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Full-Text Articles in Physical Sciences and Mathematics
How Geophysicists' Intuition Helps Seismic Data Processing, Afshin Gholamy, Vladik Kreinovich
How Geophysicists' Intuition Helps Seismic Data Processing, Afshin Gholamy, Vladik Kreinovich
Departmental Technical Reports (CS)
In geophysics, signals come with noise. It is desirable to minimize the effect of this noise. If we knew the probabilities of different values of signal and noise, we could use statistical filtering techniques. In geophysics, however, we rarely know the exact values of these probabilities; instead, we have to rely on the expertise and intuition of experts. We show how fuzzy techniques can transform this expertise into precise de-noising methods, we explain that the resulting methods indeed satisfy several natural requirements, and that these methods are in good accordance with heuristic techniques successfully used by geophysicists.
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 …