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Condo
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How can I obtain a conditional distribution from a joint distribution using a MCMC sample?

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Condo
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Suppose that $\theta = (\theta_1,\theta_2)$$\theta = (\theta_1,\theta_2) \in{\mathbb R}^2$ are the parameters of a model, and that I can obtain a MCMC sample from the posterior distribution of $\theta \mid {\bf x}$.

Using the MCMC sample, how can I obtain the conditional posterior distribution

$$\theta_2 \mid \theta_1, {\bf x}\,?$$

Suppose that $\theta = (\theta_1,\theta_2)$ are the parameters of a model, and that I can obtain a MCMC sample from the posterior distribution of $\theta \mid {\bf x}$.

Using the MCMC sample, how can I obtain the conditional posterior distribution

$$\theta_2 \mid \theta_1, {\bf x}\,?$$

Suppose that $\theta = (\theta_1,\theta_2) \in{\mathbb R}^2$ are the parameters of a model, and that I can obtain a MCMC sample from the posterior distribution of $\theta \mid {\bf x}$.

Using the MCMC sample, how can I obtain the conditional posterior distribution

$$\theta_2 \mid \theta_1, {\bf x}\,?$$

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Condo
  • 23
  • 3

How can I obtain a conditional distribution from a joint distribution using MCMC?

Suppose that $\theta = (\theta_1,\theta_2)$ are the parameters of a model, and that I can obtain a MCMC sample from the posterior distribution of $\theta \mid {\bf x}$.

Using the MCMC sample, how can I obtain the conditional posterior distribution

$$\theta_2 \mid \theta_1, {\bf x}\,?$$