Thesis (Ph. D.)--Ohio State University, 2005. / Title from first page of PDF file. Document formatted into pages; contains xi, 120 p.; also includes graphics (some col.). Includes bibliographical references (p. 114-120). Available online via OhioLINK's ETD Center

Dissertation (Ph.D.)--Auburn University, / Abstract. Vita. Includes bibliographic references (p.159-171).

The application of the jackknife in geostatistical resource estimation (in conjunction with kriging) is shown to yield two significant contributions. The first one is a robust new estimator, called jackknife kriging, which retains ordinary kriging's simplicity and global unbiasedness while at the same time reduces its local bias and oversmoothing tendency. The second contribution is the ability, through the jackknife standard deviation, to set a confidence limit for a reserve estimate of a general shape. Jackknifing the ordinary kriging estimate maximizes sample utilization, as well as information of sample spatial correlation. The jackknife kriging estimator handles the high grade smearing problem typical in ordinary kriging by assigning more weight to the closest sample(s). The result is a reduction in the local bias without sacrificing global unbiasedness. When data distribution is skewed, log transformation of the data prior to jackknifing is shown to improve the estimate by making the data behave better under jackknifing. The technique of block kriging short-cut, combined with jackknifing, are shown as an easy-to-use solution to the problem of grade estimation of a general three-dimensional digitized shape and the uncertainty associated with the estimate. The results are a single jackknife kriging estimate for the shape and its corresponding jackknife variance. This approach solves the problem of combining independent block estimation variances, and provides a simple way to set confidence levels for global estimates. Unlike the ordinary kriging variance, which is a measure of data configuration and is independent of data values, the jackknife kriging variance reflects the variability of the values being inferred, both on an individual block level and on the global level. Case studies involving two exhaustive (symmetric and highly skewed) data sets indicates the superiority of the jackknife kriging estimator over the original (ordinary kriging) estimator. Some instability of the log-transformed jackknife estimate is noted in the highly skewed situation, where the data do not generally behave well under standard jackknifing. A promising solution for future investigations seems to lie in the use of weighted jackknife formulation, which should better handle a wider spectrum of data distribution.

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Magíster en Minería / Las lateritas niquelíferas son una fuente generadora de la materia prima del acero inoxidable, el níquel. Dicho elemento se encuentra presente en diferentes tipos de rocas que son formadas por procesos externos que alteran, meteorizan y por último transforman la roca madre del depósito. La presencia de diferentes tipos de rocas, desde el punto de vista físico, químico, mecánico y, por último, de su contenido en mineralización en porcentajes (%) de níquel, hierro, magnesio, sílice, alúmina, entre otros, sugiere que cada tipo de roca debe estudiarse en forma propia. Cada perfil de meteorización o dominio geológico, conformado por diferentes tipos de rocas, tiene un comportamiento geoespacial diferente debido al proceso geológico de formación y enriquecimiento del depósito. Surge entonces la pregunta de cómo diseñar una metodología para muestrear el perfil de meteorización para la optimización de la malla de muestreo a corto plazo, partiendo del muestreo realizado en exploración, para generar el respectivo modelo de recurso. La metodología que se propone para determinar la malla de muestreo a corto plazo en lateritas niquelíferas, es la siguiente: análisis exploratorio y variográfico de datos espaciales, seguido de la construcción de múltiples escenarios mediante simulación Gaussiana secuencial y, a partir de los escenarios obtenidos, categorización de los recursos en cada dominio geológico usando gráficos tonelaje-ley sobre una ley de corte vs coeficiente de variación condicional (CCV). Lo anterior se aplica a varias mallas de muestreo tentativas para cada dominio geológico y permite estudiar y analizar la relación CBNT (relación costo/benefico, número-tiempo de muestras preparadas-analizadas en el laboratorio, tiempo en perforar cada dominio con su respectiva malla propuesta) para determinar la malla óptima de corto plazo en cada dominio. Se ilustra la propuesta con un caso de estudio de una zona particular de una laterita niquelífera subdividida en tres dominios geológicos que cubren todo el perfil de meteorización.

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Thesis (M.S.)--Tennessee Technological University, 2008. / Title from title page screen (viewed on Aug. 26, 2009). Bibliography: leaves 24-26.

This research focuses on the recovery of missing county yield observations within government data, which is used in the ARC-CO program that was authorized in the 2014 and 2018 Farm Bills. The recovered missing county values potentially solve issues with the payment process of ARC-CO, which triggers the ARC-CO payments. I examine multiple climate econometric models and the ordinary Kriging to predict the missing yield values. The results show that the ordinary Kriging is more accurate than any of the climate econometric models. After reviewing actual payments of ARC-CO, I find that farmers with irrigated land are underpaid and farmers of dryland are overpaid by the ARC-CO program as established in the 2014 Farm Bill.

Aquesta tesi estudia com estimar la distribució de les variables regionalitzades l'espai mostral i l'escala de les quals admeten una estructura d'espai Euclidià. Apliquem el principi del treball en coordenades: triem una base ortonormal, fem estadística sobre les coordenades de les dades, i apliquem els output a la base per tal de recuperar un resultat en el mateix espai original. Aplicant-ho a les variables regionalitzades, obtenim una aproximació única consistent, que generalitza les conegudes propietats de les tècniques de kriging a diversos espais mostrals: dades reals, positives o composicionals (vectors de components positives amb suma constant) són tractades com casos particulars. D'aquesta manera, es generalitza la geostadística lineal, i s'ofereix solucions a coneguts problemes de la no-lineal, tot adaptant la mesura i els criteris de representativitat (i.e., mitjanes) a les dades tractades. L'estimador per a dades positives coincideix amb una mitjana geomètrica ponderada, equivalent a l'estimació de la mediana, sense cap dels problemes del clàssic kriging lognormal. El cas composicional ofereix solucions equivalents, però a més permet estimar vectors de probabilitat multinomial. Amb una aproximació bayesiana preliminar, el kriging de composicions esdevé també una alternativa consistent al kriging indicador. Aquesta tècnica s'empra per estimar funcions de probabilitat de variables qualsevol, malgrat que sovint ofereix estimacions negatives, cosa que s'evita amb l'alternativa proposada. La utilitat d'aquest conjunt de tècniques es comprova estudiant la contaminació per amoníac a una estació de control automàtic de la qualitat de l'aigua de la conca de la Tordera, i es conclou que només fent servir les tècniques proposades hom pot detectar en quins instants l'amoni es transforma en amoníac en una concentració superior a la legalment permesa. / This Thesis presents an estimation procedure for the distribution of regionalized variables with sample space and scale admitting an Euclidean structure. We apply the principle of working on coordinates: choose an orthonormal basis; do statistics on the coordinates of your observations on that basis; and, by applying the output to the basis, you will recover a result within the original space. Applying this procedure to regionalized variables, we obtain a unified, consistent method, with the same properties of classical linear kriging techniques, but valid for several sample spaces: real data, positive data and compositions (vectors of positive components summing up to a constant) are regarded as particular cases. In this way we generalize the linear kriging techniques, and offer a solution to several well-known problems of the non-linear ones, by adapting the measure of the space and the averaging criterion (the way means are computed) to the data. The obtained estimator for positive variables is a weighted geometric mean, equivalent to estimate the median, which has none of the drawback of classical lognormal kriging. For compositional data, equivalent results are obtained, but which also serve to treat multinomial probability vectors. By combining this with a preliminary Bayesian estimation, our kriging for compositions become also a valid alternative to indicator kriging, without its order-relation problems (i.e. the rather-usual negative estimates of some probabilities). These techniques are validated by studying the ammonia pollution hazard in an automatic water quality control station placed in a small Mediterranean river. Only the proposed techniques allow us to assess when the secondary pollution by ammonia exceeds the existing legal threshold.

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