1. Decision Making Theories in Neuroscience Alexander Vostroknutov October 2008

2. Choice in the brain From Sugrue, Corrado and Newsome Nature Neuroscience, 2005, Vol 6, May 2005 Weak motion – chance performance; strong motion – optimal performance “Decision making” area should aggregate noisy signal and suggest the decision

3. Monkey brain LIP area – part of visuo-motor pathway Its activation is covaried with choice AND modulated by movement strength during motion not purely sensory (mistake trials); not purely decision oriented (modulated by strength of movement) LIP is where “deliberation” takes place From Sugrue, Corrado and Newsome Nature Neuroscience, 2005, Vol 6, May 2005

4. Three processes of choice From Bogacz, 2007, TRENDS in Cog. Sci., Vol 11(3) Neurons in Visual cortex provide evidence for alternatives (noisy) Intergation takes place (in LIP), removes noise The choice is made once certain criterion is reached (confidence level)

5. Optimal decision making This procedure can be formulated as a statistical problem Statistical test to optimize decision making It can be tested whether the brain implements optimal test (evolution) Links optimal tests with neurobiology (basal ganglia) and behavior (speed-accuracy tradeoff)

6. Optimality criterion Sequential Probability Ratio Test (Wald) A procedure to distinguish two distributions H 0 : p=p 0 and H 1 : p= p 1 given a sequence of observations {y n } Sum log-likelihood ratios of incoming data and stop once threshold is reached: S n = S n-1 + log(p 0 (y n )/p 1 (y n )) Given fixed accuracy, SPRT requires the least expected number of observations Animals would be interested in implementing SPRT: minimizes reaction time

7. Diffusion model (2 alternatives) Is there simple way to implement SPRT? Integrator accumulates evidence about the difference of inputs I n = I n-1 + A n - B n Once threshold is reached (|I n | > 5), choose A or B Input A Input B A - B Integrator (I) I > 5: choose A I < -5: choose B

8. Diffusion Model is optimal Continuous limit of SPRT can be described by Wiener process with drift (Bogacz et al, 2006) dy = (m A -m B )dt + cdW Choose once threshold is reached (assumed: A and B are normal, same variance) m A is mean of alternative A This is exactly Diffusion Model! Thus DM implements SPRT Given fixed accuracy, DM has the best reaction time (important for animals) Simple to implement in neural networks (requires only addition and subtraction)

9. Connection to the brain How can we test whether something like diffusion model is implemented in the brain? We have evidence (LIP) of the presence of intergators We need evidence for the presence of “criterion satisfying” region Good candidate: basal ganglia They resolve competition between cortical and sub- cortical systems that want expression Inhibit all actions; the “winning system” is allowed to express itself through disinhibition

10. Diffusion Model (n alternatives) DMn implements optimal MULTI SPRT Uses exponentiation Neurons which exponentiate are rare Good evidence for Diffusion Model Input A1 Input A2 A1 – ln[exp(A2)+exp(A3)] choose whenever any of these is higher than threshold Input A3 A2 – ln[exp(A1)+exp(A3)] A3 – ln[exp(A1)+exp(A2)] I1 I2 I3

11. Evidence Bogacz, 2007 reports studies that demonstrate that neurons in subthalamic nucleus (STN) perform exponentiation STN targets output nuclei of basal ganglia, that “decide” on which system to allow to act

12. More evidence

13. Diffusion Model and Economics Difficult to perceive the difference between n and n+1 grains of sugar Non-transitivity of indifference Beyond the scope of classical preferences model DM suggests a simple and natural way to model this

14. Diffusion Model and Economics Violation of Weak Axiom of Revealed Preference (recent evidence: Kroll, Vogt, 08) Again, DM with 3 alternatives gives simple explanation Prospect Theory, Regret do not account for this Can save the “existence” of underlying preferences Additional prediction of DM: smaller reaction time in second case quality price A B C A, B available: A B 80%20% A, B, C available: A B 50%

15. Diffusion Model and Economics Allais paradox: violation of Expected Utility maximization In choice between S1 and R1: information about S1 is accumulated much faster than about R1: high chance of hitting S1 threshold In choice between S2 and R2: information accumulates at comparable speeds, R2 is almost like S2, only with $5 instead of $1, high chance to hit R2 threshold first Additional prediction of DM: reaction time in S1-R1 choice is shorter than in S2-R2 No need to get rid of Expected Utility S1 = $1 R1 = ($5, 0.1; $1, 0.89; $0, 0.01) S2 = ($1, 0.11; $0, 0.89) R2 = ($5, 0.1; $0, 0. 9) EU maximizer prefers S’s or R’s Evidence: S1 > R1 and R2 > S2

16. Conclusion It seems like there is evidence that Diffusion Model is implemented in the brain Sensory inputs are integrated in the respective pre-motor regions (LIP) Basal ganglia check which option should be chosen by comparing competing “integrators” to the threshold Important for economists. DM explains with ease many different phenomena