Statistics

Objective: The Coping Inventory for Stressful Situations (CISS) is a widely used measure of trait coping that was developed to assess three basic coping styles: task-oriented, emotion-oriented, and avoidance-oriented coping. This thesis examined the psychometric properties of a short form for the CISS (CISS-SF). Method: Data from a large longitudinal sample of adults were used to conduct analyses testing the measure's factor structure, internal and test-retest reliabilities, and construct validity with respect to mental health outcomes. Results: The 3-factor model provided acceptable fit to the sample data. Internal reliabilities for the scales were acceptable across multiple administrations (by gender and age), while 1 and 2-year test-retest correlations were also consistent with what would be expected for stable coping style constructs. Relationships were found to be consistent with previous research on coping. Conclusion: Overall, the results suggest that the CISS-SF is a valid and reliable brief multi-dimensional measure of coping styles.

Author Keywords: basic personality, coping, coping styles, mental health, psychometrics

The spectral properties of time series data reveal underlying processes but require complete datasets, often unavailable due to missing values and irregular sampling.This thesis uses a computational simulations framework to evaluate the perfor- mance of the Hybrid Wiener Interpolator [3], a novel method designed to reconstruct nonstationary time series data, thus making said data amenable for spectrum analysis. This research evaluates the Hybrid Wiener Interpolator's ability to handle nonstation- ary data and data gaps, comparing its performance to other interpolation methods under different stationarity and data integrity conditions. The results illuminate the robustness of this interpolator in scenarios typical of scientific datasets, offering a promising approach for enhancing spectrum estimation in the presence of non-ideal data conditions

Author Keywords: ARIMA Models, Data Imputation, Interpolation, Stationarity, Time Series, Time Series Simulations

Climate change is a global challenge with profound environmental, health, andsocio-economic implications. Canada's diverse geography offers a unique lens to study localized climate trends. This thesis models and clusters climate variables, focusing on temperature trends, using Bayesian hierarchical models and clustering techniques to uncover regional patterns and health impacts. Three decades of hourly temperature data from the Meteorological Service of Canada were split into 18 annual parts to capture seasonal variations. Metrics like mean, minimum, and extreme temperatures were analyzed. Bayesian models revealed regional variability, with examples of British Columbia and the Northern regions exhibiting notable trends. Clustering identified regional dependencies and linked temperature trends with morbidity and mortality risks from air pollutants (PM2.5, O3). Summer risks stemmed from O3, while winter risks were PM2.5 driven. Findings highlight the need for region-specific strategies, offering actionable insights for policy makers addressing climate-health linkages.

Author Keywords: Bayesian models, Climate change, Clustering, Temperature Trends, Time Series

Accurately forecasting financial distress in companies is crucial in the turbulent economic conditions of our time. This study highlights the potential benefits of incorporating qualitative data into financial distress prediction models. The study assessed the relative effectiveness of traditional distress prediction models against integrated models, determined which variables significantly impacted the predictive performance and ascertained the consistency of the models across Africa.The study employed three distinct classification techniques to evaluate the performance of both models: logistic regression, decision trees, and random forests, to ensure that the best-performing technique was identified. The study found that incorporating governance factors into the model did not positively impact the model's performance, affirming that traditional distress prediction models are relatively effective. The study also found that Current Ratio, ROA, ROE, DCE, and Asset Turnover significantly impacted the predictive performance of the models. Finally, it identified regional discrepancies in the performance of the analyzed models.

Author Keywords: Decision Tree, Financial Distress, Integrated Models, Logistic Regression, Random Forest, Traditional Models

This thesis is part of an industry project which collaborates with an aviation technology company on pilot performance assessment. In this project, we propose utilizing the pilots' training data to develop a model that can recognize the pilots' activity patterns for evaluation. The data will present as a time series, representing a pilot's actions during maneuvers. In this thesis, the main contribution is focusing on a multivariate time series dataset, including preprocessing and transformation. The main difficulties in time series classification is the data sequence of the time dimension. In this thesis, I developed an algorithm which formats time series data into equal length data.

Three classification and two transformation methods were used. In total, there are six models for comparison. The initial accuracy was 40%. By optimization through resampling, we increased the accuracy to 60%.

Author Keywords: Data Mining, K-NN, Machine Learning, Multivariate Time Series Classification, Time Series Forest

This thesis explores the shot-term relationship between exposure to ambient air pollution and human health through metrics such as mortality and hospitalization in Canada. We begin by detailing the organization and interpolation of air pollution data from its partially quality-controlled source form. Analyses of seasonal, regional and temporal trends of all major components of PM2.5, was performed, showing a seasonal variation across most regions and validating the dataset.

A one-pollutant statistical Generalized Additive Model was applied to the data, estimating the health risk associated with exposure to thirteen different components of PM2.5. The selected components were based on those that compromised the majority of the mass and included: sulphate, nitrate, zinc, silicon, iron, nickel, vanadium, potassium, organic carbon, organic matter, elemental carbon, total carbon. Trends based on annual estimates of the association for PM2.5, and its constituents,were compared, showing that carbonaceous compounds, sulphate and nitrate had similar estimates of association. Many estimates, as is common in population ecologic epidemiology, had association estimates statistically indistinguishable from zero, but with clear features of interest, including evident differences between cold and warm season associations in Canada's temperate climate.

A method to model two correlated pollutants (in this case, PM2.5 and O3) was developed using thin plate splines. In this approach, the location of the response surface (after accounting for the temperature, a smooth function of time and day of week) that corresponds to the average pollutant concentration and the average plus one unit was used as the estimate of the joint contribution of pollutants due to a unit increase. The estimates from the thin plate spline (TPS) approach were compared to the single pollutant models, with large increases and decreases in PM2.5 and O3 being captured in the TPS estimates. However, this approach indicated significantly larger error in the estimates than would be expected, indicating a possible future area for refinement.

Author Keywords: Air pollution, Environmental Epidemiology, Generalized Additive Models, Human Health, Multivariate Models, Thin Plate Splines

The typical contrast mechanism employed in multimodal CARS microscopy involves the use of other nonlinear imaging modalities such as two-photon excitation fluorescence (TPEF) microscopy and second harmonic generation (SHG) microscopy to produce a molecule-specific pseudocolor image. In this work, I explore the use of unsupervised multivariate statistical analysis tools such as Principal Component Analysis (PCA) and Vertex Component Analysis (VCA) to provide better contrast using the hyperspectral CARS data alone. Using simulated CARS images, I investigate the effects of the quadratic dependence of CARS signal on concentration on the pixel clustering and classification and I find that a normalization step is necessary to improve pixel color assignment. Using an atherosclerotic rabbit aorta test image, I show that the VCA algorithm provides pseudocolor contrast that is comparable to multimodal imaging, thus showing that much of the information gleaned from a multimodal approach can be sufficiently extracted from the CARS hyperspectral stack itself.

Author Keywords: Coherent Anti-Stokes Raman Scattering Microscopy, Hyperspectral Imaging, Multimodal Imaging, Multivariate Analysis, Principal Component Analysis, Vertex Component Analysis

Natural populations of flowering plants rarely have perfectly uniform distributions, so trends in pollen dispersal should affect the size of the pollination neighbourhood and influence mating opportunities. Here I used spatial analysis to determine the size of the pollination neighbourhood in a stand of the herbaceous, wind-pollinated plant (Typha latifolia; broad-leaved cattail) by evaluating patterns of pollen production and seed set by individual cattail shoots. I found a positive correlation between pollen production and seed set among near-neighbour shoots (i.e., within 4 m2 patches of the stand; Pearson's r = 0.235, p < 0.05, df = 77) that was not driven by a correlation between these variables within inflorescences (Pearson's r = 0.052, p > 0.45, df = 203). I also detected significant spatial autocorrelations in seed set over short distances (up to ~ 5 m) and a significant cross-correlation between pollen production and seed set over distances of < 1 m indicating that the majority of pollination events involve short distances. Patterns of pollen availability were simulated to explore the shape of the pollen dispersal curve. Simulated pollen availability fit actual patterns of seed set only under assumptions of highly restricted pollen dispersal. Together, these findings indicate that even though Typha latifolia produces copious amounts of pollen, the vast majority of pollen dispersal was highly localized to distances of ~ 1 m. Moreover, although Typha latifolia is self-compatible and has been described as largely selfing, my results are more consistent with the importance of pollen transfer between nearby inflorescences. Therefore, realized selfing rates of Typha latifolia should largely depend on the clonal structure of populations.

Author Keywords: clonal structure, correlogram, dispersal curves, pollination, spatial analysis, Typha latifolia

Medication used to treat human illness is one of the greatest developments in human history. In Canada, prescription drugs have been developed and made available to treat a wide variety of illnesses, from infections to heart disease and so on. Records of prescription drug fulfillment at coarse Canadian geographic scales were obtained from Health Canada in order to track the use of these drugs by the Canadian population.

The obtained prescription drug fulfillment records were in a variety of inconsistent formats, including a large selection of years for which only paper tabular records were available (hard copies). In this work, we organize, digitize, proof and synthesize the full available data set of prescription drug records, from paper to final database. Extensive quality control was performed on the data before use. This data was then analyzed for temporal and spatial changes in prescription drug use across Canada from 1990-2013.

In addition, one of major research areas in environmental epidemiological studies is the study of population health risk associated with exposure to ambient air pollution. Prescription drugs can moderate public health risk, by reducing the drug user's physiological symptoms and preventing acute health effects (e.g., strokes, heart attacks, etc.). The cleaned prescription drug data was considered in the context of a common model to examine its influence on the association between air pollution exposure and various health outcomes. Since, prescription drug data were available only at the provincial level, a Bayesian hierarchical model was employed to include the prescription drugs as a covariate at regional level, which were then combined to estimate the association at national level. Although further investigations are required, the study results suggest that the prescription drugs influenced the air pollution related public health risk.

Author Keywords: Data, Error checking, Population health, Prescriptions

The spectrum of a given time series is a characteristic function describing its frequency properties. Spectrum estimation methods require time series data to be contiguous in order for robust estimators to retain their performance. This poses a fundamental challenge, especially when considering real-world scientific data that is often plagued by missing values, and/or irregularly recorded measurements. One area of research devoted to this problem seeks to repair the original time series through interpolation. There are several algorithms that have proven successful for the interpolation of considerably large gaps of missing data, but most are only valid for use on stationary time series: processes whose statistical properties are time-invariant, which is not a common property of real-world data. The Hybrid Wiener interpolator is a method that was designed for repairing nonstationary data, rendering it suitable for spectrum estimation. This thesis work presents a computational framework designed for conducting systematic testing on the statistical performance of this method in light of changes to gap structure and departures from the stationarity assumption. A comprehensive audit of the Hybrid Wiener Interpolator against other state-of-the art algorithms will also be explored.

Author Keywords: applied statistics, hybrid wiener interpolator, imputation, interpolation, R statistical software, time series