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Early notes and tutorials on Bayesian computation and signal processing.

A set of short, self-contained notes and tutorials written during my graduate years, transcribed here from their original PDFs with rendered LaTeX. They cover Bayesian computation and statistical signal processing. Use the links below (or the sidebar) to browse them.

Tutorials

• 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.
• Chirplet Decomposition — decomposing a signal into Gaussian chirplets via mixture modeling, method of moments, and nested Fisher scoring.