ream - Density, Distribution, and Sampling Functions for Evidence
Accumulation Models
Calculate the probability density functions (PDFs) for two
threshold evidence accumulation models (EAMs). These are
defined using the following Stochastic Differential Equation
(SDE), dx(t) = v(x(t),t)*dt+D(x(t),t)*dW, where x(t) is the
accumulated evidence at time t, v(x(t),t) is the drift rate,
D(x(t),t) is the noise scale, and W is the standard Wiener
process. The boundary conditions of this process are the upper
and lower decision thresholds, represented by b_u(t) and
b_l(t), respectively. Upper threshold b_u(t) > 0, while lower
threshold b_l(t) < 0. The initial condition of this process
x(0) = z where b_l(t) < z < b_u(t). We represent this as the
relative start point w = z/(b_u(0)-b_l(0)), defined as a ratio
of the initial threshold location. This package generates the
PDF using the same approach as the 'python' package it is based
upon, 'PyBEAM' by Murrow and Holmes (2023)
<doi:10.3758/s13428-023-02162-w>. First, it converts the SDE
model into the forwards Fokker-Planck equation dp(x,t)/dt =
d(v(x,t)*p(x,t))/dt-0.5*d^2(D(x,t)^2*p(x,t))/dx^2, then solves
this equation using the Crank-Nicolson method to determine
p(x,t). Finally, it calculates the flux at the decision
thresholds, f_i(t) = 0.5*d(D(x,t)^2*p(x,t))/dx evaluated at x =
b_i(t), where i is the relevant decision threshold, either
upper (i = u) or lower (i = l). The flux at each thresholds
f_i(t) is the PDF for each threshold, specifically its PDF. We
discuss further details of this approach in this package and
'PyBEAM' publications. Additionally, one can calculate the
cumulative distribution functions of and sampling from the
EAMs.
