O FBST (Full Bayesian Significance Test) é um procedimento para testar hipóteses precisas, apresentado por Pereira e Stern (1999), e baseado no cálculo da probabilidade posterior do conjunto tangente ao conjunto que define a hipótese nula. Este procedimento é uma alternativa Bayesiana aos testes de significância usuais. Neste trabalho, estudamos a relação entre os resultados do FBST e de um teste freqüentista, o TRVG (Teste da Razão de Verossimilhanças Generalizado), através de alguns problemas clássicos de testes de hipóteses. Apresentamos, também, todos os procedimentos computacionais utilizados para a resolução automática dos dois testes para grandes amostras, necessária ao estudo da relação entre os testes. / FBST (Full Bayesian Significance Test) is a procedure to test precise hypotheses, presented by Pereira and Stern (1999), which is based on the calculus of the posterior probability of the set tangent to the set that defines the null hypothesis. This procedure is a Bayesian alternative to the usual significance tests. In the present work we study the relation between the FBST\'s results and those of a frequentist test, GLRT (Generalised Likelihood Ratio Test) through some classical problems in hypotesis testing. We also present all computer procedures that compose the automatic solutions for applying FBST and GLRT on big samples what was necessary for studying the relation between both tests.

Tsang, Ka Wai. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2009. / Includes bibliographical references (leaves [121]-123). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.5 / Chapter 2 --- Inverse problems and formulations --- p.6 / Chapter 3 --- Review of some existing methods --- p.8 / Chapter 4 --- Trust Region Method --- p.16 / Chapter 4.1 --- Some Auxiliary Tools --- p.18 / Chapter 4.2 --- Trust Region Algorithm --- p.23 / Chapter 4.3 --- Convergence of trust region method --- p.28 / Chapter 4.3.1 --- Notations and Assumptions --- p.28 / Chapter 4.3.2 --- Convergence for exact data --- p.29 / Chapter 4.3.3 --- Regularity For Inexact Data --- p.36 / Chapter 4.4 --- Experiment On Trust Region Method --- p.39 / Chapter 4.4.1 --- Problem Setting --- p.39 / Chapter 4.4.2 --- Algorithm --- p.40 / Chapter 4.4.3 --- Experiment Results --- p.42 / Chapter 4.5 --- Trust Region Conjugate Gradient Method --- p.46 / Chapter 4.5.1 --- Notations and Assumptions --- p.49 / Chapter 4.5.2 --- Convergence Properties for Exact Data --- p.52 / Chapter 4.5.3 --- Regularity for Inexact Data --- p.57 / Chapter 5 --- Parameter Identification Problems --- p.60 / Chapter 5.1 --- Introduction --- p.60 / Chapter 5.1.1 --- Computation of VJ(x) --- p.67 / Chapter 5.2 --- Algorithm for Parameter Identification Problems --- p.72 / Chapter 5.2.1 --- "Finite Element Method in Two Dimensions:Ω =[0,1] x [0,1]" --- p.75 / Chapter 5.3 --- Experiments on Trust Region-CG Method for Parameter Identification Problems --- p.82 / Chapter 5.3.1 --- One Dimension Problem --- p.82 / Chapter 5.3.2 --- Two Dimensions Problem --- p.95 / Chapter 5.4 --- Conclusion --- p.119 / Bibliography --- p.121

Four-dimensional variational data assimilation (4D-Var) provides an estimate to the state of a dynamical system through the minimization of a cost functional that measures the distance to a prior state (background) estimate and observations over a time window. The analysis fit to each information input component is determined by the specification of the error covariance matrices in the data assimilation system (DAS). Weak-constraint 4D-Var (w4D-Var) provides a theoretical framework to account for modeling errors in the analysis scheme. In addition to the specification of the background error covariance matrix, the w4D-Var formulation requires information on the model error statistics and specification of the model error covariance. Up to now, the increased computational cost associated with w4D-Var has prevented its practical implementation. Various simplifications to reduce the computational burden have been considered, including writing the model error covariance as a scalar multiple of the background error covariance and modeling the model error. In this thesis, the main objective is the development of computationally feasible techniques for the improved representation of the model error statistics in a data assimilation system. Three new approaches are considered. A Monte Carlo method that uses an ensemble of w4D-Var systems to obtain flow-dependent estimates to the model error statistics. The evaluation of statistical diagnostic equations involving observation residuals to estimate the model error covariance matrix. An adaptive tuning procedure based on the sensitivity of a short-range forecast error measure to the model error DAS parametrization. The validity and benefits of these approaches are shown in two stages of numerical experiments. A proof-of-concept is shown using the Lorenz multi-scale model and the shallow water equations for a one-dimensional domain. The results show the potential of these methodologies to produce improved state estimates, as compared to other approaches in data assimilation. It is expected that the techniques presented will find an extended range of applications to assess and improve the performance of a w4D-Var system.

Wind energy forecasting can facilitate wind energy integration into a power system. In particular, the management of power system security would benefit from forecast information on plausible large, rapid change in wind power generation. Numerical Weather Prediction (NWP) systems are presently the best available tools for wind energy forecasting for projection times between 3 and 48 hours. In this thesis, the types of weather phenomena that cause large, rapid changes in wind power in southeast Australia are classified using observations from three wind farms. The results show that the majority of events are due to horizontal propagation of spatial weather features. A study of NWP systems reveals that they are generally good at forecasting the broad large-scale weather phenomena but may misplace their location relative to the physical world. Errors may result from developing single time-series forecasts from a single NWP grid point, or from a single interpolation of proximate grid points. This thesis presents a new approach that displays NWP wind forecast information from a field of multiple grid points around the wind farm location. Displaying the NWP wind speeds at the multiple grid points directly would potentially be misleading as they each reflect the estimated local surface roughness and terrain at a particular grid point. Thus, a methodology was developed to convert the NWP wind speeds at the multiple grid points to values that reflect surface conditions at the wind farm site. The conversion method is evaluated with encouraging results by visual inspection and by comparing with an NWP ensemble. The multiple grid point information can also be used to improve downscaling results by filtering out data where there is a large chance of a discrepancy between an NWP time-series forecast and observations. The converted wind speeds at multiple grid points can be downscaled to site-equivalent wind speeds and transformed to wind farm power assuming unconstrained wind farm operation at one or more wind farm sites. This provides a visual decision support tool that can help a forecast user assess the possibility of large, rapid changes in wind power from one or more wind farms.

This paper is about the computation of the stresses on a rigid body from a knowledge of the far field velocities in exterior Stokes and Oseen flows. The surface of the body is assumed to be bounded and smooth, and the body is assumed to move with constant velocity. We give fundamental solutions and derive boundary integral equations for the stresses. As it turns out, these integral equations are singular, and their null space is spanned by the normal to the body. We then discretize the problem by replacing the body by an approximating polyhedron with triangular faces. Using a collocation method, each integral equation delivers a linear system. Since its matrix approximates a singular integral operator, the matrix is ill-conditioned, and the solution is unstable. However, since we know that the problem is uniquely solvable in the hyperspace orthogonal to the normal, we use regularization methods to get stable solutions and project them in the normal direction onto the hyperspace. / Graduation date: 1999

Graduation date: 1991

No description available.

Thesis (Ph.D.)--City University of Hong Kong, 2009. / "Submitted to the Department of Building and Construction in partial fulfillment of the requirements for the degree of Doctor of Philosophy." Includes bibliographical references (leaves [170]-184)

Thesis (M.S.)--Mississippi State University. Department of Computational Engineering. / Title from title screen. Includes bibliographical references.

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