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I'm runing MCMC using Metropolis-Hasting algorithm to fit an equation with 6 parameters on a dataset composed of 30 instances. How will the fact that my dataset is so small impact the posterio distribution of each parameter? And therefore its confidence interval?

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As normally, the less data there is, the larger are the uncertainty intervals(posterior/confidence). The intervals will still be correct, just not as useful.

The 6:30 ratio is big, but I have seen examples where that would be more than enough.

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