As adults age, they lose the ability to produce maximal power and speed of movement. Success in daily living is often dependent upon power and speed. Thus these age-related decrements in performance can reduce physical independence and quality of life. An active lifestyle in older adulthood is associated with more successful aging. The purpose of this research program was to define the link between habitual activity and performance, specifically in regard to activities requiring power and speed. The hypothesis was that active older adults, compared to sedentary older adults, would be characterized by greater power production in maximal- and submaximal-effort tasks. Grouping older adults by activity level, coactivation was associated with activity level. Functional tasks are performed with a range of power requirements. Coactivation was used to distinguish groups in a maximal power task (Study 1) and submaximal power tasks (Study 2). In Study 1, the young adults demonstrated a greater maximal power than the older adults. While maximal power was not different between the older active and sedentary groups, the groups did differ on how they created maximal power. The active older adults produced a greater coactivation in the lower leg muscles compared to the older sedentary adults. In Study 2, the active older adults responded to different speeds during a submaximal power task with greater coactivation in the muscles of the lower leg at slow speeds compared with the sedentary older adults. Both older adults groups increased coactivation in the thigh muscles at high speeds. The sedentary older adults responded to speed with increased coactivation in the lower leg at fast speeds. The active older adults increased proximal thigh coactivation, EMG index, at the fastest speed compared with the sedentary older adults. Both older adult groups showed muscle activation adaptation to the change in task demands. The results of this dissertation increase our understanding about the link between physical activity and performance. Age-related differences in coactivation were observed during both maximal and submaximal tasks. Activity-related differences were observed suggesting the active older adults have a greater capability to adjust muscle activity to meet the challenges of community living. / text

Retinal pigment epithelium (RPE) is a principal site of pathogenesis in age-related macular de-generation (AMD). AMD is a main source of vision loss even blindness in the elderly and there is no effective treatment right now. Our aim is to describe the relationship between the morphology of RPE cells and the age and genotype of the eyes. We use principal component analysis (PCA) or functional principal component method (FPCA), support vector machine (SVM), and random forest (RF) methods to analyze the morphological data of RPE cells in mouse eyes to classify their age and genotype. Our analyses show that amongst all morphometric measures of RPE cells, cell shape measurements (eccentricity and solidity) are good for classification. But combination of cell shape and size (perimeter) provide best classification.

Brain decoding involves the determination of a subject’s cognitive state or an associated stimulus from functional neuroimaging data measuring brain activity. In this setting the cognitive state is typically characterized by an element of a finite set, and the neuroimaging data comprise voluminous amounts of spatiotemporal data measuring some aspect of the neural signal. The associated statistical problem is one of classification from high-dimensional data. We explore the use of functional principal component analysis, mutual information networks, and persistent homology for examining the data through exploratory analysis and for constructing features characterizing the neural signal for brain decoding. We review each approach from this perspective, and we incorporate the features into a classifier based on symmetric multinomial logistic regression with elastic net regularization. The approaches are illustrated in an application where the task is to infer from brain activity measured with magnetoencephalography (MEG) the type of video stimulus shown to a subject. / Graduate

abstract: Functional regression models are widely considered in practice. To precisely understand an underlying functional mechanism, a good sampling schedule for collecting informative functional data is necessary, especially when data collection is limited. However, scarce research has been conducted on the optimal sampling schedule design for the functional regression model so far. To address this design issue, efficient approaches are proposed for generating the best sampling plan in the functional regression setting. First, three optimal experimental designs are considered under a function-on-function linear model: the schedule that maximizes the relative efficiency for recovering the predictor function, the schedule that maximizes the relative efficiency for predicting the response function, and the schedule that maximizes the mixture of the relative efficiencies of both the predictor and response functions. The obtained sampling plan allows a precise recovery of the predictor function and a precise prediction of the response function. The proposed approach can also be reduced to identify the optimal sampling plan for the problem with a scalar-on-function linear regression model. In addition, the optimality criterion on predicting a scalar response using a functional predictor is derived when the quadratic relationship between these two variables is present, and proofs of important properties of the derived optimality criterion are also provided. To find such designs, an algorithm that is comparably fast, and can generate nearly optimal designs is proposed. As the optimality criterion includes quantities that must be estimated from prior knowledge (e.g., a pilot study), the effectiveness of the suggested optimal design highly depends on the quality of the estimates. However, in many situations, the estimates are unreliable; thus, a bootstrap aggregating (bagging) approach is employed for enhancing the quality of estimates and for finding sampling schedules stable to the misspecification of estimates. Through case studies, it is demonstrated that the proposed designs outperform other designs in terms of accurately predicting the response and recovering the predictor. It is also proposed that bagging-enhanced design generates a more robust sampling design under the misspecification of estimated quantities. / Dissertation/Thesis / Doctoral Dissertation Statistics 2020

COVID-19 has affected the lives of millions of people worldwide. This thesis includes two statistical studies on the response to COVID-19. The first study explores the impact of lockdown timing on COVID-19 transmission across US counties. We used functional principal component analysis to extract COVID-19 transmission patterns from county-wise case counts, and used supervised machine learning to identify risk factors, with the timing of lockdowns being the most significant. In particular, we found a critical time point for lockdowns, as lockdowns implemented after this time point were associated with significantly more cases and faster spread. The second study proposes an adaptive sample pooling strategy for efficient COVID-19 diagnostic testing. When testing a cohort, our strategy dynamically updates the prevalence estimate after each test if possible, and uses the updated information to choose the optimal pool size for the subsequent test. Simulation studies show that compared to traditional pooling strategies, our strategy reduces the number of tests required to test a cohort and is more resilient to inaccurate prevalence inputs. We have developed a dashboard application to guide the clinicians through the test procedure when using our strategy. / Graduate / 2023-05-27

Fault detection and diagnosis is a critical component of operations management systems. The goal of FDD is to identify the occurrence and causes of abnormal events. While many approaches are available, data-driven approaches for FDD have proven to be robust and reliable. Exploiting these advantages, the present study applied functional principal component analysis (FPCA) to carry out feature extraction for fault detection in internal combustion engines. Furthermore, a feature subset that explained 95% of the variance of the original vibrational sensor signal was used in a multilayer perceptron to carry out prediction for fault diagnosis. Of the engine states studied in the present work, the ending diagnostic performance shows the proposed approach achieved an overall prediction accuracy of 99.72 %. These results are encouraging because they show the feasibility for applying FPCA for feature extraction which has not been discussed previously within the literature relating to fault detection and diagnosis.

This research focuses on developing a crop decision planning model to help farmers make decisions for an upcoming crop year. The decisions consist of which crops to plant, the amount of land to allocate to each crop, when to grow, when to harvest, and when to sell. The objective is to maximize the overall profit subject to available resources under yield and price uncertainties. To help achieve this objective, we develop yield and price forecasting models to estimate the probable outcomes of these uncertain factors. The output from both forecasting models are incorporated into the crop decision planning model which enables the farmers to investigate and analyze the possible scenarios and eventually determine the appropriate decisions for each situation. This dissertation has three major components, yield forecasting, price forecasting, and crop decision planning. For yield forecasting, we propose a crop-weather regression model under a semiparametric framework. We use temperature and rainfall information during the cropping season and a GDP macroeconomic indicator as predictors in the model. We apply a functional principal components analysis technique to reduce the dimensionality of the model and to extract meaningful information from the predictors. We compare the prediction results from our model with a series of other yield forecasting models. For price forecasting, we develop a futures-based model which predicts a cash price from futures price and commodity basis. We focus on forecasting the commodity basis rather than the cash price because of the availability of futures price information and the low uncertainty of the commodity basis. We adopt a model-based approach to estimate the density function of the commodity basis distribution, which is further used to estimate the confidence interval of the commodity basis and the cash price. Finally, for crop decision planning, we propose a stochastic linear programming model, which provides the optimal policy. We also develop three heuristic models that generate a feasible solution at a low computational cost. We investigate the robustness of the proposed models to the uncertainties and prior probabilities. A numerical study of the developed approaches is performed for a case of a representative farmer who grows corn and soybean in Illinois.

For multivariate data, when testing homogeneity of covariance matrices arising from two or more groups, Bartlett's (1937) modified likelihood ratio test statistic is appropriate to use under the null hypothesis of equal covariance matrices where the null distribution of the test statistic is based on the restrictive assumption of normality. Zhang and Boos (1992) provide a pooled bootstrap approach when the data cannot be assumed to be normally distributed. We give three alternative bootstrap techniques to testing homogeneity of covariance matrices when it is both inappropriate to pool the data into one single population as in the pooled bootstrap procedure and when the data are not normally distributed. We further show that our alternative bootstrap methodology can be extended to testing Flury's (1988) hierarchy of covariance structure models. Where deviations from normality exist, we show, by simulation, that the normal theory log-likelihood ratio test statistic is less viable compared with our bootstrap methodology. For functional data, Ramsay and Silverman (2005) and Lee et al (2002) together provide four computational techniques for functional principal component analysis (PCA) followed by covariance structure estimation. When the smoothing method for smoothing individual profiles is based on using least squares cubic B-splines or regression splines, we find that the ensuing covariance matrix estimate suffers from loss of dimensionality. We show that ridge regression can be used to resolve this problem, but only for the discretisation and numerical quadrature approaches to estimation, and that choice of a suitable ridge parameter is not arbitrary. We further show the unsuitability of regression splines when deciding on the optimal degree of smoothing to apply to individual profiles. To gain insight into smoothing parameter choice for functional data, we compare kernel and spline approaches to smoothing individual profiles in a nonparametric regression context. Our simulation results justify a kernel approach using a new criterion based on predicted squared error. We also show by simulation that, when taking account of correlation, a kernel approach using a generalized cross validatory type criterion performs well. These data-based methods for selecting the smoothing parameter are illustrated prior to a functional PCA on a real data set.

In this dissertation, we introduce three projects in machine learning and reliability applications after the general introductions in Chapter 1. The first project concentrates on the multivariate sensory data, the second project is related to the bivariate recurrent process, and the third project introduces thermal index (TI) estimation in accelerated destructive degradation test (ADDT) data, in which an R package is developed. All three projects are related to and can be used to solve certain reliability problems. Specifically, in Chapter 2, we introduce a clustering method for multivariate functional data. In order to cluster the customized events extracted from multivariate functional data, we apply the functional principal component analysis (FPCA), and use a model based clustering method on a transformed matrix. A penalty term is imposed on the likelihood so that variable selection is performed automatically. In Chapter 3, we propose a covariate-adjusted model to predict next event in a bivariate recurrent event system. Inspired by geyser eruptions in Yellowstone National Park, we consider two event types and model their event gap time relationship. External systematic conditions are taken account into the model with covariates. The proposed covariate adjusted recurrent process (CARP) model is applied to the Yellowstone National Park geyser data. In Chapter 4, we compare estimation methods for TI. In ADDT, TI is an important index indicating the reliability of materials, when the accelerating variable is temperature. Three methods are introduced in TI estimations, which are least-squares method, parametric model and semi-parametric model. An R package is implemented for all three methods. Applications of R functions are introduced in Chapter 5 with publicly available ADDT datasets. Chapter 6 includes conclusions and areas for future works. / Doctor of Philosophy / This dissertation focuses on three projects that are all related to machine learning and reliability. Specifically, in the first project, we propose a clustering method designated for events extracted from multivariate sensory data. When the customized event is corresponding to reliability issues, such as aging procedures, clustering results can help us learn different event characteristics by examining events belonging to the same group. Applications include diving behavior segmentation based on vehicle sensory data, where multiple sensors are measuring vehicle conditions simultaneously and events are defined as vehicle stoppages. In our project, we also proposed to conduct sensor selection by three different penalizations including individual, variable and group. Our method can be applied for multi-dimensional sensory data clustering, when optimal sensor design is also an objective. The second project introduces a covariate-adjusted model accommodated to a bivariate recurrent event process system. In such systems, events can occur repeatedly and event occurrences for each type can affect each other with certain dependence. Events in the system can be mechanical failures which is related to reliability, while next event time and type predictions are usually of interest. Precise predictions on the next event time and type can essentially prevent serious safety and economy consequences following the upcoming event. We propose two CARP models with marginal behaviors as well as the dependence structure characterized in the bivariate system. We innovate to incorporate external information to the model so that model results are enhanced. The proposed model is evaluated in simulation studies, while geyser data from Yellowstone National Park is applied. In the third project, we comprehensively discuss three estimation methods for thermal index. They are the least-square method, parametric model and semi-parametric model. When temperature is the accelerating variable, thermal index indicates the temperature at which our materials can hold up to a certain time. In reality, estimating the thermal index precisely can prolong lifetime of certain product by choosing the right usage temperature. Methods evaluations are conducted by simulation study, while applications are applied to public available datasets.

The 1st and 2nd order Lee–Carter methods were compared with the Hyndman–Ullah method in regards to goodness of fit and forecasting ability of mortality rates. Swedish population data was used from the Human Mortality Database. The robust estimation property of the Hyndman–Ullah method was also tested with inclusion of the Spanish flu and a hypothetical scenario of the COVID-19 pandemic. After having presented the three methods and making several comparisons between the methods, it is concluded that the Hyndman–Ullah method is overall superior among the three methods with the implementation of the chosen dataset. Its robust estimation of mortality shocks could also be confirmed.