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May 3, 2017 at 14:43 comment added Dave Harris I would run a kernel density estimate on your parameter estimates and see what they really look like. My guess is that you are going to find a surprise in there somewhere.
May 3, 2017 at 14:25 comment added hipHopMetropolisHastings In response to your edit, that parameters I am constraining are the covariance matrix, and the Markov chain transition probabilities. Only conditional on the transition probabilities can I assume the likelihood is normal. Optimizing across co-variance matrix I believe allows to get the correct constant of integration.
May 3, 2017 at 1:42 history edited Dave Harris CC BY-SA 3.0
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May 2, 2017 at 20:10 comment added hipHopMetropolisHastings Thanks for the answer. I don't have the reputation to upvote but it was very helpful in my interpretation. Obviously I am seeing asymmetric confidence intervals. My guess is this is because I am constraining some variables. For example, if I constrain the estimation of $\beta \in (0,1)$, and the true $\beta = 0.99$, then obviously there is a lot more room to move around for values less than 0.99, resulting in bias of the mean. Does this intuition have theoretical underpinnings?
May 2, 2017 at 19:52 history answered Dave Harris CC BY-SA 3.0