Stochastic Integration Modeling Toolbox
A MATLAB toolbox for modeling decision processes based on stochastic integration. In addition to standard drift-diffusion models it also supports leaky integration, 2- and 3-dimensional stochastic processes, second guesses, etc.
Some additional information (e.g., publications in which the toolbox has been used) can be found here: https://www.peractionlab.org/software?id=5
The individual functions provide more information about what they do and their input and output arguments.
Content of Contents.m:
% Stochastic Integration Modeling Toolbox.
% Version 2.9 (29-Mar-2020)
% J. Ditterich, Center for Neuroscience, Univ. of California, Davis
%
% First passage time problems.
% msprt_fb_3d_3b_sim - Feedback implementation of MSPRT, 3 integrators, 3 boundaries, simulation.
% ou_1d_1b_mar - 1D Ornstein-Uhlenbeck process, range limit, 1 boundary, Markov chain approximation.
% ou_1d_2b_mar - 1D Ornstein-Uhlenbeck process, 2 boundaries, Markov chain approximation.
% ou_1d_2b_num - 1D Ornstein-Uhlenbeck process, 2 boundaries, numerical solution.
% ou_2d_2b_mar - 2D Ornstein-Uhlenbeck process, 2 boundaries, Markov chain approximation.
% ou_2d_2b_sim - 2D Ornstein-Uhlenbeck process, 2 boundaries, simulation.
% ou_2d_3b_mar - 2D Ornstein-Uhlenbeck process, 3 boundaries, Markov chain approximation.
% ou_2d_3b_sim - 2D Ornstein-Uhlenbeck process, 3 boundaries, simulation.
% ou_2d_3b_sim_sc - 2D Ornstein-Uhlenbeck process, 3 boundaries, simulation, also reports second choices (second guesses).
% ou_2d_3b_sim_sc_add_time - 2D Ornstein-Uhlenbeck process, 3 boundaries, simulation, also reports second choices (second guesses) based on the states of the integrators a fixed amount of time after the threshold crossing.
% ou_2d_3b_two_cross_sim - 2D Ornstein-Uhlenbeck prosess, 3 boundaries, simulation, the process waits for a second threshold crossing, which is then reported as the decision time.
% ou_2d_3b_1d_2b_sim_sc - 2D Ornstein-Uhlenbeck process, 3 boundaries, simulation; once the first threshold crossing occurs, a new 1D OU process with two boundaries is started to decide between the two remaining options as a second choice; the decision time is given by the second threshold crossing.
% ou_2d_3b_1d_fixed_time_sim_sc - 2D Ornstein-Uhlenbeck process, 3 boundaries, simulation; once the first threshold crossing occurs, a new 1D OU process is started to decide between the two remaining options as a second choice; the decision is made after a fixed amount of time based on the sign of the current state of the process.
% ou_3d_3b_sim - 3D Ornstein-Uhlenbeck process, 3 boundaries, simulation.
% ou_3d_inh_fb_3b_sim - 3D Ornstein-Uhlenbeck process with inhibitory feedback, 3 boundaries, simulation.
% ou_dropout_1d_2b_mar - 1D Ornstein-Uhlenbeck process, dropout rate, 2 boundaries, Markov chain approximation.
% ou_dropout_vd_1d_2b_mar - 1D Ornstein-Uhlenbeck process, variable drift, dropout rate, 2 boundaries, Markov chain approximation.
% ou_timelim_1d_2b_mar - 1D Ornstein-Uhlenbeck process, time limit, 2 boundaries, Markov chain approximation.
% ou_vd_1d_2b_num - 1D Ornstein-Uhlenbeck process, variable drift, 2 boundaries, numerical solution.
% probsum_1d_2b_dis - probability summation model, 1D normal process, 2 thresholds, discrete solution.
% probsum_uncor_2d_2b_dis - probability summation model, 2 normal processes, uncorrelated noise, discrete solution.
% probsum_vs_1d_2b_dis - probability summation model, 1D normal process, variable mean of the signal, 2 thresholds, discrete solution.
% wiener_1d_1b_lin_ana - 1D Wiener process, 1 linear boundary, analytical solution.
% wiener_1d_2b_num - 1D Wiener process, 2 boundaries, numerical solution.
% wiener_vb_1d_2b_num - 1D Wiener process, 2 variable boundaries, numerical solution.
% wiener_vd_1d_2b_num - 1D Wiener process, variable drift, 2 boundaries, numerical solution.
% wiener_vi_1d_2b_num - 1D Wiener process, variable initial value, 2 boundaries, numerical solution.
%
% Probability density functions (pdf).
% normpdf2 - Bivariate normal (Gaussian) density.
%
% Trajectories.
% traj_aet_ou_1d_2b_del_sim - 1D Ornstein-Uhlenbeck process, 2 boundaries, variable delays between start of trial and integration onset and between first boundary crossing and end of trial, simulation, aligned with end of trial.
% traj_aet_ou_1d_2b_lim_del_sim - 1D Ornstein-Uhlenbeck process, range limit, 2 boundaries, variable delays between start of trial and integration onset and between first boundary crossing and end of trial, simulation, aligned with end of trial.
% traj_aet_ou_2d_2b_del_sim - 2D Ornstein-Uhlenbeck process, 2 boundaries, variable delays between start of trial and integration onset and between first boundary crossing and end of trial, simulation, aligned with end of trial.
% traj_aet_ou_vd_1d_2b_del_sim - 1D Ornstein-Uhlenbeck process, variable drift, 2 boundaries, variable delays between start of trial and integration onset and between first boundary crossing and end of trial, simulation, aligned with end of trial.
% traj_aet_ou_vd_2d_2b_del_sim - 2D Ornstein-Uhlenbeck process, variable drift, 2 boundaries, variable delays between start of trial and integration onset and between first boundary crossing and end of trial, simulation, aligned with end of trial.
% traj_afp_msprt_fb_3d_3b_sim - Feedback implementation of MSPRT, 3 integrators, 3 boundaries, simulation, aligned with respect to first passage.
% traj_afp_ou_1d_2b_sim - 1D Ornstein-Uhlenbeck process, 2 boundaries, simulation, aligned with respect to first passage.
% traj_afp_ou_2d_2b_sim - 2D Ornstein-Uhlenbeck process, 2 boundaries, simulation, aligned with respect to first passage.
% traj_afp_ou_2d_3b_sim - 2D Ornstein-Uhlenbeck process, 3 boundaries, simulation, aligned with respect to first passage.
% traj_afp_ou_3d_inh_fb_3b_sim - 3D Ornstein-Uhlenbeck process with (or also without) inhibitory feedback, 3 boundaries, simulation, aligned with respect to first passage.
% traj_afp_ou_vd_1d_2b_sim - 1D Ornstein-Uhlenbeck process, variable drift, 2 boundaries, simulation, aligned with respect to first passage.
% traj_msprt_fb_3d_3b_sim - Feedback implementation of MSPRT, 3 integrators, 3 boundaries, simulation, aligned with respect to t=0.
% traj_ou_1d_2b_del_sim - 1D Ornstein-Uhlenbeck process, 2 boundaries, variable delays between start of trial and integration onset and between first boundary crossing and end of trial, simulation, aligned with start of trial.
% traj_ou_1d_2b_lim_del_sim - 1D Ornstein-Uhlenbeck process, range limit, 2 boundaries, variable delays between start of trial and integration onset and between first boundary crossing and end of trial, simulation, aligned with start of trial.
% traj_ou_2d_2b_del_sim - 2D Ornstein-Uhlenbeck process, 2 boundaries, variable delays between start of trial and integration onset and between first boundary crossing and end of trial, simulation, aligned with start of trial.
% traj_ou_1d_2b_sim - 1D Ornstein-Uhlenbeck process, 2 boundaries, simulation, aligned with respect to t=0.
% traj_ou_2d_2b_sim - 2D Ornstein-Uhlenbeck process, 2 boundaries, simulation, aligned with respect to t=0.
% traj_ou_2d_3b_sim - 2D Ornstein-Uhlenbeck process, 3 boundaries, simulation, aligned with respect to t=0.
% traj_ou_3d_inh_fb_3b_sim - 3D Ornstein-Uhlenbeck process with (or also without) inhibitory feedback, 3 boundaries, simulation, aligned with respect to t=0.
% traj_ou_vd_1d_2b_del_sim - 1D Ornstein-Uhlenbeck process, variable drift, 2 boundaries, variable delays between start of trial and integration onset and between first boundary crossing and end of trial, simulation, aligned with start of trial.
% traj_ou_vd_2d_2b_del_sim - 2D Ornstein-Uhlenbeck process, variable drift, 2 boundaries, variable delays between start of trial and integration onset and between first boundary crossing and end of trial, simulation, aligned with start of trial.
% traj_ou_vd_1d_2b_sim - 1D Ornstein-Uhlenbeck process, variable drift, 2 boundaries, simulation, aligned with respect to t=0.
%
% Comments:
% The analytical solution is the fastest and most accurate solution.
% The numerical solution of the OU process doesn't accept 0 for the leakage of the integrator.
% This is why there is a separate function for the Wiener process. The temporal resolution
% doesn't seem to be very critical. I haven't seen any big systematic errors.
% The Markov chain approximation should return results, which are identical to the numerical
% solution, if the chosen temporal and spatial resolutions are high enough. Apparently,
% they also have to match. The distributions are too flat when a too high spatial resolution is chosen.
% This is why I have built a heuristic method for automatically choosing an optimal number of states
% into the functions.