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In time series econometrics and finance, most Bayesian authors approximate their models with a Gibbs Sampler, this is especial true for state space models, SV and so forth. The dimensionality of these problems ranges from 3-20 parameters.

The thing is, that for some of the more complex time series models, I find that writing the Gibbs sampling algorithm, or trying to find out how to use good built-ins to implement it, is much more labor intensive than simply writing a likelihood and prior, taking a good guesstimate for the proposal covariance matrix, and giving the whole thing to a function like Metro_Hastings from the library MHadaptive, not to mention that you are no longer restricted to conjugate priors.

For these time series models, what are the potential consequences of using Adaptive Metropolis Hastings in place of a Gibbs sampler?

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    $\begingroup$ FYI: there is also other software (e.g. JAGS or Stan) that uses other than Gibbs sampling algorithms and in many cases they are more efficient than pure M-H or Gibbs. $\endgroup$ – Tim Aug 5 '15 at 10:32
  • $\begingroup$ The Gibbs sampler does not "estimate"a model, but approximates the exact Bayesian estimation of this model. $\endgroup$ – Xi'an Aug 5 '15 at 15:49
  • $\begingroup$ @xian I changed it. $\endgroup$ – Zachary Blumenfeld Aug 5 '15 at 16:20

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