NSCS 344, Week 3

Assignment 3: Modeling response times

*** Due date: Start of class in Week 4 ***

Part 1: Tweak the model from last week to implement the threshold crossing decision process (3 points)

Part 2: Make a function to implement one decision and have it report the accuracy and decision time (2 points)

[choice, DT] = simulate_ddm(D, f, z);

Part 3: Plot a histogram of response times (2 points)

Part 4: Compute the accuracy and decision time for different values of z (3 points)

z_vals = [2 4 8 16 32];

Part 5: Explore the analytic expressions for accuracy and response time (2 extra credit points)

In a slightly more general version of the drift diffusion model, we make things slightly more abstract and say the model is integrating "evidence" for one option or another. We call this evidence y, and at each time point we assume that the evidence changes by which is given by
where A is the "drift rate" - i.e. the average rate at which evidence comes in in favor of the correct answer - is the time step - c determines the standard deviation of the noise and is a little piece of random noise
where r is sampled from a Gaussian distribution with standard deviation 1 and mean 0.
The decision is made when y crosses a threshold at either (wrong answer) or (correct answer).
[acc, DT] = oneChoice(A, c, z);
For this model, it turns out we can actually compute analytic expressions for the accuracy and the decision time
Finally, we get use the analytic expressions to figure out an optimal threshold value that optimally balances speed and accuracy. To do this we need to figure out what we are trying to optimize. One thing we may want to do (and that humans and animals actually appear to do) is to maximize the rate at which we make correct answers. That is the average accuracy divided by the average time to make a decision - the reward rate (RR):
where denotes a fixed time we can't reduce by changing z - for example, how long it takes to press the button, or how much time passes between trials. For our purposes let's assume that is 1 second.