Instructor:
Marina Vannucci, Professor, Department of Statistics, Rice University.
Office: Duncan Hall, room 2083. Phone: 713-348-6132. E-mail: marina@rice.edu
Prerequisites:
No knowledge of wavelets is required. Some knowledge in statistics is desirable,
particularly in Bayesian inference.
Textbook:
The textbook for the course is Statistical Modeling by Wavelets,
by Brani Vidakovic, Wiley. See also books on wavelets on the webpage of the course.
Summary:
The course will start with a brief introduction to the wavelet theory, covering
continuous and discrete wavelet transformations, connections with signal processing
and Fourier analysis, constructions of wavelets and multiresolution analysis.
The second part of the course will focus on wavelet-based statistical methods and
applications. Topics will include smoothing of noisy signals, nonparametric function
estimation and representation of stochastic processes.
Emphasis will be given to Bayesian statistical modeling.
MATLAB software will be used for class demonstrations.
Tentative list of topics:
- Mathematical preliminaries and historical overview
- Continuous and discrete wavelet transformations
- Construction and properties of some families of wavelets
- Multiresolution analysis
- Overview of available wavelet software
- Wavelet shrinkage, thresholding policies, traditional and Bayesian approaches
- Wavelet regression, density and function estimation, traditional and Bayesian approaches
- Multiple curves, multivariate curve regression, hierarchical functional data
- Wavelets and time series, scalograms, variance decompositions
- Wavelet transformations of stationary processes, selfsimilarity, change point
Grades:
The course grade will be based on homeworks
and on a final project. The final project can be either an analysis of new data or
a critical review of the literature on aspects not fully covered in class.
Any available wavelet software can be used to carry out the final project (MATLAB, S-PLUS, MATHEMATICA, ...)
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