ATMO 632: Week 5

Wavelets, Bayesian Inference

Course Home Page: http://www.cgd.ucar.edu/~svn/atmo632

Reading Material

1. C. Torrence & G.P. Compo, 1998: A Practical Guide to Wavelet Analysis, Bulletin of the American Meteorological Society, v.79, 61—78.
2. Hartmann: Chapter 9 (Wavelets)
3. T.J. Loredo, 1990: From Laplace to Supernova SN 1987A: Bayesian Inference in Astrophysics

http://bayes.wustl.edu/gregory/articles.pdf

Concepts

Wavelet analysis

Relationship to filtering

Types of wavelets

Orthogonal vs. non-orthogonal

Spectral significance levels

Smoothing in space and time

Bayes’ Theorem

posterior prior likelihood

Bayesian Inference

Clarifies the notion of hypothesis testing

Probability is associated with hypotheses, not statistics

Often gives the same answer as conventional statistics for simple cases

Clearly separates what is known before analyzing data from what is learned after

Choice of prior probability distribution

both strength and weakness of Bayesian approach

Gaussian inference

Conventional approach

Bayesian approach

Comparing models: Occam’s Razor

Bayesian Spectral Analysis

No assigned Homework this week!