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[Moment Estimators and Modified Moment Estimators with Special Reference to the Negative Binomial Distribution (unpublished)], was needed.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.

This paper proposed the idea that the growth of an individual organism follows a mathematical model very closely and that different individuals follow different members of the same parametric family of models. This idea implies that the variation observed between individuals measured at the same time arises not from an additive term as has been previously supposed, but primarily from variation of the parameters of the model. A graph of data from an experiment on chickens is included which points up this individuality and the increased variation resulting from the passage of time. The four models considered were growth curves employing two, three, and four parameters with biological interpretations existing for the parameters. The parameters were allowed to follow independent uniform distributions and independent gamma distributions. / Master of Science

Honeycomb core sandwich structures are an integral part of many of today's aerospace structures. When subjected to high-speed flight, thermal loading can induce significant stresses. The need for thermal properties to perform thermal stress analyses in these structures is the motivation behind this research. The thermal property estimation approach used here involves the minimization of a least-squares function containing both measured and calculated values. In addition, an applied heat flux is necessary at one boundary for the simultaneous estimation of thermal properties. The specific objectives are to develop a thermal model to describe honeycomb core sandwich structures, optimize experimental designs for use in parameter estimation, develop a finite element-based parameter estimation algorithm, and estimate the pertinent thermal properties of the structure. A combined conductive/radiative heat transfer model was used for the analysis of the structure. Due to the composition of the structure, it was determined that a one-dimensional model would be sufficient. This model was used in both parameter estimation and experimental design. Experimental design involves finding input variables for an experiment such that the response of the system contains the highest possible amount of information on the parameters of interest which characterize the response. In this study, the design was performed by using a combination of two methods. The first involved maximizing the temperature derivatives with respect to unknown thermal properties. The second involved a scaled confidence interval approach. The experimental parameters optimized were heating time and total experiment time. A finite element program was used to perform transient temperature calculations because of the flexibility it has to analyze complex structures. Parameters estimated in this study exhibited a great deal of correlation, or interaction. This showed the need for a constrained parameter estimation algorithm. A penalty function method was developed for this purpose. The last part of this study involved the actual estimation of thermal properties. An experimental apparatus was designed and built to record the transient temperature response of the test sample. A four-sheet SPF/DB sandwich was used as the test sample. Thermal properties were estimated using four combinations of sensors and boundary conditions. It was found that in one case parameters could be simultaneously estimated despite the presence of correlation. These estimated parameters were shown to produce reasonably small errors when used in transient temperature calculations. It was also shown that large temperature gradients produce estimates with smaller confidence intervals. The importance of maintaining accurately known boundary conditions was also demonstrated. / Master of Science

In this thesis, a presentation of a new canonical representation of multi-input multi-output systems is given. The new characterization covers the full range of practical situations in linear systems according to the structural properties and model of the perturbations which are known. Its direct link to ARMA processes as well as to classical state space representation ls also given. The importance of the new representation lies in the fact that all unknown parameters and state variables appear linearly multiplied by either external variables (inputs and outputs) that appear in the data record, or by matrices that are only composed of zeroes and ones. This property enables us to perform a joint state and parameters estimation. Moreover, if the noises are gaussian and their statistics are known, an on-line algorithm that involves a standard discrete-time time-varying Kalman filter is proposed and used successfully in the estimation of unknown parameters for simulated examples. / Master of Science

Ph. D.

The task of spectrum sensing, defined here to consist of signal detection, signal parameter estimation, and signal identification, is a critically important task in a wide-variety of wireless communication applications. For example, in recent years, government and research initiatives have proposed the idea of communication systems that could gain access to spectrum opportunistically when being unused by primary licensed spectrum users. In order for these opportunistic systems to be realizable, methods by which secondary spectrum users can detect and classify these primary users will be necessary. Furthermore, detection and classification among the secondary users themselves will be important for efficient spectrum usage in these systems. As another example, spectrum sensing is also of critical importance in many military applications. This is due to the inherent expectation that a priori information of hostile wireless systems will be minimal or unavailable. The goal of this dissertation is to provide both insight and solutions in the critical area of spectrum sensing. More specifically, the research contained within this dissertation deals with the development and analysis of spectrum sensing algorithms that address key issues related to channel and radio impairments that are at present underdeveloped in the literature. First, research is presented on a method-of-moments based signal parameter estimation and likelihood-based modulation classification approach for linear digital amplitude-phase modulated signals (PAM, PSK, QAM, ...) in slowly-varying flat-fading channels. Based on this work, research is then presented on a feature-based modulation classification approach which relaxes the requirements of perfect frequency synchronization and knowledge of the phase information of the received signal that the likelihood-based approach requires. Finally, research is presented on the impact that both sensor reliability and sensor correlation information have on collaborative signal detection and intelligent sensor selection. / Ph. D.

A non-invasive blood perfusion system has been developed and tested in a phantom tissue and an animal model. The system uses a small sensor with a laminated flat thermocouple to measure the heat transfer response to an arbitrary thermal event (convective or conductive) imposed on the tissue surface. Blood perfusion and contact resistance are estimated by comparing heat flux data with a mathematical model of the tissue. The perfusion system was evaluated for repeatability and sensitivity using both a phantom tissue test stand and exposed rat liver tests. Perfusion in the phantom tissue tests was varied by controlling the flow of water into the phantom tissue test section, and the perfusion in the exposed liver tests was varied by temporarily occluding blood flow through the portal vein. The phantom tissue tests indicated that the probe can be used to detect small changes in perfusion (0.009 ml/ml/s). The probe qualitatively tracked the changes in the perfusion of the liver model due to occlusion of the portal vein. / Master of Science

Cell cycle models used in biology can be very complex. These models have parameters with initially unknown values. The values of the parameters vastly aect the accuracy of the models in representing real biological cells. Typically people search for the best parameters to these models using computers only as tools to run simulations. In this thesis methods and results are described for a computer program that searches for parameters to a series of related models using well tested algorithms. The code for this program uses ODRPACK for parameter estimation and LSODAR to solve the dierential equations that comprise the model. / Master of Science

This thesis demonstrates a parameter estimation technique for bioprocesses that utilizes measurement noise in experimental data to determine credible intervals on parameter estimates, with this information of potential use in prediction, robust control, and optimization. To determine these estimates, the work implements Bayesian inference using nested sampling, presenting an approach to develop neural network (NN) based surrogate models. To address challenges associated with non-uniform sampling of experimental measurements, an NN structure is proposed. The resultant surrogate model is utilized within a Nested Sampling Algorithm that samples possible parameter values from the parameter space and uses the NN to calculate model output for use in the likelihood function based on the joint probability distribution of the noise of output variables. This method is illustrated against simulated data, then with experimental data from a Sartorius fed-batch bioprocess. Results demonstrate the feasibility of the proposed technique to enable rapid parameter estimation for bioprocesses. / Thesis / Master of Applied Science (MASc) / Bioprocesses require models that can be developed quickly for rapid production of desired pharmaceuticals. Parameter estimation is necessary for these models, especially first principles models. Generating parameter estimates with confidence intervals is important for model based control. Challenges with parameter estimation that must be addressed are the presence of non-uniform sampling and measurement noise in experimental data. This thesis demonstrates a method of parameter estimation that generates parameter estimates with credible intervals by incorporating measurement noise in experimental data, while also employing a dynamic neural network surrogate model that can process non-uniformly sampled data. The proposed technique implements Bayesian inference using nested sampling and was tested against both simulated and real experimental fed-batch data.

Yes / In this work a simulation of detailed steady state model of an industrial fluid catalytic cracking (FCC) unit with a newly proposed six-lumped kinetic model which cracks gas oil into diesel, gasoline, liquefied petroleum gas (LPG), dry gas and coke. Frequency factors, activation energies and heats of reaction for the catalytic cracking kinetics and a number of model parameters were estimated using a model based parameter estimation technique along with data from an industrial FCC unit in Sudan. The estimated parameters were used to predict the major riser fractions; diesel as 0.1842 kg-lump/kg-feed with a 0.81% error while gasoline as 0.4863 kg-lump/kg-feed with a 2.71% error compared with the plant data. Thus, with good confidence, the developed kinetic model is able to simulate any type of FCC riser with six-lump model as catalyst-to-oil (C/O) ratios were varied and the results predicted the typical riser profiles.