BACKGROUND: Chronic ankle instability (CAI) patients have varying levels of mechanical and sensorimotor impairments that may lead to disparate functional movement patterns. Current literature on landing biomechanics in a CAI population, however, considers all patients as a homogeneous group. In our prior work, we identified 6 subgroups of movement patterns using lower extremity kinematics during a landing/cutting task and that showed promise in furthering understanding of movement patterns in a laboratory-based environment. To increase the utility of this methodology in clinical settings, there is a need to find easily administered clinical tests that can help identify multiple subgroups of movement patterns in a CAI population. The purpose of the present study was to identify clinical tests that would help identify frontal and sagittal kinematic movement pattern subgroups during a landing/cutting task. We hypothesized that clinical tests would help predict group assignment; which CAI patient is assigned to frontal and sagittal kinematic movement pattern subgroups, respectively. METHODS: We recruited 100 CAI patients from a university population. We used three-dimensional instrumented motion analysis to capture ankle, knee and hip kinematics as subjects performed a single-leg maximal jump landing/cutting task. We used sagittal and frontal joint angle waveforms to group CAI patients. We then used 12 demographic and clinical measures to predict these subgroups of CAI. These consisted of gender, Star Excursion Balance Test-Anterior (SEBT-ANT), Biodex static balance, figure 8 hop, triple crossover hop, dorsiflexion range of motion (DFROM), number of failed trials, body mass index, a score of Foot and Ankle Ability Measure-Activities of Daily Living (FAAM-ADL), a score of FAAM-Sports, number of "yes" responses on Modified Ankle Instability Index, and number of previous ankle sprains. First, we used functional principal component analysis to create representative curves for each CAI patient and plane from the 3 lower extremity joint angles. We then used these curves as inputs to a predictor-dependent product partition model to cluster each CAI patient to unique subgroups. Finally, we used a multinomial prediction model to examine the accuracy of predicting group membership from demographic and clinical metrics. RESULTS: The predictor-dependent product partition model identified 4 frontal and 5 sagittal movement pattern subgroups. Six predictors (e.g., gender, SEBT-ANT, figure 8 hop, triple crossover hop, DFROM, and FAAM-ADL) predicted group membership with 55.7% accuracy for frontal subgroups. Ten predictors (minus Biodex static balance and number of previous ankle sprains) predicted group membership with 59% accuracy for sagittal subgroups. CONCLUSION: Novel statistical analyses allowed us to predict group membership for multiple frontal and sagittal kinematic movement patterns during landing/cutting using a series of clinical predictors. However, due to relatively lower accuracy (56–59% accuracy), the clinical utility of the current prediction model may be limited. Future work should consider including other clinical predictors to maximize prediction accuracy for identifying multiple kinematic movement patterns during a landing/cutting task.

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<p>An important question in biology is the identification of functionally important sites and regions in proteins. A variety of statistical phylogenetic models have been developed to predict functionally important protein sites, e.g. ligand binding sites or protein-protein interaction interfaces, by comparing sequences from different species. However, most of the existing methods ignore the spatial clustering of functionally important sites in protein tertiary/primary structures, which significantly reduces their power to identify functionally important regions in proteins. In this thesis, we present several new statistical phylogenetic models for inferring functionally important protein regions in which Gaussian processes or hidden Markov models are used as prior distributions to model the spatial correlation of evolutionary patterns in protein tertiary/ primary structures. Both simulation studies and empirical data analyses suggest that these new models outperform classic phylogenetic models. Therefore, these new models may be useful tools for extracting functional insights from protein sequences and for guiding mutagenesis experiments. Furthermore, the new methodologies developed in these models may also be used in the development of new statistical models to answer other important questions in phylogenetics and molecular evolution.</p> / Doctor of Philosophy (PhD)

Ecological data is often fraught with many problems such as Missing Data and Spatial Correlation. In this dissertation we use a data set collected by the Ohio EPA as motivation for studying techniques to address these problems. The data set is concerned with the benthic health of Ohio's waterways. A new method for incorporating covariate structure and missing data mechanisms into missing data analysis is considered. This method allows us to detect relationships other popular methods do not allow. We then further extend this method into model selection. In the special case where the unobserved covariates are assumed normally distributed we use the Bayesian Model Averaging method to average the models, select the highest probability model and do variable assessment. Accuracy in calculating the posterior model probabilities using the Laplace approximation and an approximation based on the Bayesian Information Criterion (BIC) are explored. It is shown that the Laplace approximation is superior to the BIC based approximation using simulation. Finally, Hierarchical Spatial Linear Models are considered for the data and we show how to combine analysis which have spatial correlation within and between clusters. / Ph. D.

Bayesian Model Averaging (BMA) is a new area in modern applied statistics that provides data analysts with an efficient tool for discovering promising models and obtaining esti-mates of their posterior probabilities via Markov chain Monte Carlo (MCMC). These probabilities can be further used as weights for model averaged predictions and estimates of the parameters of interest. As a result, variance components due to model selection are estimated and accounted for, contrary to the practice of conventional data analysis (such as, for example, stepwise model selection). In addition, variable activation probabilities can be obtained for each variable of interest. This dissertation is aimed at connecting BMA and various ramifications of the multivari-ate technique called Reduced-Rank Regression (RRR). In particular, we are concerned with Canonical Correspondence Analysis (CCA) in ecological applications where the data are represented by a site by species abundance matrix with site-specific covariates. Our goal is to incorporate the multivariate techniques, such as Redundancy Analysis and Ca-nonical Correspondence Analysis into the general machinery of BMA, taking into account such complicating phenomena as outliers and clustering of observations within a single data-analysis strategy. Traditional implementations of model averaging are concerned with selection of variables. We extend the methodology of BMA to selection of subgroups of observations and im-plement several approaches to cluster and outlier analysis in the context of the multivari-ate regression model. The proposed algorithm of cluster analysis can accommodate re-strictions on the resulting partition of observations when some of them form sub-clusters that have to be preserved when larger clusters are formed. / Ph. D.

This study suggests a two-step approach to identifying and interpreting regional convergence clubs in Europe. The first step involves identifying the number and composition of clubs using a space-time panel data model for annual income growth rates in conjunction with Bayesian model comparison methods. A second step uses a Bayesian space-time panel data model to assess how changes in the initial endowments of variables (that explain growth) impact regional income levels over time. These dynamic trajectories of changes in regional income levels over time allow us to draw inferences regarding the timing and magnitude of regional income responses to changes in the initial conditions for the clubs that have been identified in the first step. This is in contrast to conventional practice that involves setting the number of clubs ex ante, selecting the composition of the potential convergence clubs according to some a priori criterion (such as initial per capita income thresholds for example), and using cross-sectional growth regressions for estimation and interpretation purposes. (authors' abstract)

Sequential experimentation is often employed in process optimization wherein a series of small experiments are run successively in order to determine which experimental factor levels are likely to yield a desirable response. Although there currently exists a framework for identifying optimal follow-up designs after an initial experiment has been run, the accepted methods frequently point to multiple designs leaving the practitioner to choose one arbitrarily. In this thesis, we apply preposterior analysis and Bayesian model-averaging to develop a methodology for further discriminating between optimal follow-up designs while controlling for both parameter and model uncertainty.

This paper presents a comprehensive review and comparison of five computational methods for Bayesian model selection, based on MCMC simulations from posterior model parameter distributions. We apply these methods to a well-known and important class of models in financial time series analysis, namely GARCH and GARCH-t models for conditional return distributions (assuming normal and t-distributions). We compare their performance vis--vis the more common maximum likelihood-based model selection on both simulated and real market data. All five MCMC methods proved feasible in both cases, although differing in their computational demands. Results on simulated data show that for large degrees of freedom (where the t-distribution becomes more similar to a normal one), Bayesian model selection results in better decisions in favour of the true model than maximum likelihood. Results on market data show the feasibility of all model selection methods, mainly because the distributions appear to be decisively non-Gaussian. / Series: Report Series SFB "Adaptive Information Systems and Modelling in Economics and Management Science"

<div>This thesis consists of two separate topics, which include the use of piecewise helical models for the inference of 3D spatial organizations of chromosomes and new approaches for general statistical inference. The recently developed Hi-C technology enables a genome-wide view of chromosome</div><div>spatial organizations, and has shed deep insights into genome structure and genome function. However, multiple sources of uncertainties make downstream data analysis and interpretation challenging. Specically, statistical models for inferring three-dimensional (3D) chromosomal structure from Hi-C data are far from their maturity. Most existing methods are highly over-parameterized, lacking clear interpretations, and sensitive to outliers. We propose a parsimonious, easy to interpret, and robust piecewise helical curve model for the inference of 3D chromosomal structures</div><div>from Hi-C data, for both individual topologically associated domains and whole chromosomes. When applied to a real Hi-C dataset, the piecewise helical model not only achieves much better model tting than existing models, but also reveals that geometric properties of chromatin spatial organization are closely related to genome function.</div><div><br></div><div><div>For potential applications in big data analytics and machine learning, we propose to use deep neural networks to automate the Bayesian model selection and parameter estimation procedures. Two such frameworks are developed under different scenarios. First, we construct a deep neural network-based Bayes estimator for the parameters of a given model. The neural Bayes estimator mitigates the computational challenges faced by traditional approaches for computing Bayes estimators. When applied to the generalized linear mixed models, the neural Bayes estimator</div><div>outperforms existing methods implemented in R packages and SAS procedures. Second, we construct a deep convolutional neural networks-based framework to perform</div><div>simultaneous Bayesian model selection and parameter estimation. We refer to the neural networks for model selection and parameter estimation in the framework as the</div><div>neural model selector and parameter estimator, respectively, which can be properly trained using labeled data systematically generated from candidate models. Simulation</div><div>study shows that both the neural selector and estimator demonstrate excellent performances.</div></div><div><br></div><div><div>The theory of Conditional Inferential Models (CIMs) has been introduced to combine information for efficient inference in the Inferential Models framework for priorfree</div><div>and yet valid probabilistic inference. While the general theory is subject to further development, the so-called regular CIMs are simple. We establish and prove a</div><div>necessary and sucient condition for the existence and identication of regular CIMs. More specically, it is shown that for inference based on a sample from continuous</div><div>distributions with unknown parameters, the corresponding CIM is regular if and only if the unknown parameters are generalized location and scale parameters, indexing</div><div>the transformations of an affine group.</div></div>

The expected equity premium is an important parameter in many financial models, especially within portfolio optimization. A good forecast of the future equity premium is therefore of great interest. In this thesis we seek to forecast the equity premium, use it in portfolio optimization and then give evidence on how sensitive the results are to estimation errors and how the impact of these can be minimized. Linear prediction models are commonly used by practitioners to forecast the expected equity premium, this with mixed results. To only choose the model that performs the best in-sample for forecasting, does not take model uncertainty into account. Our approach is to still use linear prediction models, but also taking model uncertainty into consideration by applying Bayesian model averaging. The predictions are used in the optimization of a portfolio with risky assets to investigate how sensitive portfolio optimization is to estimation errors in the mean vector and covariance matrix. This is performed by using a Monte Carlo based heuristic called portfolio resampling. The results show that the predictive ability of linear models is not substantially improved by taking model uncertainty into consideration. This could mean that the main problem with linear models is not model uncertainty, but rather too low predictive ability. However, we find that our approach gives better forecasts than just using the historical average as an estimate. Furthermore, we find some predictive ability in the the GDP, the short term spread and the volatility for the five years to come. Portfolio resampling proves to be useful when the input parameters in a portfolio optimization problem is suffering from vast uncertainty.