Motor unit number estimation via sequential Monte Carlo

A change in the number of motor units that operate a particular muscle is an important indicator for the progress of a neuromuscular disease and the efficacy of a therapy. Inference for realistic statistical models of the typical data produced when testing muscle function is difficult, and estimating the number of motor units from these data is an ongoing statistical challenge. We consider a set of models for the data, each with a different number of working motor units, and present a novel method for Bayesian inference, based on sequential Monte Carlo, which provides estimates of the marginal likelihood and, hence, a posterior probability for each model. To implement this approach in practice we require sequential Monte Carlo methods that have excellent computational and Monte Carlo properties. We achieve this by leveraging the conditional independence structure in the model, where given knowledge of which motor units fired as a result of a particular stimulus, parameters that specify the size of each unit's response are independent of the parameters defining the probability that a unit will respond at all. The scalability of our methodology relies on the natural conjugacy structure that we create for the former and an enforced, approximate conjugate structure for the latter. A simulation study demonstrates the accuracy of our method, and inferences are consistent across two different datasets arising from the same rat tibial muscle.