The vast majority of experiments examining perception and behavior are conducted using experimental paradigms that adhere to a rigid trial structure: each trial consists of a brief and discrete series of events and is regarded as independent from all other trials. The assumptions underlying this structure ignore the reality that natural behavior is rarely discrete, brain activity follows multiple time courses that do not necessarily conform to the trial structure, and the natural environment has statistical structure and dynamics that exhibit long-range temporal correlation. Modern advances in statistical modeling and analysis offer tools that make it feasible for experiments to move beyond rigid independent and identically distributed trial structures. Here we review literature that serves as evidence for the feasibility and advantages of moving beyond trial-based paradigms to understand the neural basis of perception and cognition. Furthermore, we propose a synthesis of these efforts, integrating the characterization of natural stimulus properties with measurements of continuous neural activity and behavioral outputs within the framework of sensory-cognitive-motor loops. Such a framework provides a basis for the study of natural statistics, naturalistic tasks, and/or slow fluctuations in brain activity, which should provide starting points for important generalizations of analytical tools in neuroscience and subsequent progress in understanding the neural basis of perception and cognition.
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