Modeling motor learning in juggling: A Bayesian approach

We studied the catching accuracy during the skill acquisition of juggling using a probabilistic model, which was justified by the Bayesian brain hypothesis that the internal model constantly updates its parameters based on prior experiences and new practice. We wondered how practice can increase the probability of catching a ball (θ) in juggling by changing the shape of the posterior distribution of θ.

We recorded the juggling performance of 192 students over 17 days. Using the Bayesian approach, under a prior distribution of beta(θ|1,3), we calculated the posterior distribution of θ and its expectation (E[θ]) and variance (Var(θ)) on each day of practice.

In a decelerated pattern, participants improved E[θ] from 0.43 to 0.86 and reduced Var(θ) from 0.029 to 0.001 over 17 days. Using the posterior distribution, we estimated the probability of different performance outcomes on each day of practice.

The probabilistic model suggests that during motor learning, participants shifted the weight from prior experience to current practice and updated θ in the posterior distribution. Instead of choosing θ close to its theoretically optimal value (i.e., maximum likelihood estimation) across days of practice, participants selected sub-optimal θ at the beginning and gradually improved θ to its optimal value during learning. Our model not only contributes to the theoretical understanding of skill acquisition from a probabilistic perspective but also could be applied to some other discrete motor skills requiring hand-eye coordination.