Boundary specifications for gddm()

The decision boundaries sit at plus and minus B(t), so the separation between them is 2 B(t). All three components below name the separation bs, as wiener() does, and set B(0) = bs / 2, so a boundary separation estimated here is directly comparable with one from the analytic family.

Usage

gddm_bound_constant()

gddm_bound_exponential()

gddm_bound_linear()

Value

A gddm_component.

Details

gddm_bound_constant()

B(t) = bs / 2. Free parameter bs, log link.

gddm_bound_exponential()

B(t) = (bs / 2) exp(-t / tau). Free parameters bs and the time constant tau, both log link. A large tau is a bound that barely collapses, which is why it is where the fit starts. Note PyDDM parameterizes the same bound by a rate, the reciprocal of tau.

gddm_bound_linear()

B(t) = (bs / 2) (1 - kappa t / t_max), where kappa is the fraction of the bound lost by the end of the modeled window. Free parameters bs (log link) and kappa (logit link). The usual spelling of a linear collapse clips the bound at zero, which is a comparison against a parameter and cannot be taped; bounding the fraction below one instead keeps the boundary strictly positive across the window by construction, with no clipping.

Writing your own

A bound term is the value of gddm_bound_term(). Its fn is called on the tape as fn(t, p, ctl) for a plain number t, and returns a list with B, the boundary at that time, and dlogB, its logarithmic derivative B'(t) / B(t). The solver needs the second because the change of variable that pins the walls contributes a -y B'(t)/B(t) term to the drift; supplying it rather than differencing B keeps the rescaled drift exact.

See also

gddm(), gddm-drift, gddm_start_point()