<p>Network meta-analysis (NMA) is a process by which several treatments can be simultaneously compared for relative effectiveness. When conducted in a Bayesian framework, the probability that each treatment is ranked 1st, 2nd and so on can be calculated. A square matrix of these probabilities, referred to as the rank probability matrix, can be structured with rows representing treatments and columns representing ranks. In this thesis, a simulation study was conducted to explore properties of five proposed rank probability matrix summary measures: determinant, Frobenius norm, trace, diagonal maximum and diagonal minimum. Each measure is standardized to approach 1 for absolute certainty. The goal of this simulation is to identify strengths and weaknesses of these measures for varying networks. The measures are applied to previously published NMA data for further investigation. The simulation study and real data analysis revealed pros and cons of each summary measure; the Frobenius norm was found most effective. All summary measures yielded higher values with increases in symmetry, relative effect size and number of studies in the network. If the rank probability matrix is used as the primary output of a network meta-analysis (as is often the case), a simple measure of the overall confidence in the rankings is beneficial. Future research will require exploration into the distributions of these measures.</p> / Master of Science (MSc)

Nonlinear filtering is certainly very important in estimation since most real-world problems are nonlinear. Recently a considerable progress in the nonlinear filtering theory has been made in the area of the sampling-based methods, including both random (Monte Carlo) and deterministic (quasi-Monte Carlo) sampling, and their combination. This work considers the problem of tracking a maneuvering target in a multisensor environment. A novel scheme for distributed tracking is employed that utilizes a nonlinear target model and estimates from local (sensor-based) estimators. The resulting estimation problem is highly nonlinear and thus quite challenging. In order to evaluate the performance capabilities of the architecture considered, advanced sampling-based nonlinear filters are implemented: particle filter (PF), unscented Kalman filter (UKF), and unscented particle filter (UPF). Results from extensive Monte Carlo simulations using different configurations of these algorithms are obtained to compare their effectiveness for solving the distributed target tracking problem.

Kwong Yvonne Roamy. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1999. / Includes bibliographical references (leaves 149-152). / Text in English; abstracts in English and Chinese. / Kwong Yvonne Roamy. / Overviews --- p.1 / Chapter I --- Traffic Flow Problems --- p.5 / Chapter 1 --- Microscopic Approach to ID Traffic Flow Problems --- p.6 / Chapter 1.1 --- Introduction --- p.6 / Chapter 1.2 --- Models and General Formalisms --- p.7 / Chapter 1.2.1 --- The Fukui-Ishibashi Model and its Microscopic Repre- sentations --- p.7 / Chapter 1.2.2 --- Microscopic Expression for Average Velocity --- p.10 / Chapter 1.3 --- Analysis of Special Cases --- p.12 / Chapter 1.3.1 --- vmax=1 Deterministic Model --- p.12 / Chapter 1.3.2 --- vmax = 1 Model with Random Delay --- p.16 / Chapter 1.3.3 --- vmax = 2 Deterministic Model --- p.19 / Chapter 1.3.4 --- vmax = 2 Model with Random Delay --- p.23 / Chapter 1.3.5 --- vmax = 3 Deterministic Model --- p.28 / Chapter 1.3.6 --- vmax= 3 Model with Random Delay --- p.32 / Chapter 2 --- Two-Lane Traffic Flow Model I: A Microscopic Approach --- p.40 / Chapter 2.1 --- Introduction --- p.40 / Chapter 2.2 --- The Model --- p.41 / Chapter 2.3 --- Microscopic Approach --- p.44 / Chapter 2.3.1 --- Notations --- p.44 / Chapter 2.3.2 --- Formalism --- p.45 / Chapter 2.3.3 --- Iterative Results --- p.49 / Chapter 3 --- Two-Lane Traffic Flow Model II: An Alternative Approach --- p.51 / Chapter 3.1 --- Introduction --- p.51 / Chapter 3.2 --- Steady State Equations --- p.52 / Chapter 3.3 --- Exact Solution for The Case of f = 0 --- p.54 / Chapter 3.4 --- Analytical Solutions for The General Case --- p.58 / Chapter II --- Cellular Automaton Models of Driven Diffusive Frenkel-Kontorova-type Systems --- p.61 / Chapter 4 --- Microscopic Approach to the 1D CA Model of FK Systems (Model A) --- p.62 / Chapter 4.1 --- Introduction --- p.62 / Chapter 4.2 --- Model --- p.63 / Chapter 4.2.1 --- Updating Rules of the Model --- p.63 / Chapter 4.2.2 --- Symbolic Representations of the Site States --- p.64 / Chapter 4.2.3 --- Time Evolution of the State Variables --- p.66 / Chapter 4.3 --- Theoretical Solutions to the CA Model --- p.70 / Chapter 4.3.1 --- Dynamical Mapping of Mobility --- p.70 / Chapter 4.3.2 --- Analytical Solution in Large Field Limit: α= 1 --- p.71 / Chapter 4.3.3 --- "Numerical Solutions to the General Case: α E [0,1]" --- p.78 / Chapter 5 --- Microscopic Approach to the 1D CA Model of FK Systems (Model B) --- p.83 / Chapter 5.1 --- Introduction --- p.83 / Chapter 5.2 --- The Model --- p.84 / Chapter 5.2.1 --- Updating Rules --- p.84 / Chapter 5.2.2 --- Evolution Equations of The System --- p.84 / Chapter 5.3 --- Theoretical Approach to Model B --- p.87 / Chapter 5.3.1 --- Mobility at Time t + 1 in terms of Spatial Averages at Time t --- p.87 / Chapter 5.3.2 --- Analytical Solution in Large Field Limit:α = 1 --- p.88 / Chapter 5.3.3 --- "Numerical Solutions to the General Case:α E [0,1]" --- p.90 / Chapter III --- Noninteracting Particles obeying Intermediate Statistics --- p.97 / Chapter 6 --- Recursive Relation for the Partition Functions of Noninter- acting Particles Obeying Intermediate Statistics --- p.98 / Chapter 6.1 --- Introduction --- p.98 / Chapter 6.2 --- Recursive Relation for the Partition Functions --- p.100 / Chapter 6.2.1 --- Derivation I --- p.101 / Chapter 6.2.2 --- Derivation II --- p.103 / Chapter 6.2.3 --- Derivation III --- p.105 / Chapter 6.2.4 --- Heat Capacity and Occupation Numbers --- p.106 / Chapter 6.3 --- Applications to Particles in Different Confinements --- p.107 / Chapter 6.3.1 --- Isotropic Harmonic Confinements --- p.107 / Chapter 6.3.2 --- Anisotropic Harmonic Confinements --- p.108 / Chapter 6.3.3 --- Confinements in Rigid Boxes --- p.110 / Chapter 6.4 --- Typical Results and The 'Sign' Problem --- p.111 / Chapter 7 --- Thermodynamics of Non-interacting M-ons --- p.117 / Chapter 7.1 --- Introduction --- p.117 / Chapter 7.2 --- Regime of Validity --- p.117 / Chapter 7.3 --- Derivations of Tc --- p.119 / Chapter 7.3.1 --- Harmonic Confinements --- p.120 / Chapter 7.3.2 --- Rigid Box Confinements --- p.126 / Chapter IV --- Nonlinear Random Composites --- p.135 / Chapter 8 --- Dimensional Crossover of Strongly Nonlinear Random Re- sistor Networks --- p.136 / Chapter 8.1 --- Introduction --- p.136 / Chapter 8.2 --- Formalism --- p.137 / Chapter 8.3 --- Model --- p.139 / Chapter 9 --- Dilute Limit Formula for Second Harmonic Generationin Composites of Two Non-linear Components --- p.142 / Chapter 9.1 --- Introduction --- p.142 / Chapter 9.2 --- Derivation I --- p.142 / Chapter 9.3 --- Derivation II --- p.147 / Bibliography --- p.148

Lic.-avh. Uppsala : Sveriges lantbruksuniversitet, 2009. / Härtill 2 uppsatser.

No description available.

Credible projections of future local climate change are in demand. One way to accomplish this is to statistically downscale General Circulation Models (GCM’s). A new method for statistical downscaling is proposed in which the seasonal cycle is first removed, a physically based predictor selection process is employed and principal component regression is then used to train the regression. A regression model between daily maximum and minimum temperature at Shearwater, NS, and NCEP principal components in the 1961-2000 period is developed and validated and output from the CGCM3 is then used to make future projections. Projections suggest Shearwater’s mean temperature will be five degrees warmer by 2100.

No description available.

Markov distributions describe multivariate data with conditional independence structures. Dawid and Lauritzen (1993) extended this idea to hyper Markov laws for prior distributions. A hyper Markov law is a distribution over Markov distributions whose marginals satisfy the same conditional independence constraints. These laws have been used for Gaussian mixtures (Escobar, 1994; Escobar and West, 1995) and contingency tables (Liu and Massam, 2006; Dobra and Massam, 2009). In this paper, we develop a family of non-parametric hyper Markov laws that we call hyper Dirichlet processes, combining the ideas of hyper Markov laws and non-parametric processes. Hyper Dirichlet processes are joint laws with Dirichlet process laws for particular marginals. We also describe a more general class of Dirichlet processes that are not hyper Markov, but still contain useful properties for describing graphical data. The graphical Dirichlet processes are simple Dirichlet processes with a hyper Markov base measure. This class allows an extremely straight-forward application of existing Dirichlet knowledge and technology to graphical settings. Given the wide-spread use of Dirichlet processes, there are many applications of this framework waiting to be explored. One broad class of applications, known as Dirichlet process mixtures, has been used for constructing mixture densities such that the underlying number of components may be determined by the data (Lo, 1984; Escobar, 1994; Escobar and West, 1995). I consider the use of the new graphical Dirichlet process in this setting, which imparts a conditional independence structure inside each component. In other words, given the component or cluster membership, the data exhibit the desired independence structure. We discuss two applications. Expanding on the work of Escobar and West (1995), we estimate a non-parametric mixture of Markov Gaussians using a Gibbs sampler. Secondly, we employ the Mode-Oriented Stochastic Search of Dobra and Massam (2009) for determining a suitable conditional independence model, focusing on contingency tables. In general, the mixing induced by a Dirichlet process does not drastically increase the complexity beyond that of a simpler Bayesian hierarchical models sans mixture components. We provide a specific representation for decomposable graphs with useful algorithms for local updates.

In this thesis, I derive generalization error bounds — bounds on the expected inaccuracy of the predictions — for time series forecasting models. These bounds allow forecasters to select among competing models, and to declare that, with high probability, their chosen model will perform well — without making strong assumptions about the data generating process or appealing to asymptotic theory. Expanding upon results from statistical learning theory, I demonstrate how these techniques can help time series forecasters to choose models which behave well under uncertainty. I also show how to estimate the β-mixing coefficients for dependent data so that my results can be used empirically. I use the bound explicitly to evaluate different predictive models for the volatility of IBM stock and for a standard set of macroeconomic variables. Taken together my results show how to control the generalization error of time series models with fixed or growing memory.

Thesis (B.Sc. (Hons.)) --University of Adelaide, 1957. / Typewr. copy. Includes published material.