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Physical Sciences and Mathematics Commons™
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Full-Text Articles in Physical Sciences and Mathematics
Spatially Adaptive Estimation Of Spectrum, Yi Xie
Spatially Adaptive Estimation Of Spectrum, Yi Xie
Open Access Theses & Dissertations
A time series may be analyzed either in the time or in the frequency domain. When working in the frequency domain, the main objective is to estimate the underlying spectrum. Various approaches have been proposed to this end, but most are based on smoothing the periodogram using a single smoothing parameter across all Fourier frequencies. Such a global smoothing parameter may result in a biased estimate. To improve the estimation, in this paper, we smooth the log periodogram by placing a dynamic shrinkage prior, such that varying degrees of smoothing may be applied to different regions of the Fourier frequencies, …
Bayesian Adaptive Penalized Splines In Nonparametric Regression And In Spectral Time Series Analysis, Luis Angel Mora
Bayesian Adaptive Penalized Splines In Nonparametric Regression And In Spectral Time Series Analysis, Luis Angel Mora
Open Access Theses & Dissertations
A Bayesian approach to nonparametric regression using Penalized splines (P-splines) is presented. The approach uses the linear mixed model formulation of P-spines. The usual model assumes a single value for the smoothing parameter controlling the amount of smoothing of the fitted function. The main focus of the Thesis is on spatially adaptive smoothing where the smoothing parameter is a function of the covariate so that different amounts of smoothing are applied in different regions of the covariate. An application to spectral time series analysis will be demonstrated. Markov chain Monte Carlo methods are used to make inference based on the …
Bayesian Nonparametric Regression With A Flexible Error Term Distribution, Courtney Marie Barnes
Bayesian Nonparametric Regression With A Flexible Error Term Distribution, Courtney Marie Barnes
Open Access Theses & Dissertations
Datasets often exhibit heavy tailed behavior and standard analyses are often heavily influenced by outliers. We propose a nonparametric regression model whose error term distribution is a mixture of a normal and a Student t distribution. This results in a model that is more resistant to outliers compared to a model with a normal error term.