No description available.

No description available.

No description available.

<p> We propose a data-driven estimation algorithm in survival mixture model. The objective of this study is to provide an alternative fitting procedure to the conventional EM algorithm. The EM algorithm is the classical ML fitting of the parametric mixture model. If the initial values for the EM algorithm are not properly chosen, the maximizers might be local or divergent. Traditionally, initial values are given manually according to experience or a gridpoint search. This is a heavy burden for a high-dimensional data sets. Also, specifying the ranges of parameters for a grid-point search is difficult. To avoid the specification of initial values, we employ the random partition. Then, improvement of fitting is adjusted according to model specification. This process is repeated a large number of times, so it is computer intensive. The large repetitions makes the solution more likely to be the global maximizer, and it is driven purely by the data. We conduct a simulation study for three cases of two-component Log-Normal, two-component Weibull, and two-component Log-Normal and Wei bull, in order to illustrate the effectiveness of the proposed algorithm. Finally, we apply our algorithm to a breast cancer study data which follows a cure model. The program is written in R. It calls existing R functions, so it is flexible to use in regression situations where model formula must be specified. </p> / Thesis / Master of Science (MSc)

A convenient method for testing and calibrating surface perfusion sensors has been developed. A phantom tissue model is used to mimic the non-directional blood flow of tissue perfusion. A computational fluid dynamics (CFD) model was constructed in Fluent&#61650; to design the phantom tissue and validate the experimental results. The phantom perfusion system was used with a perfusion sensor based on the clearance of thermal energy. A heat flux gage measures the heat flux response of tissue when a thermal event (convective cooling) is applied. The blood perfusion and contact resistance are estimated by a parameter estimation code. From the experimental and analytical results, it was concluded that the probe displayed good measurement repeatability and sensitivity. The experimental perfusion measurements in the tissue were in good agreement with those of the CFD models and demonstrated the value of phantom tissue system. This simple, cost effective, and noninvasive convective blood perfusion system was then tested in animal models. The perfusion system was evaluated for repeatability and sensitivity using isolated rat liver and exposed rat kidney tests. Perfusion in the isolated liver tests was varied by controlling the flow of the perfusate into the liver, and the perfusion in the exposed kidney tests was varied by temporarily occluding blood flow through the renal artery and vein. The perfusion estimated by the convective perfusion probe was in good agreement with that of the metered flow of perfusate into the liver model. The liver tests indicated that the probe can be used to detect small changes in perfusion (0.005 ml/ml/s). The probe qualitatively tracked the changes in the perfusion in kidney model due to occlusion of the renal artery and vein. / Ph. D.

Ph. D.

This dissertation addresses the task of updating finite element models with frequency response data acquired in a structural dynamics test. Standard statistical techniques are used to generate statistically qualified data, which is then used in a Bayesian statistics regression formulation to update the finite element model. The Bayesian formulation allows the analyst to incorporate engineering judgment (in the form of prior knowledge) into the analysis and helps ensure that reasonable and realistic answers are obtained. The formulation includes true statistical weights derived from experimental data as well as a new formulation of the Bayesian regression problem that reduces the effects of numerical ill-conditioning. Model updates are performed with a simulated free-free beam, a simple steel frame, and a cantilever beam. Improved finite element models of the structures are obtained and several statistical tests are used to ensure that the models are improved. / Ph. D.

This dissertation deals primarily with the development of the technique of orthogonal statistics and the use of this technique to investigate sampling properties of moment estimators of parameters of the negative binomial distribution. The general technique of orthogonal statistics which is based on the existence of an infinite set {q_r(x)} of orthogonal polynomials associated with a particular distribution, enables one to obtain expansions of sampling moments of statistics which are functions of say, the first k sample moments m₁, m₂,…, m_k. The thesis describes the technique in general, and gives tables which facilitate the expansion through terms in n⁻⁵ of sampling moments of statistics which are functions of any four sample moments. The need for the development of this technique resulted from an interest in the problem of investigating sampling properties of certain moment estimators for the case of the negative binomial distribution. Thus further work was done on the technique for this particular case. Tables are given in the thesis which simplify the procedure for moment statistics which result from a sample taken from this particular distribution. Sampling properties of moment estimators for the negative binomial distribution were investigated. The distribution forms considered in depth were due to Anscombe [Biometrika, 37 (1950}, pp. 358-362] with parameters λ and α, Evans [Biometrika, 40 (1953), pp. 186-211] with parameters m and a, and Fisher [Annals of Eugenics, 11 (1941), pp. 182-187] with parameters p and k. The purpose of this study was to obtain an insight into the behavior of expansions through high powers of 1/n (e.g., terms in n⁻⁴) of the bias, variance, and higher moments for these estimators. It was felt that the usual asymptotic properties described by the first term approximations might be misleading for practical cases (i.e., ordinary sample sizes). The results verified what was suspected. For the moment estimators of Ansaombe's form, when α > λ the sample sizes needed to make high order terms negligible for the expansion of the bias and variance were extremely large. (For one particular case, in order to use the usual asymptotic variance safely one would need an n of 2 million.) This then reveals the hazardous practice of using the first term approximation and resulting in a very serious under-assessment of the true variance of the estimate of α. Since for Fisher's form k̂ = α̂, the same applies. For Evans' form, the situation was in marked contrast. Higher order terms were "damped off" with much smaller sample sizes, and in most cases one is justified in using first term approximations. Studies for Evans' estimators were confined to the range λ > 1 and α > 1. The results for the estimators of Anscombe's form were compared with similar results for the maximum likelihood estimator of α, in order to ascertain the effect on efficiency of the chaotic nature of the n⁻³ term in the expansion of the covariance determinant of α̂. The maximum likelihood results were taken from Bowman [Thesis submitted for Ph.D. degree, Virginia Polytechnic Institute, Moments to Higher Orders for Maximum Likelihood Estimators with an Application to the Negative Binomial Distribution]. This study revealed that there is a striking similarity in the n⁻³ term in the covariance determinant for the two estimators. This made the "true" efficiency almost identical to the asymptotic efficiency in cases when sufficiently large sample sizes are used to "sink" terms beyond n⁻³. This statement cannot be generalized, however, to include any sample size, since for α > λ only relatively large sample sizes "damp off' further terms in the covariance determinants for both estimators. Hence one cannot be sure of the behavior of these determinants beyond n⁻³ unless these large sample sizes are used. Tables and charts are given which display the nature of the expansions given in the text. In particular, charts are given of minimum sample size needed in order that the expansions given can safely be used as approximations. / Ph. D.

Blood perfusion is the local, non-directional blood flow through tissue. It is measured as the volumetric flow rate of blood through a given volume of tissue. One method that has been developed for measuring blood perfusion is a probe that measures the temperature response of the tissue when a thermal event is applied. From the temperature response, the blood perfusion and contact resistance can be estimated by comparing the experimental response to a predicted response, and employing Gaussian minimization techniques to estimate the blood perfusion and contact resistance. The objective of this research was to assess the measurement repeatability and sensitivity of the blood perfusion probe by testing the probe on phantom tissue, such that the effects of physiologic or pathologic conditions on the blood perfusion could be eliminated. Another objective was to conduct a preliminary in vivo study using rats for the purpose of establishing proper experimental protocols for future testing of the blood perfusion probe. A phantom tissue test stand comprised of porous material and water to simulate tissue and blood, respectively, was constructed for the phantom study. Inlet flow rates into the porous media ranging between 0 cc/min and 30 cc/min were tested. To test the measurement repeatability 7 flow rates (0, 5, 10, 15, 20, 25 and 30 cc/min) were tested on two different days. To test the measurement sensitivity of the probe, flow rates between 0 and 10 cc/min, and 15 and 20 cc/min were tested at intervals of 1 cc/min. From the phantom study it was concluded that the probe displayed good measurement repeatability, as the trend in perfusion as a function of inlet flow rates for both days was found to be the same. It was also found that the data collected using the probe yielded significantly different perfusion estimates for different flow rates, as statistical analyses show that the average perfusion differences between flow rates are truly independent within a 90% confidence interval, for flow differences above 4 cc/min. It was found that for flow rates below 4 cc/min the probe sensitivity was significantly reduced. For the in vivo study it was concluded that the probe can be used to obtain estimates of perfusion from rats. This preliminary study also served to establish proper experimental protocols for future tests. / Master of Science

This dissertation deals with the properties of two modified moment estimators for parameters of the negative binomial distribution (NBD). Several parametric forms have been suggested for the NBD. The estimation problems vary according to the form which is used. In particular, the form proposed by Anscombe [Biometrika, 37 (1950), pp. 358-382), with parameters λ and α, has received wide attention and was selected for study in this investigation. In Anscombe's parametric form, the mean of the NBD is λ and the variance is λ + λ²/α. While the parameter λ is universally estimated by the sample mean, many different methods of estimation for α have been attempted. Among these, the maximum likelihood estimator α* and the simple moment estimator â are most often used. However, α* is quite difficult to obtain numerically and often this computation requires the use of an electronic computer. In addition, â, while not difficult to compute, is often inefficient. For these reasons, it was felt that a study of the two modified moment estimators â₁ and â₂, suggested by Shenton and Wallington [Moment Estimators and Modified Moment Estimators with Special Reference to the Negative Binomial Distribution (unpublished)], was needed. In the text, the method of obtaining modified moment estimators in general is given in detail. The application of this method to the NBD is discussed and, in particular, the derivations of â₁ and â₂ are presented. Since orthogonal statistics play an important part in this work, their definition and applications are reviewed. In order to evaluate the small sample properties of â₁ and â₂, asymptotic expansions, in powers of 1/n, of their biases, variances, covariance determinants, and higher moments were determined numerically in the parameter space (1 ≤ α ≤ 100, 1 ≤ λ ≤ 100), through terms to n⁻⁴. The computational method for this work is described in detail. Tables and charts which display the nature of the expansions are given in the text. The results show that the behavior patterns of the moment expansions for â₁ and â₂ are somewhat similar to those for â and α*. For both â₁ and â₂, the n⁻⁴ term contributes heavily in all the expansions when α > λ. Thus, as with the other estimators, a first term approximation would not suffice for the properties of â₁ and â₂. Further, the results give evidence that â₁ and â₂ are highly efficient for most α and λ, and, in some regions of the parameter space, have less bias than α* and â. Some experimental data was fitted to the NBD using the estimators â₁, â₂, â, and α*. In all of the examples given, the modified moment estimators provided a better fit of the data than did the simple moment estimator and, in one instance, a better fit than was obtained by the maximum likelihood estimator. / Ph. D.