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Activity Number: 82
Type: Contributed
Date/Time: Sunday, July 31, 2016 : 4:00 PM to 5:50 PM
Sponsor: IMS
Abstract #319247 View Presentation
Title: On Estimation of Fractal Dimension
Author(s): Khalil Shafie* and AliReza Taheriyoun and Chen Chen-Yueh
Companies: University of Northern Colorado and Shahid Beheshti University and National Chung Cheng University
Keywords: Fractal index ; Isotropic Fields ; Fractional Brownian motion ; Euler characteristic ; Bayesian analysis ; fractal dimension
Abstract:

In this work, the estimation of fractal dimension is considered for one and two-dimensional cases. For one-dimensional case, we use the Bayesian approach to estimate the fractal dimension of a fractional Brownian motion. For two-dimensional case, we propose using the Euler characteristic of the excursion set of a Gaussian random field to estimate the fractal dimension of a three-dimensional object.The Euler characteristic is used to estimate the smoothness of a polished metal surface. The Bayesian approach is applied to estimate the Hurst index of 2011 daily Taiwan Stock Index.


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