Notes

Notes and tutorials on Bayesian computation and signal processing.

These self-contained notes and tutorials were written during my graduate years and later transcribed from the original sources with rendered LaTeX. They cover Bayesian computation, time-frequency signal processing, and coding and compression.

Longer technical reports are collected under Research › Reports.

Bayesian computation

• Normal Approximation — Laplace (normal) approximation of a bivariate posterior, with a closed form for the posterior under a normal prior.
• Gaussian mixture for Multi-modal Posteriors — approximating a multi-modal posterior by a mixture of normals, with merging to select the number of components.
• EM Algorithm for Mixture Modeling — derivation of Expectation-Maximization for Gaussian mixture models.
• Numerical Methods for Bayesian Inference — quadrature, Monte Carlo integration, rejection sampling, and random-walk Metropolis with a normal prior or likelihood.

Time-frequency & signal processing

• Introduction to Time-Frequency Analysis — Cohen’s class, the Wigner–Ville and affine classes, and adaptive time-frequency representations.
• Chirplet Decomposition — decomposing a signal into Gaussian chirplets via mixture modeling, method of moments, and nested Fisher scoring.
• Computational Complexity of the Wavelet Transform — operation counts for the 1-D, 2-D, 3-D, and incomplete-3-D wavelet transforms.

Coding & compression

• Golomb–Rice Coding — prefix codes for geometrically distributed integers, and run-length coding with Golomb codes.
• Arithmetic Coding — interval-subdivision arithmetic coding, integer arithmetic, and adaptive models.
• Quad-Trees, EZW and SPIHT Codecs — quad-tree image partitioning and the EZW and SPIHT wavelet codecs.