Timeline for Only allow positive MCMC-samples: Implications for credible interval
Current License: CC BY-SA 3.0
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Mar 10, 2014 at 17:42 | answer | added | jaradniemi | timeline score: 2 | |
Feb 9, 2014 at 8:48 | comment | added | Jag Älskar | That's very neat @rasmus! Thanks! I didn't know that. I tested and it gives me the same posterior. Unfortunately it seems quite rough around 0. For the Savage-Dickey ratio we need the height of the posterior in the point 0. Because of this I still prefer the other method. I can discard all negative MCMC samples. Just need a way to calculate the credible interval afterwards. | |
Feb 8, 2014 at 22:32 | comment | added | Rasmus Bååth | But if you are looking for "easy" (it's a good thing!) use the truncation operator in jags! In probit space 0.5 is at zero. The following defines a Half-normal in jags: y ~ dnorm(1, 1) T(0, ) | |
Feb 8, 2014 at 22:26 | comment | added | Glen_b | Yes, because throwing them out (and regenerating that value again) is basically using rejection sampling within a Gibbs step to impose the prior; it corresponds to imposing the corresponding restriction on the prior at the outset. The only real problem you might run into is that in some cases you might throw out a lot of values. I'm lost now - what's the difficulty here? | |
Feb 8, 2014 at 21:52 | comment | added | Jag Älskar |
@glen @rasmus According to this paper (p. 127) it is possible to restrict after the analysis: In the Bayesian framework, order-restrictions can be implemented in several ways (...). For instance, order-restrictions can be enforced before MCMC sampling, by appropriately constraining the prior distributions, or they can be implemented after the MCMC sampling, by retaining only those MCMC samples that obey the order-restriction (...). It would like to do the latter because it seem easier.
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Feb 8, 2014 at 21:32 | comment | added | Glen_b | If values for $\theta$ below 0.5 can't appear, this information should be in a prior for $\theta$. I don't know enough about JAGS to give advice on the easiest ways to achieve that though. | |
Feb 8, 2014 at 19:30 | comment | added | Jag Älskar | So to clarify: We expect participants to achieve at least chance performance. This means that values below .5 for theta can't appear. And on probit space this means, that negative values are to be excluded | |
Feb 8, 2014 at 19:11 | comment | added | Jag Älskar | In essence we are interested in a binomial distribution with a probability parameter theta from 0 to 1. We transform this parameter to probit space so dealing with distributions is easier. A uniform prior for theta from 0 to 1 is easy: a standard normal distribution on probit space. However a prior as you suggest seems more difficult to implement. | |
S Feb 8, 2014 at 19:09 | history | suggested | Nick Stauner | CC BY-SA 3.0 |
capitalization, spelling; removed signature
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Feb 8, 2014 at 19:01 | comment | added | Rasmus Bååth | Just wondering, why not then put a uniform prior on the range (0, infinity) rather than on (-infinity, infinity)? | |
Feb 8, 2014 at 18:39 | review | Suggested edits | |||
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Feb 8, 2014 at 18:36 | history | edited | Jag Älskar | CC BY-SA 3.0 |
edited title
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Feb 8, 2014 at 18:34 | review | First posts | |||
Feb 8, 2014 at 18:39 | |||||
Feb 8, 2014 at 18:17 | history | asked | Jag Älskar | CC BY-SA 3.0 |