Level crossing times and their applications in finance are of importance, given certain threshold levels that represent the "desirable" or "sell" values of a stock. In this thesis, we make use of Wald's lemmas and various deep results from renewal theory, in the context of finance, in modelling the growth of a portfolio of stocks. Several models are employed .

Multiple regression models play an important role in analyzing and making predictions about data. Prediction accuracy becomes lower when two or more explanatory variables in the model are highly correlated. One solution is to use ridge regression. The purpose of this thesis is to study the performance of available ridge regression estimators for Poisson regression models in the presence of moderately to highly correlated variables. As performance criteria, we use mean square error (MSE), mean absolute percentage error (MAPE), and percentage of times the maximum likelihood (ML) estimator produces a higher MSE than the ridge regression estimator. A Monte Carlo simulation study was conducted to compare performance of the estimators under three experimental conditions: correlation, sample size, and intercept. It is evident from simulation results that all ridge estimators performed better than the ML estimator. We proposed new estimators based on the results, which performed very well compared to the original estimators. Finally, the estimators are illustrated using data on recreational habits.

A philosophic account of quantum physics. The thesis is divided into two parts. Part I is dedicated to laying the groundwork of quantum physics, and explaining some of the primary difficulties. Subjects of interest will include the principle of locality, the quantum uncertainty principle, and Einstein's criterion for reality. Quantum dilemmas discussed include the double-slit experiment, observations of spin and polarization, EPR, and Bell's theorem. The first part will argue that mathematical-physical descriptions of the world fall short of explaining the experimental observations of quantum phenomenon. The problem, as will be argued, is framework of the physical descriptive schema. Part I includes in-depth discussions of mathematical principles. Part II will discuss the Copenhagen interpretation as put forth by its founders. The Copenhagen interpretation will be expressed as a paradox: The classical physical language cannot describe quantum phenomenon completely and with certainty, yet this language is the only possible method of articulating the physical world. The paradox of Copenhagen will segway into Kant's critique of metaphysics. Kant's understanding of causality, things-in-themselves, and a priori synthetic metaphysics. The thesis will end with a conclusion of the quantum paradox by juxtaposing anti-materialist Martin Heidegger with quantum founder Werner Heisenberg. Our conclusion will be primarily a discussion of how we understand the world, and specifically how our understanding of the world creates potential for truth.

There is a shared desire among public and private sectors to make more reliable predictions, accurate mapping, and appropriate scaling of soil moisture and associated parameters across landscapes. A discrepancy often exists between the scale at which soil hydrologic properties are measured and the scale at which they are modeled for management purposes. Moreover, little is known about the relative importance of hydrologic modeling parameters as soil moisture fluctuates with time. More research is needed to establish which observation scales in space and time are optimal for managing soil moisture variation over large spatial extents and how these scales are affected by fluctuations in soil moisture content with time. This research fuses high resolution geoelectric and light detection and ranging (LiDAR) as auxiliary measures to support sparse direct soil sampling over a 40 hectare inner BluegrassKentucky (USA) landscape. A Veris 3100 was used to measure shallow and deep apparent electrical conductivity (aEC) in tandem with soil moisture sampling on three separate dates with ascending soil moisture contents ranging from plant wilting point to near field capacity. Terrain attributes were produced from 2010 LiDAR ground returns collected at ≤1 m nominal pulse spacing. Exploratory statistics revealed several variables best associate with soil moisture, including terrain features (slope, profile curvature, and elevation), soil physical and chemical properties (calcium, cation exchange capacity, organic matter, clay and sand) and aEC for each date. Multivariate geostatistics, time stability analyses, and spatial regression were performed to characterize scale-dependent soil moisture patterns in space with time to determine which soil-terrain parameters influence soil moisture distribution. Results showed that soil moisture variation was time stable across the landscape and primarily associated with long-range (~250 m) soil physicochemical properties. When the soils approached field capacity, however, there was a shift in relative importance from long-range soil physicochemical properties to short-range (~70 m) terrain attributes, albeit this shift did not cause time instability. Results obtained suggest soil moisture’s interaction with soil-terrain parameters is time dependent and this dependence influences which observation scale is optimal to sample and manage soil moisture variation.

The Connecticut River watershed is experiencing a rapid invasion of aggressive non-native plant species, which threaten watershed function and structure. Volunteer-based monitoring programs such as the University of Massachusetts’ OutSmart Invasives Species Project, Early Detection Distribution Mapping System (EDDMapS) and the Invasive Plant Atlas of New England (IPANE) have gathered valuable invasive plant data. These programs provide a unique opportunity for researchers to model invasive plant species utilizing citizen-sourced data. This study took advantage of these large data sources to model invasive plant distribution and to determine environmental and biophysical predictors that are most influential in dispersion, and to identify a suitable presence-only model for use by conservation biologists and land managers at varying spatial scales. This research focused on the invasive plant species of high interest - Japanese stiltgrass (Mircostegium vimineum). This was identified as a threat by U.S. Fish and Wildlife Service refuge biologists and refuge managers, but for which no mutli-scale practical and systematic approach for detection, has yet been developed. Environmental and biophysical variables include factors directly affecting species physiology and locality such as annual temperatures, growing degree days, soil pH, available water supply, elevation, closeness to hydrology and roads, and NDVI. Spatial scales selected for this study include New England (regional), the Connecticut River watershed (watershed), and the U.S. Fish and Wildlife, Silvio O. Conte National Fish and Wildlife Refuge, Salmon River Division (local). At each spatial scale, three software programs were implemented: maximum entropy habitat model by means of the MaxEnt software, ecological niche factor analysis (ENFA) using Openmodeller software, and a generalized linear model (GLM) employed in the statistical software R. Results suggest that each modeling algorithm performance varies among spatial scales. The best fit modeling software designated for each scale will be useful for refuge biologists and managers in determining where to allocate resources and what areas are prone to invasion. Utilizing the regional scale results, managers will understand what areas on a broad-scale are at risk of M. vimineum invasion under current climatic variables. The watershed-scale results will be practical for protecting areas designated as most critical for ensuring the persistence of rare and endangered species and their habitats. Furthermore, the local-scale, or fine-scale, analysis will be directly useful for on-the-ground conservation efforts. Managers and biologists can use results to direct resources to areas where M. vimineum is most likely to occur to effectively improve early detection rapid response (EDRR).

Diabetes is a major risk factor for the development of cataract [3,14,20,22]. In this thesis, we create a model that allows us to understand the incidence of one disease in the context of another; in particular, cataract in the presence of diabetes. The World Health Organization's Vision 2020 blindness-prevention initiative administers surgeries to remove cataracts, the leading cause of blindness worldwide [24]. One of the geographic areas most impacted by cataract-related blindness is Sub-Saharan Africa. In order to plan the number of surgeries to administer, the World Health Organization uses data on cataract prevalence. However, an estimation of the incidence of cataract is more useful than prevalence data for the purpose of resource planning. In 2012, Dray and Williams developed a method for estimating incidence based on prevalence data [5]. Incidence estimates can be further refined by considering associated risk factors such as diabetes. We therefore extend the Dray and Williams model to include diabetes prevalence when calculating cataract incidence estimates. We explore two possible approaches to our model construction, one a detailed extension, and the other, a simplification of that extension. We provide a discussion comparing the two approaches.

The importance of checking the normality assumption in most statistical procedures especially parametric tests cannot be over emphasized as the validity of the inferences drawn from such procedures usually depend on the validity of this assumption. Numerous methods have been proposed by different authors over the years, some popular and frequently used, others, not so much. This study addresses the performance of eighteen of the available tests for different sample sizes, significance levels, and for a number of symmetric and asymmetric distributions by conducting a Monte-Carlo simulation. The results showed that considerable power is not achieved for symmetric distributions when sample size is less than one hundred and for such distributions, the kurtosis test is most powerful provided the distribution is leptokurtic or platykurtic. The Shapiro-Wilk test remains the most powerful test for asymmetric distributions. We conclude that different tests are suitable under different characteristics of alternative distributions.

The determinants of health care use among rural, low-income mothers and their children were assessed using a multi-state, longitudinal data set, Rural Families Speak. The results indicate that rural mothers’ decisions regarding health care utilization for themselves and for their child can be best modeled using a simultaneous systems approach to negative binomial regression. Mothers’ visits to a health care provider increased with higher self-assessed depression scores, increased number of child’s doctor visits, greater numbers of total children in the household, greater numbers of chronic conditions, need for prenatal or post-partum care, development of a new medical condition, and having health insurance (Medicaid/equivalent and HMO/private). Child’s visits to a health care provider, on the other hand, increased with greater numbers of chronic conditions, development of a new medical condition, and increased mothers’ visits to a doctor. Child’s utilization of pediatric health care services decreased with higher levels of maternal depression, greater numbers of total children in the household, if the mother had HMO/private health care coverage, if the mother was pregnant, and if the mother was Latina/African American. Mother’s use of health care services decreased with her age, increased number of child’s chronic conditions, income as a percent of the federal poverty line, and if child had HMO/private health care insurance. The study expands the econometric techniques available for assessing maternal and pediatric health care use and the results contribute to an understanding of how rural, low-income mothers choose the level of health care services use for themselves and for their child. Additionally, the results would assist in formulating policies to reorient the type of health care services provided to this vulnerable population.

This paper has attempted to determine if there is a significant relationship between self-determination and client outcomes among the homeless. The study has been based upon the conceptual framework set forth in Self-Determination Theory. The purpose of the study was to explore the relationship between self-determination and client outcomes among the homeless. Using a data collection instrument, based on empirically validated instrumentation, clients from several homeless service providers in the City of San Bernardino were assessed for the level of self-determination and autonomy support they experience within these agencies. Outcome measures included such things as whether the client was going to school, had a job and had a bank account. Overall, the results of the study were inconclusive, though some interesting post hoc observations were made. It was the primary aim of this paper to increase the knowledge base of the local network of homeless service providers and to promote the compassionate, equitable, and dignified treatment of the population they serve.

Atmospheric features, such as tropical cyclones, act as a driving mechanism for many of the major hazards affecting coastal areas around the world. Accurate and efficient quantification of tropical cyclone surge hazard is essential to the development of resilient coastal communities, particularly given continued sea level trend concerns. Recent major tropical cyclones that have impacted the northeastern portion of the United States have resulted in devastating flooding in New York City, the most densely populated city in the US. As a part of national effort to re-evaluate coastal inundation hazards, the Federal Emergency Management Agency used the Joint Probability Method to re-evaluate surge hazard probabilities for Flood Insurance Rate Maps in the New York – New Jersey coastal areas, also termed the New York Bight. As originally developed, this method required many combinations of storm parameters to statistically characterize the local climatology for numerical model simulation. Even though high-performance computing efficiency has vastly improved in recent years, researchers have utilized different “Optimal Sampling” techniques to reduce the number of storm simulations needed in the traditional Joint Probability Method. This manuscript presents results from the simulation of over 350 synthetic tropical cyclones designed to produce significant surge in the New York Bight using the hydrodynamic Advanced Circulation numerical model, bypassing the need for Optimal Sampling schemes. This data set allowed for a careful assessment of joint probability distributions utilized for this area and the impacts of current assumptions used in deriving new flood-risk maps for the New York City area.