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A bivariate Cauchy distribution is equivalent to a bivariate t-distribution with 1 degree of freedom.

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    $\begingroup$ Why not generate Cauchy variates directly? Is this homework? $\endgroup$ – Neil G Jan 9 '16 at 17:43
  • $\begingroup$ It's a question from a past exam. $\endgroup$ – ori06 Jan 9 '16 at 18:03
  • $\begingroup$ I can think of using the method of composition using the fact that the t-distribution can be written in terms of the ratio of a standard normal distribution and a chi-squared distribution. I can't figure how to do Gibbs sampling for the same problem... $\endgroup$ – ori06 Jan 9 '16 at 18:06
  • $\begingroup$ Using the ratio is not Gibbs sampling. For Gibbs sampling, you only need the density of the Cauchy distribution and some proposal distribution. Do you know how Gibbs sampling works? $\endgroup$ – Neil G Jan 9 '16 at 18:36
  • $\begingroup$ I know only the basics, that you sample at each step using the full conditional distributions i.e you sample $$x_i^{t+1}$$ from $$p(x_i|y, x_2^t,... x_n^t)$$ for i: 1 to n. How does the proposal distribution come into play for Gibbs sampling? I don't know anything about that... $\endgroup$ – ori06 Jan 9 '16 at 19:40

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