There is convincing evidence that demonstrates traumatic stress and aggressive behavior are highly related among adolescents. The evidence is less clear regarding the direction of this relation. The purpose of this study was to examine the reciprocal longitudinal relations between physical aggression and traumatic stress among a predominantly African American sample of middle school students. Support was found for traumatic stress predicting increased levels of physical aggression across the winter to the spring of the sixth grade for boys and across all waves from the fall of the seventh grade to the fall of the eighth grade for both boys and girls. Conversely, physical aggression during the winter of the sixth grade predicted a decrease in traumatic stress in the spring of the sixth grade for both boys and girls. These findings suggest that interventions may need to incorporate skills that are aligned with trauma-informed care practices in order to reduce traumatic stress and physical aggression among adolescents.

As compared to short-term forecasting (e.g., 1 day), it is often challenging to accurately forecast the volume of precipitation in a medium-term horizon (e.g., 1 week). As a result, fluctuations in water inflow can trigger generation shortage and electricity price spikes in a power system with major or predominant hydro resources. In this paper, we study a two-stage robust scheduling approach for a hydrothermal power system. We consider water inflow uncertainty and employ a vector autoregressive (VAR) model to represent its seasonality and accordingly construct an uncertainty set in the robust optimization approach. We design a Benders' decomposition algorithm to solve this problem. Results are presented for the proposed approach on a real-world case study.

This thesis introduces the concept of an encoder-decoder neural network and develops architectures for the construction of such networks. Encoder-decoder neural networks are probabilistic conditional generative models of high-dimensional structured items such as natural language utterances and natural images. Encoder-decoder neural networks estimate a probability distribution over structured items belonging to a target set conditioned on structured items belonging to a source set. The distribution over structured items is factorized into a product of tractable conditional distributions over individual elements that compose the items. The networks estimate these conditional factors explicitly. We develop encoder-decoder neural networks for core tasks in natural language processing and natural image and video modelling. In Part I, we tackle the problem of sentence modelling and develop deep convolutional encoders to classify sentences; we extend these encoders to models of discourse. In Part II, we go beyond encoders to study the longstanding problem of translating from one human language to another. We lay the foundations of neural machine translation, a novel approach that views the entire translation process as a single encoder-decoder neural network. We propose a beam search procedure to search over the outputs of the decoder to produce a likely translation in the target language. Besides known recurrent decoders, we also propose a decoder architecture based solely on convolutional layers. Since the publication of these new foundations for machine translation in 2013, encoder-decoder translation models have been richly developed and have displaced traditional translation systems both in academic research and in large-scale industrial deployment. In services such as Google Translate these models process in the order of a billion translation queries a day. In Part III, we shift from the linguistic domain to the visual one to study distributions over natural images and videos. We describe two- and three- dimensional recurrent and convolutional decoder architectures and address the longstanding problem of learning a tractable distribution over high-dimensional natural images and videos, where the likely samples from the distribution are visually coherent. The empirical validation of encoder-decoder neural networks as state-of- the-art models of tasks ranging from machine translation to video prediction has a two-fold significance. On the one hand, it validates the notions of assigning probabilities to sentences or images and of learning a distribution over a natural language or a domain of natural images; it shows that a probabilistic principle of compositionality, whereby a high- dimensional item is composed from individual elements at the encoder side and whereby a corresponding item is decomposed into conditional factors over individual elements at the decoder side, is a general method for modelling cognition involving high-dimensional items; and it suggests that the relations between the elements are best learnt in an end-to-end fashion as non-linear functions in distributed space. On the other hand, the empirical success of the networks on the tasks characterizes the underlying cognitive processes themselves: a cognitive process as complex as translating from one language to another that takes a human a few seconds to perform correctly can be accurately modelled via a learnt non-linear deterministic function of distributed vectors in high-dimensional space.

Interest in mediation analysis has increased over time, with particular excitement in the social and behavioral sciences. A mediator is defined as an intermediate in the causal sequence between an independent and dependent variable. Previous research has demonstrated that the cross-sectional form of mediation analysis is inherently flawed, evidenced by the inability of the cross-sectional mediation model to account for temporal precedence and estimation of the indirect effect being biased in nearly all situations. For these reasons, a longitudinal model is recommended. However, a method for determining the exact time points to measure the variables used in mediation analysis has not been adequately examined. In this study, we examined methods for determining an appropriate time lag when designing a mediation study. The methods implemented include correlation analysis, the quadratic and exponential forms of the lag as a moderator approach, and knot estimation using basis splines. The data for the study was simulated for three distinct trends generated using a linear piecewise model, a sigmoid model, and a sigmoid piecewise model. Additionally, two sampling approaches, an intense sampling approach and a three-measure approach, were examined as well as six sample sizes and three effect sizes for the total effect on the outcome. The estimation methods were additionally compared by considering different types of error structures used in data generation as well as by examining equal and unequal time lag lengths between the predictor and mediator, and the mediator and outcome. The intent of the study is to provide methods so that researchers can estimate the best time to evaluate mediator and outcome measurements that will be used in mediation analysis. The results from this study showed that the best estimation method varied depending on the lag being estimated, the sampling approach, and the length of the lag. However, the knot estimation approach worked reasonably well in most scenarios considered even with small sample sizes of 5 or 10 per group. The findings from this study have the potential to improve study design for research implementing longitudinal mediation analysis by reducing bias in the estimate of the indirect effect when adequate time points are used.

Water quality and river/stream ecosystems are important for all living creatures. To protect human health, aquatic life and the surrounding ecosystem, a considerable amount of time and money has been spent on sampling and monitoring streams and rivers. Water quality monitoring and analysis can help researchers predict and learn from natural processes in the environment and determine human impacts on an ecosystem. Measurements such as temperature, pH, nitrogen concentration, algae and fish count collected along the network are all important factors in water quality analysis. The main purposes of the statistical analysis in this thesis are (1) to assess the relationship between the variable measured in the water (response variable) and other variables that describe either the locations on/along the stream network or certain characteristics at each location (explanatory variable), and (2) to assess the degree of similarity between the response variable values measured at different locations of the stream, i.e. spatial dependence structure. It is commonly accepted that measurements taken at two locations close to each other should have more similarity than locations far away. However, this is not always true for observations from stream networks. Observations from two sites that do not share water flow could be independent of each other even if they are very close in terms of stream distance, especially those observations taken on objects that move passively with the water flow. To model stream network data correctly, it is important to quantify the strength of association between observations from sites that do not share water.

This thesis is mainly concerned with the estimation of parameters of a first-order Smooth Threshold Autoregressive (STAR) model with delay parameter one. The estimation procedures include classical and Bayesian methods from a parametric and a semiparametric point of view.As the theoretical importance of stationarity is a primary concern in estimation of time series models, we begin the thesis with a thorough investigation of necessary or sufficient conditions for ergodicity of a first-order STAR process followed by the necessary and sufficient conditions for recurrence and classification for null-recurrence and transience.The estimation procedure is started by using Bayesian analysis which derives posterior distributions of parameters with a noninformative prior for the STAR models of order p. The predictive performance of the STAR models using the exact one-step-ahead predictions along with an approximation to multi-step-ahead predictive density are considered. The theoretical results are then illustrated by simulated data sets and the well- known Canadian lynx data set.The parameter estimation obtained by conditional least squares, maximum likelihood, M-estimator and estimating functions are reviewed together with their asymptotic properties and presented under the classical and parametric approaches. These estimators are then used as preliminary estimators for obtaining adaptive estimates in a semiparametric setting. The adaptive estimates for a first-order STAR model with delay parameter one exist only for the class of symmetric error densities. At the end, the numerical results are presented to compare the parametric and semiparametric estimates of this model.

<p>In this paper, we study the industrial production index of Sweden from Jan, 2000 to latest Feb, 2010. We find out there is a structural break at time point Dec, 2007, when the global financial crisis burst out first in U.S then spread to Europe. To model the industrial production index, one of the business cycle indicators which may behave nonlinear feature suggests utilizing a smooth transition autoregressive (STAR) model. Following the procedures given by Teräsvirta (1994), we carry out the linearity test against the STAR model, determine the delay parameter and choose between the LSTAR model and the ESTAR model. The results from the estimated model suggest the STAR model is better performing than the linear autoregressive model.</p>

In this paper, we study the industrial production index of Sweden from Jan, 2000 to latest Feb, 2010. We find out there is a structural break at time point Dec, 2007, when the global financial crisis burst out first in U.S then spread to Europe. To model the industrial production index, one of the business cycle indicators which may behave nonlinear feature suggests utilizing a smooth transition autoregressive (STAR) model. Following the procedures given by Teräsvirta (1994), we carry out the linearity test against the STAR model, determine the delay parameter and choose between the LSTAR model and the ESTAR model. The results from the estimated model suggest the STAR model is better performing than the linear autoregressive model.

Time of Flight Diffraction (TOFD) is one of the most accurate ultrasonic methods for crack detection and sizing in pipeline girth welds. Its performance, however, is limited by the temporal resolution of the signal. In this thesis, we develop a signal processing method based on autoregressive spectral extrapolation to improve the temporal resolution of ultrasonic signals. The original method cannot be used in industrial applications since its performance is highly dependent on selection of a number of free parameters. This method is modified by optimizing its various steps and limiting the number of free parameters, and an automated algorithm for selection of values for the remaining free parameters is proposed based on the analysis of a large set of synthetic signals. The performance of the final algorithm is evaluated using experimental data; it is shown that the uncertainty in crack sizing accuracy can be reduced by as much as 80%. Furthermore, the proposed method is shown to be capable of resolving overlapping echoes; therefore, smaller cracks that have echoes that are not clearly resolved in the raw signal, can be detected and sized in the enhanced signal.

Time of Flight Diffraction (TOFD) is one of the most accurate ultrasonic methods for crack detection and sizing in pipeline girth welds. Its performance, however, is limited by the temporal resolution of the signal. In this thesis, we develop a signal processing method based on autoregressive spectral extrapolation to improve the temporal resolution of ultrasonic signals. The original method cannot be used in industrial applications since its performance is highly dependent on selection of a number of free parameters. This method is modified by optimizing its various steps and limiting the number of free parameters, and an automated algorithm for selection of values for the remaining free parameters is proposed based on the analysis of a large set of synthetic signals. The performance of the final algorithm is evaluated using experimental data; it is shown that the uncertainty in crack sizing accuracy can be reduced by as much as 80%. Furthermore, the proposed method is shown to be capable of resolving overlapping echoes; therefore, smaller cracks that have echoes that are not clearly resolved in the raw signal, can be detected and sized in the enhanced signal.