Sunnyson Y.F. Seid. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1997. / Includes bibliographical references (leaves 65-66). / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Applications in parameter identifications --- p.1 / Chapter 1.2 --- Inverse problems --- p.6 / Chapter 1.3 --- Difficulties arising in inverse problems --- p.7 / Chapter 2 --- Methods in Parameter Identifications --- p.9 / Chapter 2.1 --- Output Least Squares Method --- p.9 / Chapter 2.2 --- Equation Error Method --- p.11 / Chapter 2.3 --- Augmented Lagrangian Techniques --- p.12 / Chapter 2.4 --- Variational Techniques --- p.14 / Chapter 2.5 --- Adaptive Control Methods --- p.15 / Chapter 2.6 --- Method of Characteristics --- p.16 / Chapter 2.7 --- Our Proposed Method --- p.17 / Chapter 3 --- Parameter Identifications in Elliptic Systems --- p.19 / Chapter 3.1 --- Introduction --- p.19 / Chapter 3.2 --- Finite element approach and its convergence --- p.21 / Chapter 3.3 --- Unconstrained minimization problems --- p.28 / Chapter 3.4 --- Armijo algorithm --- p.31 / Chapter 3.5 --- Numerical experiments --- p.34 / Chapter 3.6 --- Multi-level coarse grid techniques --- p.55 / Bibliography --- p.65

In finance, various stochastic models have been used to describe the price movements of financial instruments. After Merton's [38] seminal work, several jump diffusion models for option pricing and risk management have been proposed. In this dissertation, we add alpha-stable Levy motion to the process related to dynamics of log-returns in the Black-Scholes model where the volatility is assumed to be constant. We use the sample characteristic function approach in order to study parameter estimation for discretely observed stochastic differential equations driven by Levy noises. We also discuss the consistency and asymptotic properties of the proposed estimators. Simulation results of the model are also presented to show the validity of the estimators. We then propose a new model where the volatility is not a constant. We consider generalized alpha-stable geometric Levy processes where the stochastic volatility follows the Cox-Ingersoll-Ross (CIR) model in Cox et al. [9]. A number of methods have been proposed for estimating parameters for stable laws. However, a complication arises in estimation of the parameters in our model because of the presence of the unobservable stochastic volatility. To combat this complication we use the sample characteristic function method proposed by Press [48] and the conditional least squares method as mentioned in Overbeck and Ryden [47] to estimate all the parameters. We then discuss the consistency and asymptotic properties of the proposed estimators and establish a Central Limit Theorem. We perform simulations to assess the validity of the estimators. We also present several tables to show the comparison of estimators using different choices of arguments ui's. We conclude that all the estimators converge as expected regardless of the choice of ui's. / Includes bibliography. / Dissertation (Ph.D.)--Florida Atlantic University, 2019. / FAU Electronic Theses and Dissertations Collection

Analytical performance analysis on Direction-Of-Arrival (DOA) estimation algorithms has attracted much excellent research in recent years, various statistical properties have been revealed. However, in most of these analyses, insights of the performance were masked because of the involvement of singular values and singular vectors which depend on the character of the algorithms and data structures in a complex and nonlinear manner.

The estimation of sinewave parameters has many practical applications in test and data processing systems. Measuring the effective bits of an analog-to-digital converter and linear circuit identification are some typical examples. If a sinew ave's frequency is known, there is an established linear method to estimate the other parameters. But when none of the parameters are known (which is usually the case in practical situations), the estimation problem becomes more difficult. Traditional approaches to this task applied an iterative, sinewave curve-fit algorithm. Two problems with this technique are that convergence is often slow and not always guaranteed and the results of different trials may be inconsistent due to trapping at a local minimum. Recently, a non-iterative algorithm has been developed which computes all four sine wave parameters directly. The algorithm combines a nonlinear technique and windowing to compute the estimates. Although this method is faster and more consistent than the curve-fit approach, one disadvantage is that the accuracy of some estimates tends to deteriorate rapidly if the sinusoid is corrupted by a high level of noise distortion. This study presents an improved algorithm to extract the four parameters of an unknown sinusoid from a sampled data record even though the samples may be distorted by a high level of noise. Given this record, the proposed method first computes the FFT (Fast Fourier Transform) of the data. Analysis of the resulting frequency spectrum provides a rough estimate of the sinewave's fundamental frequency. Next, a bandpass filter designed around this frequency is used to eliminate much of the noise from the samples. Applying the existing four-parameter estimation algorithm to the filtered data, yields a more accurate frequency estimate. Finally, this new value, together with the original (noisy) data record is input to the three-parameter estimation algorithm to determine the remaining sinewave parameters. Simulation results indicate this proposed (new) algorithm not only shows substantial improvement in the accuracy of parameter estimates, but also produces consistent results for higher levels of noise distortion than previous methods have achieved.

Residual mapping is an automated groundwater-model calibration technique which rapidly identifies parameter-zone configurations, while limiting tendencies to over-parameterize. Residual mapping analyzes the model residual, or the difference between model-calculated head and spatially-interpolated observation data, for non-random trends. These trends are entered in the model as parameter zones. The values of hydrologic variables in each parameter zone are then optimized, using parameter-estimation software. Statistics calculated by the parameter-estimation software are used to determine the statistical significance of the parameter zones. If the parameter-value ranges for adjacent zones do not have significant overlap, the zones are considered to be valid. This technique was applied to a finite-difference, transient groundwater flow model of a major municipal well field, located in west-central Florida. A computer conde automates the residual mapping process, making it practical for application to large, transient flow models. The calibration data set includes head values from 37 monitor wells over a period of 181 days, including a 96-day well-field scale aquifer-performance test. The transient residual-mapping technique identified five significant transmissivity zones and one leakance zone.

This thesis is mainly concerned with the estimation of parameters of a first-order Smooth Threshold Autoregressive (STAR) model with delay parameter one. The estimation procedures include classical and Bayesian methods from a parametric and a semiparametric point of view.As the theoretical importance of stationarity is a primary concern in estimation of time series models, we begin the thesis with a thorough investigation of necessary or sufficient conditions for ergodicity of a first-order STAR process followed by the necessary and sufficient conditions for recurrence and classification for null-recurrence and transience.The estimation procedure is started by using Bayesian analysis which derives posterior distributions of parameters with a noninformative prior for the STAR models of order p. The predictive performance of the STAR models using the exact one-step-ahead predictions along with an approximation to multi-step-ahead predictive density are considered. The theoretical results are then illustrated by simulated data sets and the well- known Canadian lynx data set.The parameter estimation obtained by conditional least squares, maximum likelihood, M-estimator and estimating functions are reviewed together with their asymptotic properties and presented under the classical and parametric approaches. These estimators are then used as preliminary estimators for obtaining adaptive estimates in a semiparametric setting. The adaptive estimates for a first-order STAR model with delay parameter one exist only for the class of symmetric error densities. At the end, the numerical results are presented to compare the parametric and semiparametric estimates of this model.

<p>To determine parameter values for models of reactions in the human body, like the glycolysis, good methods of parameter estimation are needed. Those models are often non-linear and estimation of the parameters can be very time consuming if it is possible at all. The goal of this work is to test different methods to improve the calculation speed of the parameter estimation of an example system. If the parameter estimation speed for the example system can be improved it is likely that the method could also be useful for systems similar to the example system.</p><p>One approach to improve the calculation speed is to construct a new cost function whose evaluation does not require any simulation of the system. Simulation free parameter estimation can be much quicker than using simulations to evaluate the cost function since the cost function is evaluated many times. Also a modication of the simulated annealing optimization method has been implemented and tested.</p><p>It turns out that some of the methods significantly reduced the time needed for the parameter estimations. However the quick methods have disadvantages in the form of reduced robustness. The most successful method was using a spline approximation together with a separation of the model into several submodels, and repeated use of the simulated annealing optimization algorithm to estimate the parameters.</p>

Example-based methods are effective for parameter estimation problems when the underlying system is simple or the dimensionality of the input is low. For complex and high-dimensional problems such as pose estimation, the number of required examples and the computational complexity rapidly becme prohibitively high. We introduce a new algorithm that learns a set of hashing functions that efficiently index examples relevant to a particular estimation task. Our algorithm extends a recently developed method for locality-sensitive hashing, which finds approximate neighbors in time sublinear in the number of examples. This method depends critically on the choice of hash functions; we show how to find the set of hash functions that are optimally relevant to a particular estimation problem. Experiments demonstrate that the resulting algorithm, which we call Parameter-Sensitive Hashing, can rapidly and accurately estimate the articulated pose of human figures from a large database of example images.

Thesis (Ph. D.)--Chalmers tekniska högskola and Göteborgs universitet, 2006. / Includes bibliographical references (p. 219-224) and index.

Despite the immense progress made by molecular biology in cataloging andcharacterizing molecular elements of life and the success in genome sequencing, therehave not been comparable advances in the functional study of complex phenotypes.This is because isolated study of one molecule, or one gene, at a time is not enough byitself to characterize the complex interactions in organism and to explain the functionsthat arise out of these interactions. Mathematical modeling of biological systems isone way to meet the challenge.My research formulates the modeling of gene regulation as a control problem andapplies systems and control theory to the identification, analysis, and optimal controlof genetic regulatory networks. The major contribution of my work includes biologicallyconstrained estimation, dynamical analysis, and optimal control of genetic networks.In addition, parameter estimation of nonlinear models of biological networksis also studied, as a parameter estimation problem of a general nonlinear dynamicalsystem. Results demonstrate the superior predictive power of biologically constrainedstate-space models, and that genetic networks can have differential dynamic propertieswhen subjected to different environmental perturbations. Application of optimalcontrol demonstrates feasibility of regulating gene expression levels. In the difficultproblem of parameter estimation, generalized EM algorithm is deployed, and a set of explicit formula based on extended Kalman filter is derived. Application of themethod to synthetic and real world data shows promising results.