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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