Approximate credibility intervals on electromyographic decomposition algorithms within a Bayesian framework

This thesis develops a framework to uncover the probability of correctness of algorithmic results. Specifically, this thesis is not concerned with the correctness of these algorithms, but with the uncertainty of their results arising from existing uncertainty in their inputs. This is achieved using a Bayesian approach. This framework is then demonstrated using independent component analysis with electromyographic data. Blind source separation (BSS) algorithms, such as independent component analysis (ICA), are often used to solve the inverse problem arising when, for example, attempting to retrieve the activation patterns of motor units (MUs) from electromyographic (EMG) data. BSS, or similar algorithms, return a result but do not generally provide any indication on the quality of that result or certainty one can have in it being the actual original pattern and not one strongly altered by the noise/errors in the input. This thesis uses Bayesian inference to extend ICA both to incorporate prior physiological information, thus making it in effect a semi-blind source separation (SBSS) algorithm, and to quantify the uncertainties around the values of the sources as estimated by ICA. To this end, this thesis also presents a way to put a prior on a mixing matrix given a physiological model as well as a re-parametrisation of orthogonal matrices which is helpful in pre-empting floating point errors when incorporating this prior of the mixing matrix into an algorithm which estimates the un-mixing matrix. In experiments done using EMG data, it is found that the addition of the prior is of benefit when the input is very noisy or very short in terms of samples or both. The experiments also show that the information about the certainty can be used as a heuristic for feature extraction or general quality control provided an appropriate baseline has been determined.