The PEST Convergence Procedure

The experiments described in Chapter 4 and in Appendix B used successive approximations to find the inertial amplitude at which participants crossed over between inertial and visual dominance (i.e., between having their perception of self-motion determined by inertial and visual cues). The inertial amplitude adjustments after each trial were made following the Parameter Estimation by Sequential Testing (PEST) procedure [99], which is a simple convergence algorithm developed for psychophysics experiments.

The PEST procedure obeys the following four rules:

1.

On every reversal of step direction, halve the step size.

2.

The second step in a given direction, if called for, is the same size as the first.

3.

The fourth and subsequent steps in a given direction are each double their predecessor (except that... large steps may be disturbing to a human observer and an upper limit on permissible step size may be needed).

4.

Whether a third successive step in a given direction is the same as or double the second depends on the sequence of steps leading to the most recent reversal. If the step immediately preceding that reversal resulted from a doubling, then the third step is not doubled, while if the step leading to the most recent reversal was not the result of a doubling, then this third step is double the second.

The PEST procedure ends when the step size drops to a pre-determined amount. The estimate is the level called for by the last step.

In practice, the fact that each trial in the visual-inertial nulling experiments required a few minutes forced a fairly rapid convergence, which in turn required a final step size sufficient to allow for a rapid convergence (this was taken to be an amplitude of 5$^{\circ}$/sec in the experiment reported in Chapter 4, or 3$^{\circ}$/sec if the two conditions run in parallel would otherwise be tied). Hence, the subtleties of rules 3 and 4, above, rarely came into play.

Human Interface Technology Lab