A Bayesian changepoint analysis on spatio-temporal point processes

Changepoint analysis is a well established area of statistical research, but in the context of spatio-temporal point processes it is as yet relatively unexplored. Some substantial differences with regard to standard changepoint analysis have to be taken into account: firstly, at every time point the datum is an irregular pattern of points; secondly, in real situations issues of spatial dependence between points and temporal dependence within time segments raise. Our motivating example consists of data concerning the monitoring and recovery of radioactive particles from Sandside beach, North of Scotland; there have been two major changes in the equipment used to detect the particles, representing known potential changepoints in the number of retrieved particles. In addition, offshore particle retrieval campaigns are believed may reduce the particle intensity onshore with an unknown temporal lag; in this latter case, the problem concerns multiple unknown changepoints. We therefore propose a Bayesian approach for detecting multiple changepoints in the intensity function of a spatio-temporal point process, allowing for spatial and temporal dependence within segments. We use Log-Gaussian Cox Processes, a very flexible class of models suitable for environmental applications that can be implemented using integrated nested Laplace approximation (INLA), a computationally efficient alternative to Monte Carlo Markov Chain methods for approximating the posterior distribution of the parameters. Once the posterior curve is obtained, we propose a few methods for detecting significant change points. We present a simulation study, which consists in generating spatio-temporal point pattern series under several scenarios; the performance of the methods is assessed in terms of type I and II errors, detected changepoint locations and accuracy of the segment intensity estimates. We finally apply the above methods to the motivating dataset and find good and sensible results about the presence and quality of changes in the process.

Gait analysis using a single wearable inertial measurement unit

Procedures for quantitative walking analysis include the assessment of body segment movements within defined gait cycles. Recently, methods to track human body motion using inertial measurement units have been suggested. It is not known if these techniques can be readily transferred to clinical measurement situations. This work investigates the aspects necessary for one inertial measurement unit mounted on the lower back to track orientation, and determine spatio-temporal features of gait outside the confines of a conventional gait laboratory. Apparent limitations of different inertial sensors can be overcome by fusing data using methods such as a Kalman filter. The benefits of optimizing such a filter for the type of motion are unknown. 3D accelerations and 3D angular velocities were collected for 18 healthy subjects while treadmill walking. Optimization of Kalman filter parameters improved pitch and roll angle estimates when compared to angles derived using stereophotogrammetry. A Weighted Fourier Linear Combiner method for estimating 3D orientation angles by constructing an analytical representation of angular velocities and allowing drift free integration is also presented. When tested this method provided accurate estimates of 3D orientation when compared to stereophotogrammetry. Methods to determine spatio-temporal features from lower trunk accelerations generally require knowledge of sensor alignment. A method was developed to estimate the instants of initial and final ground contact from accelerations measured by a waist mounted inertial device without rigorous alignment. A continuous wavelet transform method was used to filter and differentiate the signal and derive estimates of initial and final contact times. The technique was tested with data recorded for both healthy and pathologic (hemiplegia and Parkinson’s disease) subjects and validated using an instrumented mat. The results show that a single inertial measurement unit can assist whole body gait assessment however further investigation is required to understand altered gait timing in some pathological subjects.

Assessment of gait spatio-temporal parameters in neurological disorders using wearable inertial sensors

Movement analysis carried out in laboratory settings is a powerful, but costly solution since it requires dedicated instrumentation, space and personnel. Recently, new technologies such as the magnetic and inertial measurement units (MIMU) are becoming widely accepted as tools for the assessment of human motion in clinical and research settings. They are relatively easy-to-use and potentially suitable for estimating gait kinematic features, including spatio-temporal parameters. The objective of this thesis regards the development and testing in clinical contexts of robust MIMUs based methods for assessing gait spatio-temporal parameters applicable across a number of different pathological gait patterns. First, considering the need of a solution the least obtrusive as possible, the validity of the single unit based approach was explored. A comparative evaluation of the performance of various methods reported in the literature for estimating gait temporal parameters using a single unit attached to the trunk first in normal gait and then in different pathological gait conditions was performed. Then, the second part of the research headed towards the development of new methods for estimating gait spatio-temporal parameters using shank worn MIMUs on different pathological subjects groups. In addition to the conventional gait parameters, new methods for estimating the changes of the direction of progression were explored. Finally, a new hardware solution and relevant methodology for estimating inter-feet distance during walking was proposed. Results of the technical validation of the proposed methods at different walking speeds and along different paths against a gold standard were reported and showed that the use of two MIMUs attached to the lower limbs associated with a robust method guarantee a much higher accuracy in determining gait spatio-temporal parameters. In conclusion, the proposed methods could be reliably applied to various abnormal gaits obtaining in some cases a comparable level of accuracy with respect to normal gait.