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I have this very simple MCMC there I have 

-an initial state and a posterior
-loop :
   - add or subtract (each prob 0.5) a small number from the current state
   - compute posterior
   - move if the posterior if better
   - otherwise, move with probability proportional to the ratio of 
     the posteriors

The problem is that my posteriors are very narrow. Can I modify the last step to allow moves to less desirable areas of the space ?

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  • $\begingroup$ You can change the "small number" so that the places you move to are more reasonable. $\endgroup$
    – guy
    Commented Feb 20, 2015 at 19:37
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    $\begingroup$ Do you know whether the problem is i) that the posteriors of your model are more narrow than you want or ii) that your MCMC algorithm outputs too narrow posteriors compared to the true posteriors of your model? $\endgroup$
    – Juho Kokkala
    Commented Feb 20, 2015 at 19:41
  • $\begingroup$ hey Juho. We have no clue about the true posteriors as this is simulated data and the values of the parameters are single values (no range just single numbers). We think the posteriors are too narrow since if we run subsampling with replacement, our values are a lot wider. $\endgroup$
    – madreblu
    Commented Feb 20, 2015 at 20:24
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    $\begingroup$ Since the parameter is a scalar, you should be able to evaluate the posterior for a range of values, renormalize, and have a very good approximation to the posterior to compare with your Metroplis samples. $\endgroup$
    – jaradniemi
    Commented Feb 22, 2015 at 15:49

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