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Informed forest management requires accurate, up-to-date information. Ground-based forest inventory is commonly conducted to generate estimates of forest characteristics with a predetermined level of statistical confidence. As the importance of monitoring forest resources has increased, budgetary and logistical constraints often limit the resources needed for precise estimates. In this research, the incorporation of ancillary information in planted loblolly pine (Pinus taeda L.) forest inventory was investigated. Additionally, a simulation study using synthetic populations provided the basis for investigating the effects of plot and stand-level inventory aggregations on predictions and projections of future forest conditions. Forest regeneration surveys are important for assessing conditions immediately after plantation establishment. An unmanned aircraft system was evaluated for its ability to capture imagery that could be used to automate seedling counting using two computer vision approaches. The imagery was found to be unreliable for consistent detection in the conditions evaluated. Following establishment, conditions are assessed throughout the lifespan of forest plantations. Using small area estimation (SAE) methods, the incorporation of light detection and ranging (lidar) and thinning status improved the precision of inventory estimates compared with ground data alone. Further investigation found that reduced density lidar point clouds and lower resolution elevation models could be used to generate estimates with similar increases in precision. Individual tree detection estimates of stand density were found to provide minimal improvements in estimation precision when incorporated into the SAE models. Plot and stand level inventory aggregations were found to provide similar estimates of future conditions in simulated stands without high levels of spatial heterogeneity. Significant differences were noted when spatial heterogeneity was high. Model form was found to have a more significant effect on the observed differences than plot size or thinning status. The results of this research are of interest to forest managers who regularly conduct forest inventories and generate estimates of future stand conditions. The incorporation of auxiliary data in mid-rotation stands using SAE techniques improved estimate precision in most cases. Further, guidance on strategies for using this information for predicting future conditions is provided. / Doctor of Philosophy / Informed forest management requires accurate, up-to-date information. Groundbased sampling (inventory) is commonly used to generate estimates of forest characteristics such as total wood volume, stem density per unit area, heights, and regeneration survival. As the importance of assessing forest resources has increased, resources are often not available to conduct proper assessments. In this research, the incorporation of ancillary information in planted loblolly pine (Pinus taeda L.) forest inventory was investigated. Additionally, a simulation study investigated the effects of two forest inventory data aggregation methods on predictions and projections of future forest conditions. Forest regeneration surveys are important for assessing conditions immediately after tree planting. An unmanned aircraft system was evaluated for its ability to capture imagery that could be used to automate seedling counting. The imagery was found to be unreliable for use in accurately detecting seedlings in the conditions evaluated. Following establishment, forest conditions are assessed at additional points in forest development. Using a class of statistical estimators known as small-area estimation, a combination of ground and light detection and ranging data generated more confident estimates of forest conditions. Further investigation found that more coarse ancillary information can be used with similar confidence in the conditions evaluated. Forest inventory data are used to generate estimates of future conditions needed for management decisions. The final component of this research found that there are significant differences between two inventory data aggregation strategies when forest conditions are highly spatially variable. The results of this research are of interest to forest managers who regularly assess forest resources with inventories and models. The incorporation of ancillary information has potential to enhance forest resource assessments. Further, managers have guidance on strategies for using this information for estimating future conditions.

The use of small area estimation (SAE) in forest inventory has shown promise for improving the precision of estimates needed for informed decision-making when sample data are sparse. We evaluated the potential of unit-level SAE for increasing the precision of stand-level estimates of basal area, volume, and above-ground biomass estimates in loblolly pine plantations in coastal Georgia. Following the unit-level approach, field plots sampled in plantations owned by Rayonier Inc. were georeferenced to aerial lidar data using high-quality GPS field coordinates. Results focused on A) gains in precision for stand-level basal area, volume, and above-ground biomass estimates achieved by combining data from field plots with lidar-derived canopy height models in a SAE framework, B) impacts of small sample sizes on the precision of estimated stand level attributes, and C) the effects of nonrandom field plot placement in stands of interest when using unit-level SAE. Findings indicate that higher precision is achievable with greater variance stability than what is possible from very small samples of field data alone. This was true for all three attributes of interest. With careful attention to checking assumptions of the unit-level SAE approach, the use of non-random sampling does not appear to impair SAE's ability to deliver unbiased estimates for forest plantation stands. Simulating the entire population's basal area to test for the effects of non-random plot placement showed that SAE is robust to the type of sampling technique used. However, results can be affected when sampling is intentionally biased. This work can be useful to landowners and forest managers working with southern loblolly pine plantations. By leveraging simulation techniques to generate non-random sampling data from the available random sampling data, this study attempted to bridge the gap between the available empirical data and the desired sampling framework, ultimately widening the applicability of SAE in forest inventory settings. / Master of Science / Accurate forest inventory estimates are essential to make important decisions for forest management. Our research explored how advanced statistical methods, specifically small area estimation (SAE), can enhance forest inventories when only limited data is available. We focused on loblolly pine plantations in coastal Georgia, using data from field plots combined with aerial lidar technology to estimate important forest metrics: basal area (tree density), wood volume, and above-ground biomass. By pairing field and lidar data, we found that SAE significantly improved the accuracy of forest estimates, even when the number of field samples was very small. We also tested how different sampling strategies, such as non-random plot selection, affected the results. Our results showed that SAE proved resilient to non-random sampling as long as certain assumptions were met. However, deliberate biases in sampling could still lead to less reliable estimates. Our findings provide valuable tools for forest managers and landowners, especially those managing loblolly pine plantations in the Southeastern US. By applying simulation techniques to extend the use of existing data, this study showed how SAE can fill data gaps and provide more accurate forest measurements, helping to guide better management and conservation decisions.

Thesis (Ph.D. (Statistics)) -- University of Limpopo, 2019 / This study presents the application of Direct and Indirect methods of Small AreaEstimation(SAE)techniques. Thestudyisaimedatestimatingthetrends and the proportions of households accessing water, sanitation, and electricity for lighting at small areas of the Limpopo Province, South Africa. The study modified Statistics South Africa’s General Household Survey series 2009-2015 and Census 2011 data. The option categories of three variables: Water, Sanitation and Electricity for lighting, were re-coded. Empirical Bayes and Hierarchical Bayes models known as Markov Chain Monte Carlo (MCMC) methods were used to refine estimates in SAS. The Census 2011 data aggregated in ‘Supercross’ was used to validate the results obtained from the models. The SAE methods were applied to account for the census undercoverage counts and rates. It was found that the electricity services were more prioritised than water and sanitation in the Capricorn District of the Limpopo Province. The greatest challenge, however, lies with the poor provision of sanitation services in the country, particularly in the small rural areas. The key point is to suggestpolicyconsiderationstotheSouthAfricangovernmentforfutureequitable provisioning of water, sanitation and electricity services across the country.

In this dissertation, we first develop new statistical methodologies for small area estimation problems with measurement errors. The prediction of small area means for the unit-level regression model with the functional measurement error in the area-specific covariate is considered. We obtain the James-Stein (JS) estimate of the true area-specific covariate. Consequently, we construct the pseudo Bayes (PB) and pseudo empirical Bayes (PEB) predictors of small area means and estimate the mean squared prediction error (MSPE) associated with each predictor. Secondly, we modify the point estimation of the true area-specific covariate obtained earlier such that the histogram of the predictors of the small area means gets closer to its true one. We propose the constrained Bayes (CB) estimate of the true area-specific covariate. We show the superiority of the CB over the maximum likelihood (ML) estimate in terms of the Bayes risk. We also show the PB predictor of the small area mean based on the CB estimate of the true area-specific covariate dominates its counterpart based on the ML estimate in terms of the Bayes risk. We compare the performance of different predictors of the small area means using measures such as sensitivity, specificity, positive predictive value, negative predictive value, and MSPE. We believe that using the PEB and pseudo hierarchical Bayes predictors of small area means based on the constrained empirical Bayes (CEB) and constrained hierarchical Bayes (CHB) offers higher precision in recognizing socio-economic groups which are in danger of the prehypertension. Clustering the small areas to understand the behavior of the random effects better and accordingly, to predict the small area means is the final problem we address. We consider the Fay-Herriot model for this problem. We design a statistical test to evaluate the assumption of the equality of the variance components in different clusters. In the case of rejection of the null hypothesis of the equality of the variance components, we implement a modified version of Tukey's method. We calculate the MSPE to evaluate the effect of the clustering on the precision of predictors of the small area means. We apply our methodologies to real data sets. / February 2017

It is a standard practice in small area estimation (SAE) to use a model-based approach to borrow information from neighboring areas or from areas with similar characteristics. However, survey data tend to have gaps, ties and outliers, and parametric models may be problematic because statistical inference is sensitive to parametric assumptions. We propose nonparametric hierarchical Bayesian models for multi-stage finite population sampling to robustify the inference and allow for heterogeneity, outliers, skewness, etc. Bayesian predictive inference for SAE is studied by embedding a parametric model in a nonparametric model. The Dirichlet process (DP) has attractive properties such as clustering that permits borrowing information. We exemplify by considering in detail two-stage and three-stage hierarchical Bayesian models with DPs at various stages. The computational difficulties of the predictive inference when the population size is much larger than the sample size can be overcome by the stick-breaking algorithm and approximate methods. Moreover, the model comparison is conducted by computing log pseudo marginal likelihood and Bayes factors. We illustrate the methodology using body mass index (BMI) data from the National Health and Nutrition Examination Survey and simulated data. We conclude that a nonparametric model should be used unless there is a strong belief in the specific parametric form of a model.

Significant efforts have been undertaken in medicine to identify hospital and primary care service areas (eg, the Dartmouth Atlas of Health Care) using patient origin information. Similar research in dentistry is nonexistent. The goal of this dissertation was to develop and refine methods of defining dentist service areas (DSAs) using dental insurance claims. These service areas were then used as spatial units of analysis in studies that examined relationships between utilization of oral health services, dentist workforce supply, and service area characteristics. Enrollment and claims data were obtained from the Iowa Medicaid program for children and adolescents ages 3-18 years during calendar years 2008 through 2010. The first study described rates of treatment by orthodontists in children ages 6-18 years. Orthodontic DSAs were identified by small area analysis in order to examine regional variability in utilization. The overall rate of utilization was approximately 3%; 19 DSAs were delineated. Interestingly, children living in small towns and rural areas were significantly more likely to have received orthodontic services than those living in metropolitan and micropolitan areas. The second study identified 113 DSAs using claims submitted by primary care dentists (ie, general and pediatric dentists). Characteristics of these primary care DSAs were then compared with counties. Localization of care was used as a measure of how well each region approximated a dental market area. Approximately 59% of care received by Medicaid-enrolled children took place within their assigned service area versus 52% of care within their county of residence. Hierarchical logistic regression was used in the final study to examine the influence of spatial accessibility and the importance of place on the receipt of preventive dental visits among Medicaid-enrolled children. Children living in urban areas were more likely to have received a visit than those living in more rural areas. Spatial accessibility assessed using measures of dentist workforce supply and travel cost did not appear to be a major barrier to care in this population. More studies are needed to explore the importance of spatial accessibility and other geographic barriers on access to oral health services. The methods used in this dissertation to identify service areas can be applied to other populations and offer an appropriate method for examining revealed patient preferences for oral health care.

This dissertation models K-12 enrollment within an urban school district using two grade progression ratio (gpr)-based and two housing choice methods. The housing choice methods provide, for the first time, a new spatio-demographic model for projecting school enrollments by grade for any flexibly defined set of individual catchment areas. All methods use the geocoded pattern of individual, address-matched, enrollments within the study district but are different in the way they model this data to estimate key parameters. The conventional method projects the intra-urban pattern of enrollment by assuming no change in grade progression ratios (gprs), which are themselves functions of enrollment change. The adaptive kernel ratio estimation (KRE) of local gprs successfully predicts local changes in gprs from three preceding two-year periods of gpr change. The two housing choice methods are based on different mixtures of a generalized linear and a periodic model, each of which use housing counts and characteristics. Results are clearly sensitive to these differences. Using the above predictions of gpr change, the adaptive KRE enrollment projections are 4.1% better than those made using the conventional model. The two housing choice models were 2.0% less accurate than the conventional model for the first three years of the projection but were 5.1% more accurate than this model for the fourth and fifth years of the projection. Limitations are discussed. These findings help close a major gap in the literature of small-area enrollment projections, shed new light on spatial dynamics collected at areas below the scale of the school district, and permit new kinds of investigations of urban/suburban school district demography.

The thesis investigates the optimal expansion planning of substations for the distribution system of Taipei City District of Taiwan Power Company. The small area load forecasting is executed with the support of Outage Management System(OMS) database. The capacity expansion of distribution substations is obtained by considering the annual load growth of each service area to achieve the cost effectiveness of substation investment. The geographic information of each service zone has been retrieved form the OMS data. With the land use planning of Taipei City Government, the load density of each small area for the target year is derived according to the final floor area and development strength of the land base. The load forecasting of each small area is then solved by considering the load growth of each customer class, which is then used for the expansion planning of substations. After determining the small area load forecasting for the final target year, the center of gravity method is applied to find the geographic blocks of all substations and the corresponding service areas at the target year. The power loading of each small area is used to calculate the power loading loss of which service area to solve the optimal location within the block for each substation. Based on the annual load forecasting of all small areas, the expansion planning of distribution substations for Taipei City District is derived by Dynamic Programming(DP) and Immune Algorithm(IA) to achieve minimization of power loading loss with subject to the operation constraint. By the proposed methodology, the unit commitment of distribution substations is determined to meet the load growth of service area and achieve power loading loss minimization of distribution systems.

This dissertation is composed of three chapters, each an application of Bayesian statistical models to particular research questions. In Chapter 1, we evaluate systemic risk exposure of financial institutions. Building upon traditional regime switching approaches, we propose a network model for volatility contagion to assess linkages between institutions in the financial system. Focusing empirical analysis on the financial sector, we find that network connectivity has dynamic properties, with linkages between institutions increasing immediately before the recent crisis. Out-of-sample forecasts demonstrate the ability of the model to predict losses during distress periods. We find that institutional exposure to crisis events depends upon the structure of linkages, not strictly the number of linkages. In Chapter 2, we develop procedures for benchmarking small area estimates. In sample surveys, precision can be increased by introducing small area models which "borrow strength" by incorporating auxiliary covariate information. One consequence of using small area models is that small area estimates at lower geographical levels typically will not aggregate to the estimate at the corresponding higher geographical levels. Benchmarking is the statistical procedure for reconciling these differences. Two new approaches to Bayesian benchmarking are introduced, one procedure based on Minimum Discrimination Information, and another for Bayesian self-consistent conditional benchmarking. Notably the proposed procedures construct adjusted posterior distributions whose moments all satisfy benchmarking constraints. In the context of the Fay-Herriot model, simulations are conducted to assess benchmarking performance. In Chapter 3, we exploit the Pair Copula Construction (PCC) to develop a flexible multivariate model for time-varying dependence. The PCC is an extremely flexible model for capturing complex, but static, multivariate dependency. We use a Bayesian framework to extend the PCC to account for time dynamic dependence structures. In particular, we model the time series of a transformation of parameters of the PCC as an autoregressive model, conducting inference using a Markov Chain Monte Carlo algorithm. We use financial data to illustrate empirical evidence for the existence of time dynamic dependence structures, show improved out-of-sample forecasts for our time dynamic PCC, and assess performance of dynamic PCC models for forecasting Value-at-Risk. / Statistics