Testing Bayesian Models of Human Coincidence Timing

Nature, 2004

When we learn a new motor skill, such as playing an approaching tennis ball, both our sensors and the task possess variability. Our sensors provide imperfect information about the ball's velocity, so we can only estimate it. Combining information from multiple modalities can reduce the error in this estimate 1-4 . On a longer time scale, not all velocities are a priori equally probable, and over the course of a match there will be a probability distribution of velocities. According to bayesian theory 5,6 , an optimal estimate results from combining information about the distribution of velocities-the prior-with evidence from sensory feedback. As uncertainty increases, when playing in fog or at dusk, the system should increasingly rely on prior knowledge. To use a bayesian strategy, the brain would need to represent the prior distribution and the level of uncertainty in the sensory feedback. Here we control the statistical variations of a new sensorimotor task and manipulate the uncertainty of the sensory feedback. We show that subjects internally represent both the statistical distribution of the task and their sensory uncertainty, combining them in a manner consistent with a performance-optimizing bayesian process 4,5 . The central nervous system therefore employs probabilistic models during sensorimotor learning.

bioRxiv (Cold Spring Harbor Laboratory), 2023

During timing tasks, the brain learns the statistical distribution of target intervals and integrates this prior knowledge with sensory inputs to optimise task performance. Daily events can have different temporal statistics (e.g. fastball/slowball in baseball batting), making it important to learn and retain multiple priors. However, the rules governing this process are not yet understood. Here, we demonstrate that the learning of multiple prior distributions in a coincidence timing task is characterised by body-part specificity. In our experiments, two prior distributions (short and long intervals) were imposed on participants. When using only one body part for timing responses, regardless of the priors, participants learned a single prior by generalising over the two distributions. However, when the two priors were assigned to different body parts, participants concurrently learned the two independent priors. Moreover, body-part specific prior acquisition was faster when the priors were assigned to anatomically distant body parts (e.g. hand/foot) than when they were assigned to close body parts (e.g. index/middle fingers). This suggests that the body-part specific learning of priors is organised according to somatotopy.

2017

If the brain is inherently Bayesian, then behavior should show the signatures of Bayesian computation from an early stage in life without the need for learning. Children should integrate probabilistic information from prior and likelihood distributions to reach decisions and should be as statistically efficient as adults. To test this idea, we examined the integration of prior and likelihood information in a simple position estimation task comparing children aged 6-11 years and adults. During development, estimation performance became closer to the statistical optimum. Children use likelihood information as well as adults but are limited in their use of priors. This finding suggests that Bayesian behavior is not inherent but learnt over the course of development.

The Journal of Physical Fitness and Sports Medicine, 2013

Despite the variability of internal and external environments, the human central nervous system (CNS) can generate precise and stable perception and motor behaviors. What mechanism enables this ability? Answering this question is one of the significant goals in the human sciences, including neuroscience, cognitive science, physical education and sports science. The Bayesian integration theory proposes that the CNS learns the prior distribution of a task and integrates it with sensory information to minimize the effect of sensory noise. In this article, we introduce psychophysical reports using motor timing and temporal order judgment (TOJ) tasks that support the Bayesian integration theory. Subsequently, we demonstrate the event-related potentials (ERPs) behind Bayesian integration that operates in somatosensory TOJ.

Social Science Research Network, 2021

Human Movement Science, 2022

An experiment was designed to determine the effects of sensory uncertainty on sensorimotor estimation in elite athletes compared to non-athletes. Nineteen elite athletes and 16 non-athletes were required to estimate when and where a cursor arrived at a target location. The cursor position was displayed through its entire trajectory in the certain condition while only briefly in the uncertain condition. Accuracy and variability in time and spatial domains were calculated. A Bayesian analysis using subsets of subjects' total spatial variance was also performed. The results indicated that athletes and non-athletes used estimation strategies consistent with Bayesian integration. The results also showed a decrease in variability for spatial performance for both groups during the uncertain condition compared to the certain condition, especially when the cursor location was further away from the prior mean. This decrease in variability was significantly greater for non-athletes. By concentrating performance around the end-point mean location, an increase in spatial error occurred. More spatial and timing errors were observed in nonathletes than athletes, indicating athletes were more certain about likelihood information or their interpretation of likelihood information than non-athletes. These results suggest that athletic experience may facilitate the use of probabilistic information for optimal sensorimotor estimations.

Journal of Neurophysiology, 2009

2013

Precise timing is crucial to decision-making and behavioral control, yet subjective time can be easily distorted by various temporal contexts. Application of a Bayesian framework to various forms of contextual calibration reveals that, contrary to popular belief, contextual biases in timing help to optimize overall performance under noisy conditions. Here, we review recent progress in understanding these forms of temporal calibration, and integrate a Bayesian framework with information-processing models of timing. We show that the essential components of a Bayesian framework are closely related to the clock, memory, and decision stages used by these models, and that such an integrated framework offers a new perspective on distortions in timing and time perception that are otherwise difficult to explain.

PLoS ONE, 2012

Several studies have shown that human motor behavior can be successfully described using optimal control theory, which describes behavior by optimizing the trade-off between the subject's effort and performance. This approach predicts that subjects reach the goal exactly at the final time. However, another strategy might be that subjects try to reach the target position well before the final time to avoid the risk of missing the target. To test this, we have investigated whether minimizing the control effort and maximizing the performance is sufficient to describe human motor behavior in timeconstrained motor tasks. In addition to the standard model, we postulate a new model which includes an additional cost criterion which penalizes deviations between the position of the effector and the target throughout the trial, forcing arrival on target before the final time. To investigate which model gives the best fit to the data and to see whether that model is generic, we tested both models in two different tasks where subjects used a joystick to steer a ball on a screen to hit a target (first task) or one of two targets (second task) before a final time. Noise of different amplitudes was superimposed on the ball position to investigate the ability of the models to predict motor behavior for different levels of uncertainty. The results show that a cost function representing only a trade-off between effort and accuracy at the end time is insufficient to describe the observed behavior. The new model correctly predicts that subjects steer the ball to the target position well before the final time is reached, which is in agreement with the observed behavior. This result is consistent for all noise amplitudes and for both tasks.

PLOS Computational Biology, 2015

Previous studies have shown that sensorimotor processing can often be described by Bayesian learning, in particular the integration of prior and feedback information depending on its degree of reliability. Here we test the hypothesis that the integration process itself can be tuned to the statistical structure of the environment. We exposed human participants to a reaching task in a three-dimensional virtual reality environment where we could displace the visual feedback of their hand position in a two dimensional plane. When introducing statistical structure between the two dimensions of the displacement, we found that over the course of several days participants adapted their feedback integration process in order to exploit this structure for performance improvement. In control experiments we found that this adaptation process critically depended on performance feedback and could not be induced by verbal instructions. Our results suggest that structural learning is an important meta-learning component of Bayesian sensorimotor integration.