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Bayesian reference analysis is a method of determining the prior under the Bayesian paradigm. It incorporates as little information as possible from the experiment. Estimation of the ratio of two independent Poisson rates is a common practical problem. In this thesis, the method of reference analysis is applied to derive the posterior distribution of the ratio of two independent Poisson rates, and then to construct point and interval estimates based on the reference posterior. In addition, the Frequentist coverage property of HPD intervals is verified through simulation.

Silver nanoparticles (AgNPs) are known to cause ecotoxic effects, but there are no existing derived ambient water quality criteria (AWQC) for these nanomaterials to protect freshwater aquatic life due to insufficient toxicological data. We exposed Hyalella azteca to silver nitrate, citrate-coated AgNPs (citrate-AgNPs), and polyvinylpyrrolidone-coated AgNPs (PVP-AgNPs) in a 10-day and 28-day water-only static renewal system with clean sand as a substrate for the amphipods and compared their point estimates with the United States Environmental Protection Agency (USEPA) AWQC for silver. We observed that all treatments decreased the survival, growth, and biomass of H. azteca, and the order of toxicity was AgNO > citrate-AgNPs > PVP-AgNPs. The LC50s of AgNO, citrate-AgNPs, and PVP-AgNPs were 3.0, 9.6, and 296.0 µg total Ag L, respectively, for the acute exposure and 2.4, 3.2, and 61.4 µg total Ag L, respectively, for the chronic exposure. Acute and chronic EC20s of citrate-AgNPs ranged from 0.5 to 3.5 µg total Ag L while that of PVP-AgNPs ranged from 31.2 to 175 µg total Ag L for growth and biomass. Both Ag released from AgNPs and the nanoparticles contributed to the observed toxicity. The dissolution and toxicity of AgNPs were influenced by surface coating agents, particle size, and surface charge. Most point estimates for AgNPs were above AWQC for silver (4.1 µg L) and the lowest concentration (0.12 µg/L) at which Ag is expected to cause chronic adverse effects to freshwater aquatic life. Our study demonstrates that the current AWQC for silver, in general, is protective of freshwater aquatic life against AgNPs tested in the present study.

[pt] Na prática geotécnica, a estabilidade de taludes é atualmente estudada apenas com análises determinísticas, obtendo-se o valor do Fator de Segurança (FS) da estrutura geotécnica. Estas análises são simplificadas, pois fornecem valores de FS sem considerar a variabilidade intrínseca dos solos e rochas. Desprezar as incertezas dos parâmetros geotécnicos pode levar a resultados pouco confiáveis sobre a segurança de taludes. Análises fundamentadas em conceitos estatísticos, chamadas probabilísticas, passam ser mais frequentes na geotecnia por permitirem considerar efeitos da variabilidade inerente aos materiais. Estas análises incorporam elementos estatísticos que possibilitam tratar FS como uma função e estudar suas propriedades. Como resultados finais, os métodos probabilísticos fornecem o índice de confiabilidade (beta) e a probabilidade de ruptura (Pr) da estrutura averiguada. Este trabalho aplica análises determinísticas e probabilísticas de um talude de 200m de altura da Mina do Cauê, Itabira, MG. A estabilidade do talude foi analisada por cinco métodos determinísticos usuais e três probabilísticos (FOSM, EP e MC). Os resultados indicam que a fixação da superfície crítica de ruptura fornece, em geral, valores de beta e Pr semelhantes aos obtidos quando a superfície pode variar livremente. Com a superfície crítica fixa observou-se, também, que os resultados de beta e Pr do talude variam significativamente com o método de equilíbrio limite adotado. Após comparação dos resultados, pode-se recomendar o uso de análises probabilísticas FOSM com base no método de Morgenstern-Price em análises semelhantes ao caso estudado. / [en] In current geotechnical practice, slope stability assessments are usually carried out only based on deterministic methods, obtaining a value of Safety Factor (FS). These analyses are simplified because the FS values do not consider the natural variability of soils and rocks. Disregarding the uncertainties inherent to geotechnical parameters may lead to unreliable results of slope safety. Probabilistic analyses, based on statistical concepts, have become more frequent in geotechnical practice, as they allow incorporating the materials intrinsic variability. These analyses are based on statistical elements that allow treating the FS as a function and studying its properties. The probabilistic methods indicate the reliability index (beta) and the probability of failure (Pr) of the verified geotechnical structure. This work presents deterministic and probabilistic analyses of a 200m high slope at the Cauê Mine, located in Itabira, Minas Gerais, Brazil, with basis on five usual deterministic methods and three probabilistic techniques (FOSM, Point Estimates and Monte Carlo). The results indicate that fixing the critical deterministic surface generally gives values of beta and Pr similar to those achieved when the surface is free to vary. It was also concluded that, with a fixed critical surface, beta and Pr results change significantly, when different Limit Equilibrium methods are adopted. It is recommended to use probabilistic FOSM analysis with Morgenstern and Price stability method in analyses similar to the one presented herein.