With the recent increase in the threat of biological terrorism as well as the continual risk of other diseases, the research in public health surveillance and disease monitoring has grown tremendously. There is an abundance of data available in all sorts of forms. Hospitals, federal and local governments, and industries are all collecting data and developing new methods to be used in the detection of anomalies. Many of these methods are developed, applied to a real data set, and incorporated into software. This research, however, takes a different view of the evaluation of these methods. We feel that there needs to be solid statistical evaluation of proposed methods no matter the intended area of application. Using proof-by-example does not seem reasonable as the sole evaluation criteria especially concerning methods that have the potential to have a great impact in our lives. For this reason, this research focuses on determining the properties of some of the most common anomaly detection methods. A distinction is made between metrics used for retrospective historical monitoring and those used for prospective on-going monitoring with the focus on the latter situation. Metrics such as the recurrence interval and time-to-signal measures are therefore the most applicable. These metrics, in conjunction with control charts such as exponentially weighted moving average (EWMA) charts and cumulative sum (CUSUM) charts, are examined. Two new time-to-signal measures, the average time-between-signal events and the average signal event length, are introduced to better compare the recurrence interval with the time-to-signal properties of surveillance schemes. The relationship commonly thought to exist between the recurrence interval and the average time to signal is shown to not exist once autocorrelation is present in the statistics used for monitoring. This means that closer consideration needs to be paid to the selection of which of these metrics to report. The properties of a commonly applied scan method are also studied carefully in the strictly temporal setting. The counts of incidences are assumed to occur independently over time and follow a Poisson distribution. Simulations are used to evaluate the method under changes in various parameters. In addition, there are two methods proposed in the literature for the calculation of the p-value, an adjustment based on the tests for previous time periods and the use of the recurrence interval with no adjustment for previous tests. The difference in these two methods is also considered. The quickness of the scan method in detecting an increase in the incidence rate as well as the number of false alarm events that occur and how long the method signals after the increase threat has passed are all of interest. These estimates from the scan method are compared to other attribute monitoring methods, mainly the Poisson CUSUM chart. It is shown that the Poisson CUSUM chart is typically faster in the detection of the increased incidence rate. / Ph. D.

As técnicas de lente térmica (LT) e \"Z-scan\" foram usadas para estudar as propriedades termo-óticas (difusividade térmica, condutividade térmica, taxa de variação do caminho ótico em função da temperatura e eficiência quântica de fluorescência) e não-lineares (partes real e imaginária do índice de refração não-linear, diferença de polarizabilidade e da seção de choque de absorção entre os estados excitado e fundamental, respectivamente) de sólidos dopados com Neodímio e Cromo. Uma nova extensão da técnica de LT foi proposta para determinar a eficiência quântica de fluorescência sem necessitar de amostra referência, como é feito na maioria dos métodos fototérmicos. Além disso, ambas técnicas foram usadas como espectroscopia, ou seja, a LT foi usada para estudar a forma de linha do calor gerado no material quando a excitação é feita próximo da banda de absorção do material, possibilitando assim a determinação da eficiência de transferência entre a matriz e o íon dopante, e a técnica \"Z-scan\" foi adaptada para medir a forma de linha do índice de refração não-linear próximo das linhas de emissão laser nos cristais dopados com Cromo. / The Thermal Lens (TL) and Z-scan technique were used to study the thermo-optical (thermal diffusivity, thermal conductivity, temperature coefficient of the optical path length change and fluorescence quantum efficiency) and nonlinear optical (parts real and imaginary of the refractive index, polarizability difference and absorption cross section between the excited and ground states, respectively) properties of Neodymium and Chromium doped solids. A new extension of the TL technique was proposed to determine the fluorescence quantum efficiency without measuring a reference sample, as done by any photothermal method Moreover, both techniques were used as an spectroscopy one, i. e., the TL was used to study the line shape of the heat created in material when the excitation is done near at the host absorption band, allowing the determination of the energy transfer efficiency between the host and the dopant ion, and the 2-scan technique was adapted to measure the line shape of the nonlinear refractive index near the laser lines in Chromium doped crystals.

As técnicas de lente térmica (LT) e \"Z-scan\" foram usadas para estudar as propriedades termo-óticas (difusividade térmica, condutividade térmica, taxa de variação do caminho ótico em função da temperatura e eficiência quântica de fluorescência) e não-lineares (partes real e imaginária do índice de refração não-linear, diferença de polarizabilidade e da seção de choque de absorção entre os estados excitado e fundamental, respectivamente) de sólidos dopados com Neodímio e Cromo. Uma nova extensão da técnica de LT foi proposta para determinar a eficiência quântica de fluorescência sem necessitar de amostra referência, como é feito na maioria dos métodos fototérmicos. Além disso, ambas técnicas foram usadas como espectroscopia, ou seja, a LT foi usada para estudar a forma de linha do calor gerado no material quando a excitação é feita próximo da banda de absorção do material, possibilitando assim a determinação da eficiência de transferência entre a matriz e o íon dopante, e a técnica \"Z-scan\" foi adaptada para medir a forma de linha do índice de refração não-linear próximo das linhas de emissão laser nos cristais dopados com Cromo. / The Thermal Lens (TL) and Z-scan technique were used to study the thermo-optical (thermal diffusivity, thermal conductivity, temperature coefficient of the optical path length change and fluorescence quantum efficiency) and nonlinear optical (parts real and imaginary of the refractive index, polarizability difference and absorption cross section between the excited and ground states, respectively) properties of Neodymium and Chromium doped solids. A new extension of the TL technique was proposed to determine the fluorescence quantum efficiency without measuring a reference sample, as done by any photothermal method Moreover, both techniques were used as an spectroscopy one, i. e., the TL was used to study the line shape of the heat created in material when the excitation is done near at the host absorption band, allowing the determination of the energy transfer efficiency between the host and the dopant ion, and the 2-scan technique was adapted to measure the line shape of the nonlinear refractive index near the laser lines in Chromium doped crystals.

As social networks become more prevalent, there is significant interest in studying these network data, the focus often being on detecting anomalous events. This area of research is referred to as social network surveillance or social network change detection. While there are a variety of proposed methods suitable for different monitoring situations, two important issues have yet to be completely addressed in network surveillance literature. First, performance assessments using simulated data to evaluate the statistical performance of a particular method. Second, the study of aggregated data in social network surveillance. The research presented tackle these issues in two parts, evaluation of a popular anomaly detection method and investigation of the effects of different aggregation levels on network anomaly detection. / Ph. D.