A motorway network is handled as a linear network. The purpose of this study is to highlight dangerous motorways via estimating the intensity of accidents and study its pattern across the UK motorway network. Two mechanisms have been adopted to achieve this aim. The first, the motorway-specific intensity is estimated by modelling the point pattern of the accident data using a homogeneous Poisson process. The homogeneous Poisson process is used to model all intensities but heterogeneity across motorways is incorporated using two-level hierarchical models. The data structure is multilevel since each motorway consists of junctions that are joined by grouped segments. In the second mechanism, the segment-specific intensity is estimated by modelling the point pattern of the accident data. The homogeneous Poisson process is used to model accident data within segments but heterogeneity across segments is incorporated using three-level hierarchical models. A Bayesian method via Markov Chain Monte Carlo simulation algorithms is used in order to estimate the unknown parameters in the models and a sensitivity analysis to the prior choice is assessed. The performance of the proposed models is checked through a simulation study and an application to traffic accidents in 2016 on the UK motorway network. The performance of the three-level frequentist model was poor. The deviance information criterion (DIC) and the widely applicable information criterion (WAIC) are employed to choose between the two-level Bayesian hierarchical model and the three-level Bayesian hierarchical model, where the results showed that the best fitting model was the three-level Bayesian hierarchical model.

To aid in resolving some of the ambiguity in the literature about the impact of different forms of WOM on brand performance, this dissertation investigates how WOM influences three consumer responses to WOM: purchase, WOM retransmission, and additional information search. The author investigates these questions by analyzing a database comprising more than three years of detailed WOM data from a unique, nationally representative panel merged with other secondary sources that provide various measures of brand strength (the American Consumer Satisfaction Index and Harris Interactive’s Equitrend). Using a series of hierarchical regression models, the results from this study reveal numerous insights into the contextual factors that moderate the impact of a WOM episode. For example, negative WOM about a brand has a larger absolute effect on consumer purchase intentions than positive WOM, but positive WOM has a larger positive effect on WOM retransmission than the positive effect of negative WOM. Offline WOM tends to exacerbate the effect of positive and negative brand sentiment on purchase intentions. WOM between stronger social ties tends to have greater impact on brand-related responses than WOM between weak ties, except in the case of motivating additional information search. The results also indicate that strong brands (those with higher levels of brand equity) tend to reap greater benefits from WOM. For example, negative, mixed, or neutral WOM has greater influence on purchase, and WOM from weak social ties about strong brands motivates higher levels of information search than when WOM from weak ties is about weaker brands.

To aid in resolving some of the ambiguity in the literature about the impact of different forms of WOM on brand performance, this dissertation investigates how WOM influences three consumer responses to WOM: purchase, WOM retransmission, and additional information search. The author investigates these questions by analyzing a database comprising more than three years of detailed WOM data from a unique, nationally representative panel merged with other secondary sources that provide various measures of brand strength (the American Consumer Satisfaction Index and Harris Interactive’s Equitrend). Using a series of hierarchical regression models, the results from this study reveal numerous insights into the contextual factors that moderate the impact of a WOM episode. For example, negative WOM about a brand has a larger absolute effect on consumer purchase intentions than positive WOM, but positive WOM has a larger positive effect on WOM retransmission than the positive effect of negative WOM. Offline WOM tends to exacerbate the effect of positive and negative brand sentiment on purchase intentions. WOM between stronger social ties tends to have greater impact on brand-related responses than WOM between weak ties, except in the case of motivating additional information search. The results also indicate that strong brands (those with higher levels of brand equity) tend to reap greater benefits from WOM. For example, negative, mixed, or neutral WOM has greater influence on purchase, and WOM from weak social ties about strong brands motivates higher levels of information search than when WOM from weak ties is about weaker brands.

Approved for public release; distribution in unlimited. / Some battlefield models have a component in them which models the time it takes for an observer to detect a target. Different observers may have different mean detection times due to various factors such as the type of sensor used, environmental conditions, fatigue of the observer, etc. Two parametric models for the distribution of time to target detection are considered which can incorporate these factors. Maximum likelihood estimation procedures for the parameters are described. Results of simulation experiments to study the small sample behavior of the estimators are presented. / http://archive.org/details/modelsfortargetd00baed / Major, Korean Air Force

Bayesian hierarchical models are effective tools for small area estimation by pooling small datasets together. The pooling procedures allow individual areas to “borrow strength” from each other to desirably improve the estimation. This work is an extension of Nandram and Choi (2002), NC, to perform inference on finite population proportions when there exists non-identifiability of the missing pattern for nonresponse in binary survey data. We review the small-area selection model (SSM) in NC which is able to incorporate the non-identifiability. Moreover, the proposed SSM, together with the individual-area selection model (ISM), and the small-area pattern-mixture model (SPM) are evaluated by real crime data in Stasny (1991). Furthermore, the methodology is compared to ISM and SPM using simulated small area datasets. Computational issues related to the MCMC are also discussed.

A probability distribution is a statistical function that describes the probability of possible outcomes in an experiment or occurrence. There are many different probability distributions that give the probability of an event happening, given some sample size n. An important question in statistics is to determine the distribution of the sum of independent random variables when the sample size n is fixed. For example, it is known that the sum of n independent Bernoulli random variables with success probability p is a Binomial distribution with parameters n and p: However, this is not true when the sample size is not fixed but a random variable. The goal of this thesis is to determine the distribution of the sum of independent random variables when the sample size is randomly distributed as a Poisson distribution. We will also discuss the mean and the variance of this unconditional distribution.

Maximal oxygen consumption (VO2max) is considered by many to be the best overall measure of an individual's cardiovascular health. Collecting the measurement, however, requires subjecting an individual to prolonged periods of intense exercise until their maximal level, the point at which their body uses no additional oxygen from the air despite increased exercise intensity, is reached. Collecting VO2max data also requires expensive equipment and great subject discomfort to get accurate results. Because of this inherent difficulty, it is often avoided despite its usefulness. In this research, we propose a set of Bayesian hierarchical models to predict VO2max levels in adolescents, ages 12 through 17, using less extreme measurements. Two models are developed separately, one that uses submaximal exercise data and one that uses physical fitness questionnaire data. The best submaximal model was found to include age, gender, BMI, heart rate, rate of perceived exertion, treadmill miles per hour, and an interaction between age and heart rate. The second model, designed for those with physical limitations, uses age, gender, BMI, and two separate questionnaire results measuring physical activity levels and functional ability levels, as well as an interaction between the physical activity level score and gender. Both models use separate model variances for males and females.

Growth plays a key role in regulating ecological and population dynamics. Life history characteristics such as age at maturity, fecundity and age and size at migration are tightly linked to growth rate. In addition, size can often determine survival and individual breeding success. To fully understand the process of growth it is important to understand the mechanisms that drive growth rates. In Atlantic salmon, growth is critical in determining life history pathways. Models to estimate growth could be useful in the broader context of predicting population dynamics. In this dissertation I investigate the growth process in juvenile Atlantic salmon (Salmo salar). I first used basic modeling approaches and data on individually tagged salmon to investigate the assumptions of different growth metrics. I demonstrate the size-dependency in certain growth metrics when assumptions are violated. Next, I assessed the efficacy of linear mixed effects models in modeling length-weight relationships from longitudinal data. I show that combining a random effects approach with third order polynomials can be an effective way to model length-weight relationships with mark-recapture data. I extend this hierarchical modeling approach to develop a Bayesian growth model. With limited assumptions, I derive a relatively simple discrete time model from von Bertalanffy growth that includes a nonparametric seasonal growth function. The linear dynamics of this model allow for efficient estimation of parameters in a Bayesian framework. Finally, I investigated the role of life history in driving compensatory growth patterns in immature Atlantic salmon. This analysis demonstrates the importance of considering life history as a mechanism in compensatory growth. Information provided in this dissertation will help provide ecologists with statistical tools to estimate growth rates, estimate length-weight relationships, and forecast growth from mark-recapture data. In addition, comparisons of seasonal growth within and among life history groups and within and among tributaries should make a valuable contribution to the important literature on growth in Atlantic salmon.

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.

Global marketing managers are keenly interested in being able to predict the sales of their new products. Understanding how a product is adopted over time allows the managers to optimally allocate their resources. With the world becoming ever more global, there are strong and complex interactions between the countries in the world. My work explores how to describe the relationship between those countries and determines the best way to leverage that information to improve the sales predictions. In Chapter II, I describe how diffusion speed has changed over time. The most recent major study on this topic, by Christophe Van den Bulte, investigated new product di ffusions in the United States. Van den Bulte notes that a similar study is needed in the international context, especially in developing countries. Additionally, his model contains the implicit assumption that the diffusion speed parameter is constant throughout the life of a product. I model the time component as a nonparametric function, allowing the speed parameter the flexibility to change over time. I find that early in the product's life, the speed parameter is higher than expected. Additionally, as the Internet has grown in popularity, the speed parameter has increased. In Chapter III, I examine whether the interactions can be described through a reference hierarchy in addition to the cross-country word-of-mouth eff ects already in the literature. I also expand the word-of-mouth e ffect by relating the magnitude of the e ffect to the distance between the two countries. The current literature only applies that e ffect equally to the n closest countries (forming a neighbor set). This also leads to an analysis of how to best measure the distance between two countries. I compare four possible distance measures: distance between the population centroids, trade ow, tourism ow, and cultural similarity. Including the reference hierarchy improves the predictions by 30 percent over the current best model. Finally, in Chapter IV, I look more closely at the Bass Diffusion Model. It is prominently used in the marketing literature and is the base of my analysis in Chapter III. All of the current formulations include the implicit assumption that all the regression parameters are equal for each country. One dollar increase in GDP should have more of an eff ect in a poor country than in a rich country. A Dirichlet process prior enables me to cluster the countries by their regression coefficients. Incorporating the distance measures can improve the predictions by 35 percent in some cases.