 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.

Keywords {#keywords .unnumbered}
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Motor Unit Number Estimation; Sequential Monte Carlo; Model Selection

Introduction {#sec:Intro}
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Motor unit number estimation (MUNE) is a continuing challenge for clinical neurologists. An ability to determine the number of motor units (MUs) that operate a particular muscle provides important insights into the progression of various neuromuscular ailments such as amyotrophic lateral sclerosis [@She06; @Bro07], and aids the assessment of the efficacy of potential therapy treatments [@Cas10].

A MU is the fundamental component of the neuromuscular system and consists of a single motor neuron and the muscle fibres whos contraction it governs. Restriction to a MU’s operation may be a result of impaired communication between the motor neuron and muscle fibres, abnormaility in their function, or atrophy of either cell type. A direct investigation into the number of MUs via a biopsy, for example, is not helpful since this only determines the presence of each MU, not its functionality. Electromyography (EMG) provides a set of electrical stimulii of varying intensity to a group of motor neurons; each stimulus artificially induces a twitch in the targeted muscle, providing an *in situ* measurement of the functioning of the MUs. The effect on the muscle may be measured by recording either the minute variation in muscle membrane potential or the physical force the muscle exerts [@Maj05]. The generic methods developed in this article are applicable to either type of measurement. Since our data consist 