published_or_final_version / abstract / Electrical and Electronic Engineering / Master / Master of Philosophy

published_or_final_version / Statistics and Actuarial Science / Doctoral / Doctor of Philosophy

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Sensor network plays a significant role in determining the performance of network inference tasks. A wireless sensor network with a large number of sensor nodes can be used as an effective tool for gathering data in various situations. One of the major issues in WSN is developing an efficient protocol which has a significant impact on the convergence of the network. Parameter estimation is one of the most important applications of sensor network. In order to model such large and complex networks for estimation, efficient strategies and algorithms which take less time to converge are being developed. To deal with this challenge, an approach of having multilayer network structure to estimate parameter and reach convergence in less time is estimated by comparing it with known gossip distributed algorithm. Approached Multicast multilayer algorithm on a network structure of Gaussian mixture model with two components to estimate parameters were compared and simulated with gossip algorithm. Both the algorithms were compared based on the number of iterations the algorithms took to reach convergence by using Expectation Maximization Algorithm.Finally a series of theoretical and practical results that explicitly showed that Multicast works better than gossip in large and complex networks for estimation in consensus building strategies.

Contemporary cosmology is a vibrant field, with data and observations increasing rapidly. This allows for accurate estimation of the parameters describing our cosmological model. In this thesis we present new research based on two different types of cosmological observations, which probe the universe at multiple epochs. We begin by reviewing the current concordance cosmological paradigm, and the statistical tools used to perform parameter estimation from cosmological data. We highlight the initial conditions in the universe and how they are detectable using the Cosmic Microwave Background radiation. We present the angular power spectrum data from temperature observations made with the Atacama Cosmology Telescope (ACT) and the methods used to estimate the power spectrum from temperature maps of the sky. We then present a cosmological analysis using the ACT data in combination with observations from the Wilkinson Microwave Anisotropy Probe to constrain parameters such as the effective number of relativistic species and the spectral index of the primordial power spectrum, which we constrain to deviate from scale invariance at the 99% confidence limit. We then use this combined dataset to constrain the primordial power spectrum in a minimally parametric framework, finding no evidence for deviation from a power-law spectrum. Finally we present Bayesian Estimation Applied to Multiple Species, a parameter estimation technique using photometric Type Ia Supernova data to estimate cosmological parameters in the presence of contaminated data. We apply this algorithm to the full season of the Sloan Digital Sky Survey II Supernova Search, and find that the constraints are improved by a factor of three relative to the case where one uses a smaller, spectroscopically confirmed subset of supernovae.

The main contribution of this thesis is the introduction of Bayesian quantile regression for hidden Markov models, especially when we have to deal with extreme quantile regression analysis, as there is a limited research to inference conditional quantiles for hidden Markov models, under a Bayesian approach. The first objective is to compare Bayesian extreme quantile regression and the classical extreme quantile regression, with the help of simulated data generated by three specific models, which only differ in the error term’s distribution. It is also investigated if and how the error term’s distribution affects Bayesian extreme quantile regression, in terms of parameter and confidence intervals estimation. Bayesian extreme quantile regression is performed by implementing a Metropolis-Hastings algorithm to update our parameters, while the classical extreme quantile regression is performed by using linear programming. Moreover, the same analysis and comparison is performed on a real data set. The results provide strong evidence that our method can be improved, by combining MCMC algorithms and linear programming, in order to obtain better parameter and confidence intervals estimation. After improving our method for Bayesian extreme quantile regression, we extend it by including hidden Markov models. First, we assume a discrete time finite state-space hidden Markov model, where the distribution associated with each hidden state is a) a Normal distribution and b) an asymmetric Laplace distribution. Our aim is to explore the number of hidden states that describe the extreme quantiles of our data sets and check whether a different distribution associated with each hidden state can affect our estimation. Additionally, we also explore whether there are structural changes (breakpoints), by using break-point hidden Markov models. In order to perform this analysis we implement two new MCMC algorithms. The first one updates the parameters and the hidden states by using a Forward-Backward algorithm and Gibbs sampling (when a Normal distribution is assumed), and the second one uses a Forward-Backward algorithm and a mixture of Gibbs and Metropolis-Hastings sampling (when an asymmetric Laplace distribution is assumed). Finally, we consider hidden Markov models, where the hidden state (latent variables) are continuous. For this case of the discrete-time continuous state-space hidden Markov model we implement a method that uses linear programming and the Kalman filter (and Kalman smoother). Our methods are used in order to analyze real interest rates by assuming hidden states, which represent different financial regimes. We show that our methods work very well in terms of parameter estimation and also in hidden state and break-point estimation, which is very useful for the real life applications of those methods.

by Ming-long Lam. / Thesis (M.Ph.)--Chinese University of Hong Kong, 1987. / Bibliography: leaves 41-43.

by Linda Hoi-ying Yau. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1991. / Includes bibliographical references. / Chapter Chapter 1 --- Preliminary / Chapter § 1.1 --- Introduction page --- p.1 / Chapter § 1.2 --- Notations page --- p.3 / Chapter Chapter 2 --- Multilevel Analysis of Structural Equation Models with Multivariate Normal Distribution / Chapter § 2.1 --- The Multilevel Structural Equation Model page --- p.4 / Chapter § 2.2 --- "First Stage Estimation of and Σkmkm-1---ki+1wo for i=1,...,m-1 page" --- p.5 / Chapter § 2:3 --- Second Stage Estimation of Structural Parameters page --- p.10 / Chapter Chapter 3 --- Generalization to Arbitrary and Elliptical Distributions / Chapter § 3.1 --- Asymptotically Distribution-Free Estimation page --- p.25 / Chapter § 3.2 --- Elliptical Distribution Estimation page --- p.30 / Chapter Chapter 4 --- Artificial Examples / Chapter § 4.1 --- Examples on Multivariate Normal Distribution Estimation Page --- p.34 / Chapter § 4.2 --- Examples on Elliptical Distribution Estimation page --- p.40 / Chapter §4.3 --- Findings and Summary Page --- p.42 / Chapter Chapter 5 --- Conclusion and Discussion page --- p.44 / References page --- p.47 / Figure 1 page --- p.49 / Appendices page --- p.50 / Tables Page --- p.59

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