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Distributions

Read Chapter 2 of Bishop, which will be discussed on the lectures.

Topics:

• Bernoulli and binomial distributions
• beta distribution
• conjugate prior for mu parameter of Bernoulli and binomial distributions
• Why are conjugate priors important?
• multinomial distribution
• Dirichlet distribution
• conjugate prior for multinomial distribution
• Gaussian distribution
• its own conjugate prior for mean
• Gamma distribution
• conjugate prior for variance
• Gaussian-Gamma distribution
• conjugate prior for mean and variance
• note this is not directly Gaussian multiplied by Gamma
• Wishart and Gaussian-Wishart distributions
• conjugate priors for multivariate Gaussian
• Student's t-distribution
• marginal of Gaussian with Gamma prior for precision
• von Mises distribution
• exponential family distributions have conjugate priors