A Classical Model of Decision Making: The Drift Diffusion Model of Choice Between Two Alternatives At each time step a small sample of noisy information is obtained; each sample adds to a cumulative relative evidence variable. Mean of the noisy samples is +m for one alternative, –m for the other, with standard deviation s. When a bound is reached, the corresponding choice is made. Alternatively, in ‘time controlled’ or ‘interrogation’ tasks, respond when signal is given, based on the value of the relative evidence variable.

The DDM is an optimal model It achieves the fastest possible decision on average for a given level of accuracy It can be adapted to optimize performance to capture effects of various additional factors: Different prior probabilities of different stimuli Different costs/payoffs for responses to different stimuli Variation in the time between trials…

DDM is consistent with some aspects of Monkey Physiology Data Data are averaged over many different neurons that are associated with intended eye movements to the location of target.

Mazurek, Roitman, Ditterich and Shadlen (2003) variant of DDM

Two Problems with the DDM Easy Accuracy should gradually improve toward ceiling levels as more time is allowed, even for very hard discriminations, but this is not what is observed in human data. Incorrect RT’s are generally slower than correct RT’s, and the DDM/Roitman et al models do not capture this. Prob. Correct Hard Errors Correct Responses RT Coherence

Usher and McClelland (2001) Leaky Competing Accumulator Model Inspired by known neural mechanisms Addresses the process of deciding between two alternatives based on external input (r1 + r2 = 1) with leakage, mutual inhibition, and noise: dx1/dt = r1-k(x1)–bf(x2)+x1 dx2/dt = r2-k(x2)–bf(x1)+x2 f(x) = [x]+

Wong & Wang (2006) ~Usher & McClelland (2001)

Usher and McClelland (2001) Leaky Competing Accumulator Model Inspired by known neural mechanisms Addresses the process of deciding between two alternatives based on external input (r1 + r2 = 1) with leakage, mutual inhibition, and noise: dx1/dt = r1-k(x1)–bf(x2)+x1 dx2/dt = r2-k(x2)–bf(x1)+x2 f(x) = [x]+ r1 r2 X1 X2

Capturing the time-accuracy data

Dynamics of decision in the LCA Final time slice

Support for Inhibition-dominant LCA Early signals more important than late in many experiments. (e.g., Kiani et al). Compatible with reward acting to offset the initial state of the accumulators (Rorie, Newsome et al). It’s also consistent with a subtle feature of the data from a human analog of the Rorie-Newsome experiment.

Kiani, Tanks and Shadlen 2008 Random motion stimuli of different coherences. Stimulus duration follows an exponential distribution. ‘go’ cue can occur at stimulus offset; response must occur within 500 msec to ear reward.

The earlier the pulse, the more it matters (Kiani et al, 2008)

Human Reward Bias Experiment

Design follows Rorie et al Design follows Rorie et al. but there is a variable delay between stimulus onset and go cue. Reward cue signals which alternative is worth 2 points 750 msec before Stimulus onset. Stimulus is a rectangle 1,3, or 5 pixels longer to the Left or Right. Participant must respond within 250 msec of go cue.

Simulation of Inhibition-Dominant LCA using Parameters Derived from 1-D Reduction

Relationship between response speed and choice accuracy

Different levels of activation of correct and incorrect responses in Inhibition-dominant LCA Final time slice errors correct