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I know what is a conditional probability distribution. But what is exactly full conditional probability?

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You're just going to get an answer stating the definition of conditional probability (or linking here en.wikipedia.org/wiki/Conditional_probability) but I don't think that's what you're looking for. Can you explain exactly what your question is? – Macro Jul 2 '12 at 19:43
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It would help to put the term in context say by quoting the sentence where you saw it. – Michael Chernick Jul 2 '12 at 20:37

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I think the context is a MCMC algorithm, because this terminology is rather standard in such a context. The goal is to simulate a multivariate distribution, that is, the distribution of a random vector $(\theta_1, \ldots,\theta_p)$. The full conditional distribution of $\theta_1$ is then nothing but the conditional distribution of $\theta_1$ given all other variables.

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could you please explain how "conditional" differs from "marginal"? – Abe Jul 3 '12 at 13:02
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@Abe "marginal" is precisely "unconditional" :) – Stéphane Laurent Jul 3 '12 at 13:18

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