A Bayesian classifier for fractal characterization of short behavioral series.

Abstract

Serial tasks in behavioral research often lead to correlated responses, invalidating the application of generalized linear models and leaving the analysis of serial correlations as the only viable option. We present a Bayesian analysis method suitable for classifying even relatively short behavioral series according to their correlation structure. Our classifier consists of three phases. Phase 1 distinguishes between monoand possible multifractal series by modeling the distribution of the increments of the series. To the series labeled as monofractal in Phase 1, classification proceeds in Phase 2 with a Bayesian version of the evenly spaced averaged detrended fluctuation analysis (Bayesian esaDFA). Finally, Phase 3 refines the estimates from the Bayesian esaDFA. We tested our classifier with very short series (viz., 256 points), both simulated and empirical ones. For the simulated series, our classifier revealed to be maximally efficient in distinguishing between mono-and multifractality and highly efficient in assigning the monofractal class. For the empirical series, our classifier identified monofractal classes specific to experimental designs, tasks, and conditions. Monofractal classes are particularly relevant for skilled, repetitive behavior. Short behavioral series are crucial for avoiding potential confounders such as mind wandering or fatigue. Our classifier thus contributes to broadening the scope of time series analysis for behavioral series and to understanding the impact of fundamental behavioral constructs (e.g., learning, coordination, and attention) on serial performance.