Functional Adaptive Sequential Testing

Abstract

The study of cognition, perception, and behavior often requires the estimation of thresholds as a function of continuous independent variables (e.g., contrast threshold as a function of spatial frequency, subjective value as a function of reward delay, tracking speed as a function of the number of objects tracked). Unidimensional adaptive testing methods make estimation of single threshold values faster and more efficient, but substantial efficiency can be further gained by taking into account the relationship between thresholds at different values of an independent variable. Here we present a generic method -functional adaptive sequential testing (FAST) -for estimating thresholds as a function of another variable. This method allows efficient estimation of parameters relating an independent variable (e.g., stimulus spatial frequency; or reward delay) to the measured threshold along a stimulus strength dimension (e.g., contrast; or present monetary value). We formally describe the FAST algorithm and introduce a Matlab toolbox implementation thereof; we then evaluate several possible sampling and estimation algorithms for such two-dimensional functions. Our results demonstrate that efficiency can be substantially increased by considering the functional relationship between thresholds at different values of the independent variable of interest.

Cardiac Signals Are Independently Associated with Temporal Discounting and Time Perception

“…Participants made a series of choices between immediately available amounts ranging from $20 to $30, and delayed (1, 2, 4, 6, 9 and 12 months) amounts that were chosen based on an algorithm constrained to estimate a threshold function that followed Equation 1 (Vul et al, 2010), as well as a softmax psychometric link function to map subjective values into choice probabilities (Miedl et al, 2012). …”

Different effects of aging and gender on the temporal resolution in attentional tracking

“…Each condition was tested at four speed levels equally spaced over the range of speeds indicated above, for a minimum of eight trials per speed. After these 32 trials, a Bayesian adaptive procedure (Vul, Bergsma, & MacLeod, 2010) took over control of the speed levels and continued presenting speeds chosen to reduce the uncertainty on the estimated speed threshold, taking into account previously accumulated data. The range of speeds allowed by the algorithm was much wider (0.01 to 2 rps) to account for the possibility that the manually chosen speed range was not appropriate.…”

Bayesian Inference of Two-Dimensional Contrast Sensitivity Function from Data Obtained with Classical One-Dimensional Algorithms Is Efficient

“…As shown in Figure 1A (blue rectangle), these methods select stimulus strength according to previous responses of the subject, and are referred to as adaptive psychometric methods, or in psychology, adaptive optimization designs (Watson and Pelli, 1983; Leek et al, 1992; Leek, 2001; Cavagnaro et al, 2010; Vul et al, 2010; Myung et al, 2013). Some of the adaptive methods of psychophysics use 1-D non-parametric samplings, which select the next stimulus based on the subject's responses to past trials (Levitt, 1971; Kaernbach, 1991), and the final psychophysical parameters of interest are obtained either by fitting the data (Treutwein and Strasburger, 1999), or simply by averaging the data collected (Levitt, 1971).…”

“…These novel methods search the 2-D stimulus space for the next most informative stimulus based on a parametric model, thereby facilitating more efficient estimation of the threshold contour than more common procedures (Kujala and Lukka, 2006; Lesmes et al, 2006, 2010; Hou et al, 2010; Vul et al, 2010). The more common procedures, such as QUEST, Ψ, and staircase, map responses to one dimension (the contrast) of the stimulus only, and require repetitive measurements along the other dimension (the SF), a process that seems inefficient.…”