Giving a univariate Gaussian mixture model $$\pi_1N(x|\mu_1,\sigma_1)+(1-\pi_1)N(x|\mu_2,\sigma_2),$$ are there any priors for $\pi_1$, $\mu_1$, $\sigma_1$, $\mu_2$, $\sigma_2$ which gives a closed form posterior?

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    $\begingroup$ It depends what you call closed form. A conjugate prior gives a closed form posterior mixture but with $2^n$ terms (Dielbolt & Robert, 1994). $\endgroup$ – Xi'an Feb 12 at 16:51
  • $\begingroup$ $2^n$ where $n$ is the number of observed independent random variables $x_1, \ldots, x_n$ as stated in jstor.org/stable/2345907, am I right? $\endgroup$ – Alessandro Jacopson Feb 12 at 18:02
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    $\begingroup$ $n$ is the sample size. $\endgroup$ – Xi'an Feb 12 at 18:22

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