PAL_AMPM_Demo: Psi adaptive method (Kontsevich & Tyler, 1999, Vision Research, 39, 2729-2737). We
(Prins, 2013; www.journalofvision.org/content/13/7/3) modified the Psi method to allow any of the four parameters of the PF to be treated as either a parameter of primary interest
whose estimation should be optimized, a nuisance parameter whose estimation should subserve optimal estimation of parameters
of primary interest or as a fixed parameter. We call this the Psi-marginal method. In the simulation shown in the figure,
threshold and slope were set as parameters of primary interest, lapse rate was set as nuisance parameter and guess rate was
fixed. Shown in the figure are a plot of the posterior, a plot of proportion correct and stimulus placement (area of symbol
proportional to N), Bayesian fit (blue) and generating function (black), and a plot showing trial-to-trial stimulus placement.
The blue line in the latter shows the trial-by-trial Bayesian estimate of threshold. Note that the PAL_AMPM routines will
still run the original Psi method if so instructed (as a matter of fact, this is the default setting). See PAL_AMPM_Basic_Demo
for a minimal-code, no frills example of basic psi-method.