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Estimating Dependence Structures with Gaussian Graphical Models : A Simulation Study in R / Beroendestruktur Skattning med Gaussianska Grafiska Modeller : En Simuleringsstudie i R

Graphical models are powerful tools when estimating complex dependence structures among large sets of data. This thesis restricts the scope to undirected Gaussian graphical models. An initial predefined sparse precision matrix was specified to generate multivariate normally distributed data. Utilizing the generated data, a simulation study was conducted reviewing accuracy, sensitivity and specificity of the estimated precision matrix. The graphical LASSO was applied using four different packages available in R with seven selection criteria's for estimating the tuning parameter. The findings are mostly in line with previous research. The graphical LASSO is generally faster and feasible in high dimensions, in contrast to stepwise model selection. A portion of the selection methods for estimating the optimal tuning parameter obtained the true network structure. The results provide an estimate of how well each model obtains the true, predefined dependence structure as featured in our simulation. As the simulated data used in this thesis is merely an approximation of real-world data, one should not take the results as the only aspect of consideration when choosing a model.

Identiferoai:union.ndltd.org:UPSALLA1/oai:DiVA.org:umu-184925
Date January 2021
CreatorsAngelchev Shiryaev, Artem, Karlsson, Johan
PublisherUmeå universitet, Statistik, Umeå universitet, Statistik
Source SetsDiVA Archive at Upsalla University
LanguageEnglish
Detected LanguageEnglish
TypeStudent thesis, info:eu-repo/semantics/bachelorThesis, text
Formatapplication/pdf
Rightsinfo:eu-repo/semantics/openAccess

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