Bayesian models for longitudinal data

Longitudinal data, where data are repeatedly observed or measured on a temporal basis of time or age provides the foundation of the analysis of processes which evolve over time, and these can be referred to as growth or trajectory models. One of the traditional ways of looking at growth models is to employ either linear or polynomial functional forms to model trajectory shape, and account for variation around an overall mean trend with the inclusion of random eects or individual variation on the functional shape parameters. The identification of distinct subgroups or sub-classes (latent classes) within these trajectory models which are not based on some pre-existing individual classification provides an important methodology with substantive implications. The identification of subgroups or classes has a wide application in the medical arena where responder/non-responder identification based on distinctly diering trajectories delivers further information for clinical processes. This thesis develops Bayesian statistical models and techniques for the identification of subgroups in the analysis of longitudinal data where the number of time intervals is limited. These models are then applied to a single case study which investigates the neuropsychological cognition for early stage breast cancer patients undergoing adjuvant chemotherapy treatment from the Cognition in Breast Cancer Study undertaken by the Wesley Research Institute of Brisbane, Queensland. Alternative formulations to the linear or polynomial approach are taken which use piecewise linear models with a single turning point, change-point or knot at a known time point and latent basis models for the non-linear trajectories found for the verbal memory domain of cognitive function before and after chemotherapy treatment. Hierarchical Bayesian random eects models are used as a starting point for the latent class modelling process and are extended with the incorporation of covariates in the trajectory profiles and as predictors of class membership. The Bayesian latent basis models enable the degree of recovery post-chemotherapy to be estimated for short and long-term followup occasions, and the distinct class trajectories assist in the identification of breast cancer patients who maybe at risk of long-term verbal memory impairment.

Evolution of vocational rehabilitation competencies in Australia

Over the past decade, there has been growth in the delivery of vocational rehabilitation services globally, as countries seek to control disability-related expenditure, yet there has been minimal research outside the United States on competencies required to work in this area. This study reports on research conducted in Australia to determine current job function and knowledge areas in terms of their importance and frequency of use in the provision of vocational rehabilitation. A survey comprising items from the Rehabilitation Skills Inventory-Amended and International Survey of Disability Management was completed by 149 rehabilitation counselors and items submitted to factor analysis. T-tests and analyses of variance were used to determine differences between scores of importance and frequency and differences in scores based on work setting and professional training. Six factors were identified as important and frequently used: (i) vocational counseling, (ii) professional practice, (iii) personal counseling, (iv) rehabilitation case management, (v) workplace disability case management, and (vi) workplace intervention and program management. Vocational counseling, professional practice and personal counseling were significantly more important and performed more frequently by respondents in vocational rehabilitation settings than those in compensation settings. These same three factors were rated significantly higher in importance and frequency by those with rehabilitation counselor training when compared with those with other training. In conclusion, although ‘traditional’ knowledge and skill areas such as vocational counseling, professional practice, and personal counseling were identified as central to vocational rehabilitation practice in Australian rehabilitation agencies, mean ratings suggest a growing emphasis on knowledge and skills associated with disability management practice.

The modulation of outdoor running speed : the influence of gradient

This thesis aimed to investigate the way in which distance runners modulate their speed in an effort to understand the key processes and determinants of speed selection when encountering hills in natural outdoor environments. One factor which has limited the expansion of knowledge in this area has been a reliance on the motorized treadmill which constrains runners to constant speeds and gradients and only linear paths. Conversely, limits in the portability or storage capacity of available technology have restricted field research to brief durations and level courses. Therefore another aim of this thesis was to evaluate the capacity of lightweight, portable technology to measure running speed in outdoor undulating terrain. The first study of this thesis assessed the validity of a non-differential GPS to measure speed, displacement and position during human locomotion. Three healthy participants walked and ran over straight and curved courses for 59 and 34 trials respectively. A non-differential GPS receiver provided speed data by Doppler Shift and change in GPS position over time, which were compared with actual speeds determined by chronometry. Displacement data from the GPS were compared with a surveyed 100m section, while static positions were collected for 1 hour and compared with the known geodetic point. GPS speed values on the straight course were found to be closely correlated with actual speeds (Doppler shift: r = 0.9994, p < 0.001, Δ GPS position/time: r = 0.9984, p < 0.001). Actual speed errors were lowest using the Doppler shift method (90.8% of values within ± 0.1 m.sec -1). Speed was slightly underestimated on a curved path, though still highly correlated with actual speed (Doppler shift: r = 0.9985, p < 0.001, Δ GPS distance/time: r = 0.9973, p < 0.001). Distance measured by GPS was 100.46 ± 0.49m, while 86.5% of static points were within 1.5m of the actual geodetic point (mean error: 1.08 ± 0.34m, range 0.69-2.10m). Non-differential GPS demonstrated a highly accurate estimation of speed across a wide range of human locomotion velocities using only the raw signal data with a minimal decrease in accuracy around bends. This high level of resolution was matched by accurate displacement and position data. Coupled with reduced size, cost and ease of use, the use of a non-differential receiver offers a valid alternative to differential GPS in the study of overground locomotion. The second study of this dissertation examined speed regulation during overground running on a hilly course. Following an initial laboratory session to calculate physiological thresholds (VO2 max and ventilatory thresholds), eight experienced long distance runners completed a self- paced time trial over three laps of an outdoor course involving uphill, downhill and level sections. A portable gas analyser, GPS receiver and activity monitor were used to collect physiological, speed and stride frequency data. Participants ran 23% slower on uphills and 13.8% faster on downhills compared with level sections. Speeds on level sections were significantly different for 78.4 ± 7.0 seconds following an uphill and 23.6 ± 2.2 seconds following a downhill. Speed changes were primarily regulated by stride length which was 20.5% shorter uphill and 16.2% longer downhill, while stride frequency was relatively stable. Oxygen consumption averaged 100.4% of runner’s individual ventilatory thresholds on uphills, 78.9% on downhills and 89.3% on level sections. Group level speed was highly predicted using a modified gradient factor (r2 = 0.89). Individuals adopted distinct pacing strategies, both across laps and as a function of gradient. Speed was best predicted using a weighted factor to account for prior and current gradients. Oxygen consumption (VO2) limited runner’s speeds only on uphill sections, and was maintained in line with individual ventilatory thresholds. Running speed showed larger individual variation on downhill sections, while speed on the level was systematically influenced by the preceding gradient. Runners who varied their pace more as a function of gradient showed a more consistent level of oxygen consumption. These results suggest that optimising time on the level sections after hills offers the greatest potential to minimise overall time when running over undulating terrain. The third study of this thesis investigated the effect of implementing an individualised pacing strategy on running performance over an undulating course. Six trained distance runners completed three trials involving four laps (9968m) of an outdoor course involving uphill, downhill and level sections. The initial trial was self-paced in the absence of any temporal feedback. For the second and third field trials, runners were paced for the first three laps (7476m) according to two different regimes (Intervention or Control) by matching desired goal times for subsections within each gradient. The fourth lap (2492m) was completed without pacing. Goals for the Intervention trial were based on findings from study two using a modified gradient factor and elapsed distance to predict the time for each section. To maintain the same overall time across all paced conditions, times were proportionately adjusted according to split times from the self-paced trial. The alternative pacing strategy (Control) used the original split times from this initial trial. Five of the six runners increased their range of uphill to downhill speeds on the Intervention trial by more than 30%, but this was unsuccessful in achieving a more consistent level of oxygen consumption with only one runner showing a change of more than 10%. Group level adherence to the Intervention strategy was lowest on downhill sections. Three runners successfully adhered to the Intervention pacing strategy which was gauged by a low Root Mean Square error across subsections and gradients. Of these three, the two who had the largest change in uphill-downhill speeds ran their fastest overall time. This suggests that for some runners the strategy of varying speeds systematically to account for gradients and transitions may benefit race performances on courses involving hills. In summary, a non – differential receiver was found to offer highly accurate measures of speed, distance and position across the range of human locomotion speeds. Self-selected speed was found to be best predicted using a weighted factor to account for prior and current gradients. Oxygen consumption limited runner’s speeds only on uphills, speed on the level was systematically influenced by preceding gradients, while there was a much larger individual variation on downhill sections. Individuals were found to adopt distinct but unrelated pacing strategies as a function of durations and gradients, while runners who varied pace more as a function of gradient showed a more consistent level of oxygen consumption. Finally, the implementation of an individualised pacing strategy to account for gradients and transitions greatly increased runners’ range of uphill-downhill speeds and was able to improve performance in some runners. The efficiency of various gradient-speed trade- offs and the factors limiting faster downhill speeds will however require further investigation to further improve the effectiveness of the suggested strategy.

Fingerprint analysis using wavelet transform with application to compression and feature extraction

The main goal of this research is to design an efficient compression al~ gorithm for fingerprint images. The wavelet transform technique is the principal tool used to reduce interpixel redundancies and to obtain a parsimonious representation for these images. A specific fixed decomposition structure is designed to be used by the wavelet packet in order to save on the computation, transmission, and storage costs. This decomposition structure is based on analysis of information packing performance of several decompositions, two-dimensional power spectral density, effect of each frequency band on the reconstructed image, and the human visual sensitivities. This fixed structure is found to provide the "most" suitable representation for fingerprints, according to the chosen criteria. Different compression techniques are used for different subbands, based on their observed statistics. The decision is based on the effect of each subband on the reconstructed image according to the mean square criteria as well as the sensitivities in human vision. To design an efficient quantization algorithm, a precise model for distribution of the wavelet coefficients is developed. The model is based on the generalized Gaussian distribution. A least squares algorithm on a nonlinear function of the distribution model shape parameter is formulated to estimate the model parameters. A noise shaping bit allocation procedure is then used to assign the bit rate among subbands. To obtain high compression ratios, vector quantization is used. In this work, the lattice vector quantization (LVQ) is chosen because of its superior performance over other types of vector quantizers. The structure of a lattice quantizer is determined by its parameters known as truncation level and scaling factor. In lattice-based compression algorithms reported in the literature the lattice structure is commonly predetermined leading to a nonoptimized quantization approach. In this research, a new technique for determining the lattice parameters is proposed. In the lattice structure design, no assumption about the lattice parameters is made and no training and multi-quantizing is required. The design is based on minimizing the quantization distortion by adapting to the statistical characteristics of the source in each subimage. 11 Abstract Abstract Since LVQ is a multidimensional generalization of uniform quantizers, it produces minimum distortion for inputs with uniform distributions. In order to take advantage of the properties of LVQ and its fast implementation, while considering the i.i.d. nonuniform distribution of wavelet coefficients, the piecewise-uniform pyramid LVQ algorithm is proposed. The proposed algorithm quantizes almost all of source vectors without the need to project these on the lattice outermost shell, while it properly maintains a small codebook size. It also resolves the wedge region problem commonly encountered with sharply distributed random sources. These represent some of the drawbacks of the algorithm proposed by Barlaud [26). The proposed algorithm handles all types of lattices, not only the cubic lattices, as opposed to the algorithms developed by Fischer [29) and Jeong [42). Furthermore, no training and multiquantizing (to determine lattice parameters) is required, as opposed to Powell's algorithm [78). For coefficients with high-frequency content, the positive-negative mean algorithm is proposed to improve the resolution of reconstructed images. For coefficients with low-frequency content, a lossless predictive compression scheme is used to preserve the quality of reconstructed images. A method to reduce bit requirements of necessary side information is also introduced. Lossless entropy coding techniques are subsequently used to remove coding redundancy. The algorithms result in high quality reconstructed images with better compression ratios than other available algorithms. To evaluate the proposed algorithms their objective and subjective performance comparisons with other available techniques are presented. The quality of the reconstructed images is important for a reliable identification. Enhancement and feature extraction on the reconstructed images are also investigated in this research. A structural-based feature extraction algorithm is proposed in which the unique properties of fingerprint textures are used to enhance the images and improve the fidelity of their characteristic features. The ridges are extracted from enhanced grey-level foreground areas based on the local ridge dominant directions. The proposed ridge extraction algorithm, properly preserves the natural shape of grey-level ridges as well as precise locations of the features, as opposed to the ridge extraction algorithm in [81). Furthermore, it is fast and operates only on foreground regions, as opposed to the adaptive floating average thresholding process in [68). Spurious features are subsequently eliminated using the proposed post-processing scheme.

Adaptive instantaneous frequency estimation: Techniques and algorithms

This thesis deals with the problem of the instantaneous frequency (IF) estimation of sinusoidal signals. This topic plays significant role in signal processing and communications. Depending on the type of the signal, two major approaches are considered. For IF estimation of single-tone or digitally-modulated sinusoidal signals (like frequency shift keying signals) the approach of digital phase-locked loops (DPLLs) is considered, and this is Part-I of this thesis. For FM signals the approach of time-frequency analysis is considered, and this is Part-II of the thesis. In part-I we have utilized sinusoidal DPLLs with non-uniform sampling scheme as this type is widely used in communication systems. The digital tanlock loop (DTL) has introduced significant advantages over other existing DPLLs. In the last 10 years many efforts have been made to improve DTL performance. However, this loop and all of its modifications utilizes Hilbert transformer (HT) to produce a signal-independent 90-degree phase-shifted version of the input signal. Hilbert transformer can be realized approximately using a finite impulse response (FIR) digital filter. This realization introduces further complexity in the loop in addition to approximations and frequency limitations on the input signal. We have tried to avoid practical difficulties associated with the conventional tanlock scheme while keeping its advantages. A time-delay is utilized in the tanlock scheme of DTL to produce a signal-dependent phase shift. This gave rise to the time-delay digital tanlock loop (TDTL). Fixed point theorems are used to analyze the behavior of the new loop. As such TDTL combines the two major approaches in DPLLs: the non-linear approach of sinusoidal DPLL based on fixed point analysis, and the linear tanlock approach based on the arctan phase detection. TDTL preserves the main advantages of the DTL despite its reduced structure. An application of TDTL in FSK demodulation is also considered. This idea of replacing HT by a time-delay may be of interest in other signal processing systems. Hence we have analyzed and compared the behaviors of the HT and the time-delay in the presence of additive Gaussian noise. Based on the above analysis, the behavior of the first and second-order TDTLs has been analyzed in additive Gaussian noise. Since DPLLs need time for locking, they are normally not efficient in tracking the continuously changing frequencies of non-stationary signals, i.e. signals with time-varying spectra. Nonstationary signals are of importance in synthetic and real life applications. An example is the frequency-modulated (FM) signals widely used in communication systems. Part-II of this thesis is dedicated for the IF estimation of non-stationary signals. For such signals the classical spectral techniques break down, due to the time-varying nature of their spectra, and more advanced techniques should be utilized. For the purpose of instantaneous frequency estimation of non-stationary signals there are two major approaches: parametric and non-parametric. We chose the non-parametric approach which is based on time-frequency analysis. This approach is computationally less expensive and more effective in dealing with multicomponent signals, which are the main aim of this part of the thesis. A time-frequency distribution (TFD) of a signal is a two-dimensional transformation of the signal to the time-frequency domain. Multicomponent signals can be identified by multiple energy peaks in the time-frequency domain. Many real life and synthetic signals are of multicomponent nature and there is little in the literature concerning IF estimation of such signals. This is why we have concentrated on multicomponent signals in Part-H. An adaptive algorithm for IF estimation using the quadratic time-frequency distributions has been analyzed. A class of time-frequency distributions that are more suitable for this purpose has been proposed. The kernels of this class are time-only or one-dimensional, rather than the time-lag (two-dimensional) kernels. Hence this class has been named as the T -class. If the parameters of these TFDs are properly chosen, they are more efficient than the existing fixed-kernel TFDs in terms of resolution (energy concentration around the IF) and artifacts reduction. The T-distributions has been used in the IF adaptive algorithm and proved to be efficient in tracking rapidly changing frequencies. They also enables direct amplitude estimation for the components of a multicomponent