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I want to run Metropolis-Hastings on a problem which involves two parameters that are not independent. I.e. I want to estimate both of these parameters. At the moment I'm trying to understand if this is possible and if so how or what to watch out for... I considered implementing a single-component-MH, but as far as I understand that's only for independent variables?

Edit

1) Maybe as a first try I could rephrase the question as: what are (in-)dependency requirements on the variables in Metropolis-Hastings? If there are any.

2) Why I think the dependency is a problem, is that I am seeing clear dependence in the traceplots of the two variables. Our professor said that is a bad thing (I guess that's because the chains are not moving around the state space as freely as they should)

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    $\begingroup$ Can you clarify why you think there would any problems? Or what you mean by dependent/independent - that the parameters as random variables are dependent in the target (typically posterior) distribution, that they are independent in the prior distribution, or something completely different? $\endgroup$ Nov 30, 2015 at 10:59
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    $\begingroup$ It would help if you could include your target distribution in the question. You can obviously run MCMC with dependent variables, while using dependent or independent proposals. Take for instance Metropolis-within-Gibbs as an illustration. $\endgroup$
    – Xi'an
    Nov 30, 2015 at 11:46

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