence

6. = observed sequence Bayesian Solution = prediction Subject 4 – change detection too slow Subject 12 – change detection too fast (sequence from block 5)

7. Tradeoffs Detecting the change too slowly will result in lower accuracy and less variability in predictions than an optimal observer. Detecting the change too quickly will result in false detections, leading to lower accuracy and higher variability in predictions.

8. Average Error vs. Movement = subject

9. “Ideal” observer: inferring the HMM that generated the data... Time12tt+1 Measurements states changepoints Change probability

10. Gibbs sampling Model prediction Inferred changepoint Sample from distribution over change points. Prediction is based on average measurement after last inferred changepoint

11. Average Error vs. Movement = subject

12. A simple process model 1.Make new prediction some fraction α of the way between recent outcome and old prediction α = change proportion 2.Fraction α is a linear function of the error made on last trial 3.Two free parameters: A, B A<B bigger jumps with higher error A=B constant smoothing α 0 1 A B B A

13. Average Error vs. Movement = subject = model

14. One-dimensional Prediction Task 1 2 3 4 5 6 7 8 9 10 11 12 12 Possible Locations Where will next blue square arrive on right side?

15. Average Error vs. Movement = subject = model

16. New Experiments Prediction judgments might not be best measurement for assessing psychological change New experiments: –Inference judgment: what currently is the state of the system?

17. Inference Task (aka filtering)... Time12tt+1 What is the cause of y t+1 ?

18. Tomato Cans Experiment Cans roll out of pipes A, B, C, or D Machine perturbs position of cans (normal noise) At every trial, with probability 0.1, change to a new pipe (uniformly chosen) (real experiment has response buttons and is subject paced) ABCDABCD

19. Tomato Cans Experiment (real experiment has response buttons and is subject paced) ABCDABCD Cans roll out of pipes A, B, C, or D Machine perturbs position of cans (normal noise) At every trial, with probability 0.1, change to a new pipe (uniformly chosen) Curtain obscures sequence of pipes

20. Tasks ABCDABCD Inference: what pipe produced the last can? A, B, C, or D?

21. Cans Experiment 136 subjects 16 blocks of 50 trials Vary change probability across blocks –0.08 –0.16 –0.32 Question: are subjects sensitive to the number of changes?

22. ideal Prob. =.08 Prob. =.16 Prob. =.32

23. Plinko/ Quincunx Experiment Physical version Web version

24. Conclusion Adaptation in non-stationary decision environments Individual differences –Over-reaction: perceiving too much change –Under-reaction: perceiving too little change

25. Do the experiments yourself: http://psiexp.ss.uci.edu

26. Number of Perceived Changes per Subject Low medium high Change Probability (Red line shows ideal number of changes) Subject #1

27. Number of Perceived Changes per Subject 55% of subjects show increasing pattern 45% of subjects show non- increasing pattern Low, medium, high change probability Red line shows ideal number of changes

28. Tasks ABCDABCD Inference: what pipe produced the last can? A, B, C, or D? Prediction: in what region will the next can arrive? 1, 2, 3, or 4? 12341234

29. Cans Experiment 2 63 subjects 12 blocks –6 blocks of 50 trials for inference task –6 blocks of 50 trials for prediction task –Identical trials for inference and prediction

30. INFERENCE PREDICTION Sequence ABCDABCD Trial

31. INFERENCE PREDICTION Sequence Ideal Observer ABCDABCD Trial

32. INFERENCE PREDICTION Sequence Ideal Observer Individual subjects Trial ABCDABCD

33. INFERENCE PREDICTION Sequence Ideal Observer Trial ABCDABCD Individual subjects

34. INFERENCE PREDICTION Sequence Ideal Observer Trial ABCDABCD Individual subjects

35. = Subject ideal INFERENCEPREDICTION

36. ideal INFERENCEPREDICTION = Process model = Subject