1. Causal inference in cue combination Konrad Kording www.koerding.com

2. Modeling: Where do cues come from? Generate

3. Traditional Bayesian model Infer Alais & Burr 04, Battaglia et al 03, Knill & Pouget 04, Ernst & Banks 02, Gahramani 95, van Beers et al, etc

4. Visual Auditory combination (Ventriloquist effect) Both cues

5. What would happen now?

6. Do we believe this kind of model? Assumes there is one and only one cause!

7. Alternative model or Kording, Beierholm, Ma, Quartz, Tenenbaum, Shams, 2007

8. Calculate probability of model Using Bayes rule:

9. Independent causes: where is the auditory stimulus Audio Visual Best estimate

10. Common cause: where is the auditory stimulus Audio Visual Combined Best estimate

11. Mean squared error estimate Audio Visual Combine Best estimate Remark: Knill uses virtually identical math

12. Experimental test Wallace et al 2005 Hairston et al 2004 Button: common cause or two

13. Measured gain Wallace et al 2005 Hairston et al 2004 Data Kording et alSato et al, in press

14. How can the gain be negative?

15. Predicting the variance Worse prediction if we assume model selection

16. Take home message Uncertainty about causal structure Bayesian framework is modular Easy to extend Causality problems occur in many domains

17. Acknowledgements Ulrik Beierholm Wei Ji Ma Steven Quartz Joshua Tenenbaum Ladan Shams Kunlin Wei