A Bayesian model of capacity across time

In this work we derive and illustrate a Bayesian time series model of the capacity coefficient to investigate processing efficiency across time. The workload capacity coefficient is a well-established measure from systems factorial technology that allows researchers to quantify a participant's multisource information processing efficiency. In most applications of the capacity coefficient, the analyses assume stationary performance across time. However, in many contexts participants' performance varies across time (e.g., vigilance decrements, training). This variation could be either due to changes in processing each source or the efficiency of combining the sources. A time-varying capacity measure would be valuable in determining the nature of the change over time, but dropping the stationarity assumption results in a severe loss in power. In an attempt to estimate a time-varying capacity coefficient, we developed a measure relying on Bayesian estimation. We used the Weibull distribution to approximately characterize the processing time of each source, with an inverse gamma distribution prior for the scale parameter and a known shape. This provided us a tractable way to update our prior estimate for real-time estimation of capacity. The prior was updated by weighting the observation's contribution to the likelihood by how recently they occurred. Samples from the posterior Weibull estimates were then combined using the appropriate capacity coefficient equation to obtain posterior distributions for the capacity coefficient. We demonstrate the approach with both simulated and human data. We believe the time-varying capacity coefficient will be a valuable tool for measuring cognitive tasks such as adaptive interface design.