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Particle Markov Chain Monte Carlo for Partially Observed Markov Jump Processes
(2011)Master Thesis -
Bayesian Inference for Multivariate t Copulas Modeling Financial Market Risk
(2011)The main objective of this thesis is to develop a Markov chain Monte Carlo (MCMC) method under the Bayesian inference framework for estimating meta-t copula functions for modeling financial market risks. The complete posterior distribution of the copula parameters resulting from Bayesian MCMC allows further analysis such as calculating the risk measures that incorporate the parameter uncertainty. The simulation study of the fictitious and ...Master Thesis -
Determination of chlorophyll-a distribution in Lake Eymir using regression and artificial neural network models with hybrid inputs
(2011)Chlorophyll-a is a parameter which can be used to understand the trophic state of water bodies. Therefore, monitoring of this parameter is required. Yet, distribution of chlorophyll-a in water bodies is not homogeneous and exhibits both spatial and temporal variations. Therefore, frequent sampling and high sample sizes are needed for the determination of chlorophyll-a quantities. This would in return increase the sampling costs and labor ...Master Thesis -
Multi-level Monte Carlo Finite Volume methods for non-linear systems of conservation laws in multi-dimensions with random initial data
(2011)We extend the Multi-Level Monte Carlo (MLMC) algorithm of [19] in order to quantify uncertainty in the solutions of multi-dimensional hyperbolic systems of conservation laws with uncertain initial data. The algorithm is presented and several issues arising in the massively parallel numerical implementation are addressed. In particular, we present a novel load balancing procedure that ensures scalability of the MLMC algorithm on massively ...Master Thesis -
Subsampling estimates of the Lasso distribution
(2011)We investigate possibilities offered by subsampling to etimate the distribution of the Lasso estimator and construct confidence intervals/hypothesis tests. Despite being inferior to the bootstrap in terms of higher-order accuracy in situations where the later is consistent,subsampling offers the advantage to work under very weak assumptions. Thus, building upon Knight and Fu (2000), we first study the asymptotics of the Lasso estimator ...Master Thesis -