// Display mode
mode(0);
// Display warning for floating point exception
ieee(1);
// Exercise 2.1
//
// This Scilab script accompanies the chapter "Distinguishing between models
// of perceptual decision making" by J. Ditterich in the book "An
// Introduction to Model-Based Cognitive Neuroscience". It demonstrates that
// an integration-to-threshold mechanism can make accurate decisions based
// on a relatively small number of required samples. Please note that this
// script has been optimized for readability, not execution speed.
//
// J. Ditterich, 12/2012
clear;
xdel(winsid());
// Parameters
// Adjust the decision threshold (between 5 and 20) until an accuracy of
// approximately 90% is obtained!
thr = 15; // decision threshold (A)
dist_mean = 1; // mean of normal distribution from which random samples are drawn
dist_sd = 3; // standard deviation of normal distribution from which random samples are drawn
trials = 20000; // number of trials to be simulated
// Let's go...
dt_vec = []; // vector of decision times
num_correct = 0; // number of correct decisions
disp("Starting simulation...");
for i = 1:trials // simulate each trial
cur_sum = 0; // initialize current sum
num_samples = 0; // initialize number of drawn samples
while 1 // loop for sequential sampling
cur_samp = grand(1,1,"nor",dist_mean,dist_sd); // draw a new random number
num_samples = num_samples + 1; // update number of random samples (reflecting decision time)
cur_sum = mtlb_a(cur_sum,cur_samp); // update the sum
if mtlb_logic(cur_sum,">",thr) then // Did we exceed the upper threshold?
dt_vec = [dt_vec,num_samples]; // store the decision time
num_correct = num_correct + 1; // keep track of accuracy
break; // terminate the loop for this trial
end;
if mtlb_logic(cur_sum,"<",-thr) then // Did we cross the lower threshold?
dt_vec = [dt_vec,num_samples]; // store the decision time
break; // terminate the loop for this trial
end;
end;
if pmodulo(i,1000)==0 then
disp(string(i)+" trials completed.");
end;
end;
disp(" ");
disp("Accuracy: "+msprintf("%.1f",(num_correct/trials)*100)+"%");
disp("Average number of evaluated samples: "+msprintf("%.1f",mean(dt_vec,"m")));