User:Paulpeeling/Sandbox

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[edit] Stubs

  • Generalized gamma distribution
  • Scale mixture of normals
  • Probability hypothesis density filter
  • Variable rate particle filter

[edit] Scratchpad

Conjugate prior of a Gamma distribution when n \neq 1

p(\beta) \propto \beta^{\alpha_0-1} \exp(\beta \beta_0) \prod_n \left( \exp(x_n \beta) \beta^\alpha \right) \propto \beta^{\alpha_0 + n\alpha - 1} \exp\left(\beta \left( \beta_0+\sum_n x_n \right) \right) = \Gamma\left(\alpha_0+n\alpha,\beta_0+\sum_n x_n\right)