Testing Bayesian Models of Human Coincidence Timing

Abstract

. A sensorimotor control task often requires an accurate estimation of the timing of the arrival of an external target (e.g., when hitting a pitched ball). Conventional studies of human timing processes have ignored the stochastic features of target timing: e.g., the speed of the pitched ball is not generally constant, but is variable. Interestingly, based on Bayesian theory, it has been recently shown that the human sensorimotor system achieves the optimal estimation by integrating sensory information with prior knowledge of the probabilistic structure of the target variation. In this study, we tested whether Bayesian integration is also implemented while performing a coincidencetiming type of sensorimotor task by manipulating the trial-by-trial variability (i.e., the prior distribution) of the target timing. As a result, within several hundred trials of learning, subjects were able to generate systematic timing behavior according to the width of the prior distribution, as predicted by the optimal Bayesian model. Considering the previous studies showing that the human sensorimotor system uses Bayesian integration in spacing and forcegrading tasks, our result indicates that Bayesian integration is fundamental to all aspects of human sensorimotor control. Moreover, it was noteworthy that the subjects could adjust their behavior both when the prior distribution was switched from wide to narrow and vice versa, although the adjustment was slower in the former case. Based on a comparison with observations in a previous study, we discuss the flexibility and adaptability of Bayesian sensorimotor learning. I N T R O D U C T I O NOur sensorimotor system often requires that motor responses are timed precisely in accordance with the behavior of a certain external target. For example, to hit a pitched ball while playing baseball or cricket, the batter has to control the timing of the swing based on the speed of the ball. Such timing behavior, which is referred to as coincidence timing, has been studied extensively in sports science (e.g., Ripoll and Latiri 1997; Williams et al. 2002). Because the external environment that we usually encounter is variable, not constant, we need to monitor visual and other sensory signals to estimate the current behavior of the external target accurately. Naturally, these sensory signals are exposed to internal and external noise (Körding and Wolpert 2004; van Beers et al. 2002), so they cannot always provide sufficient information for precise estimates. To compensate for the sensory uncertainty, prior knowledge or experience of the target behavior is helpful information for the estimation. By observing the external target behavior for a long time, we can determine its predictable probabilistic structure. Considering various phenomena in our world, such as human behavior and physical events, the trial-by-trial variability has a certain probabilistic structure, such as a Gaussian distribution (e.g., Chen et al. 1997). That is, the speeds of all pitched balls do not appear with the same probab...

The brain uses adaptive internal models of scene statistics for sensorimotor estimation and planning

“…The fact that stimulus history biases perceptual judgments is well-known. Broadly speaking, it appears in two ways-biases to (or away from) the mean of a stimulus distribution (1)(2)(3)(4)(5)(6)(7)(8)(9), referred to as central-tendency biases, and biases to (or away from) recently observed stimuli (10)(11)(12)(13)(14)(15)(16), referred to as n − 1 biases.…”

“…It has been proposed that central-tendency biases reflect the behavior of a perceptual system that optimally integrates noisy sensory measurements with prior knowledge of the distribution of stimulus values to make perceptual judgments (2,4,(7)(8)(9). Evidence for this hypothesis comes from studies showing that centraltendency biases in perceptual judgments increase when the sensory uncertainty of a stimulus increases (4) or the variance of a stimulus set decreases (2,(7)(8)(9).…”

“…Evidence for this hypothesis comes from studies showing that centraltendency biases in perceptual judgments increase when the sensory uncertainty of a stimulus increases (4) or the variance of a stimulus set decreases (2,(7)(8)(9). It also has been suggested that observers learn the mean and variance of a stimulus distribution in a statistically optimal fashion (8) and continuously update internal estimates of mean and variance (7).…”

Probabilistic optimization in the human perceptuo-motor system

“…In recent years, psychophysical studies have revealed that our brain implements Bayesian integration in a variety of sensory-motor tasks, including spatial reaching 1,5) , reproducing forces 6) , timing 7,8) , and somatosensory temporal order judgment (TOJ) 9,10) (also see Yamamoto et al 2012 11) ). In this article, we first introduce a report that studied the coincidence timing task 8) .…”

“…In this article, we first introduce a report that studied the coincidence timing task 8) . In this task, the timing component of ball hitting or catching behaviors by humans was extracted.…”