andrew_gelman_stats andrew_gelman_stats-2010 andrew_gelman_stats-2010-234 knowledge-graph by maker-knowledge-mining
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Introduction: Mike McLaughlin writes: In general, is there any way to do MCMC with a fixed constraint? E.g., suppose I measure the three internal angles of a triangle with errors ~dnorm(0, tau) where tau might be different for the three measurements. This would be an easy BUGS/WinBUGS/JAGS exercise but suppose, in addition, I wanted to include prior information to the effect that the three angles had to total 180 degrees exactly. Is this feasible? Could you point me to any BUGS model in which a constraint of this type is implemented? Note: Even in my own (non-hierarchical) code which tends to be component-wise, random-walk Metropolis with tuned Laplacian proposals, I cannot see how I could incorporate such a constraint. My reply: See page 508 of Bayesian Data Analysis (2nd edition). We have an example of such a model there (from this paper with Bois and Jiang).
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1 Mike McLaughlin writes: In general, is there any way to do MCMC with a fixed constraint? [sent-1, score-0.094]
2 , suppose I measure the three internal angles of a triangle with errors ~dnorm(0, tau) where tau might be different for the three measurements. [sent-4, score-1.875]
3 This would be an easy BUGS/WinBUGS/JAGS exercise but suppose, in addition, I wanted to include prior information to the effect that the three angles had to total 180 degrees exactly. [sent-5, score-1.36]
4 Could you point me to any BUGS model in which a constraint of this type is implemented? [sent-7, score-0.509]
5 Note: Even in my own (non-hierarchical) code which tends to be component-wise, random-walk Metropolis with tuned Laplacian proposals, I cannot see how I could incorporate such a constraint. [sent-8, score-0.647]
6 My reply: See page 508 of Bayesian Data Analysis (2nd edition). [sent-9, score-0.075]
7 We have an example of such a model there (from this paper with Bois and Jiang). [sent-10, score-0.121]
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Introduction: Mike McLaughlin writes: In general, is there any way to do MCMC with a fixed constraint? E.g., suppose I measure the three internal angles of a triangle with errors ~dnorm(0, tau) where tau might be different for the three measurements. This would be an easy BUGS/WinBUGS/JAGS exercise but suppose, in addition, I wanted to include prior information to the effect that the three angles had to total 180 degrees exactly. Is this feasible? Could you point me to any BUGS model in which a constraint of this type is implemented? Note: Even in my own (non-hierarchical) code which tends to be component-wise, random-walk Metropolis with tuned Laplacian proposals, I cannot see how I could incorporate such a constraint. My reply: See page 508 of Bayesian Data Analysis (2nd edition). We have an example of such a model there (from this paper with Bois and Jiang).
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Introduction: Mike McLaughlin writes: Consider the Seeds example in vol. 1 of the BUGS examples. There, a binomial likelihood has a p parameter constructed, via logit, from two covariates. What I am wondering is: Would it be legitimate, in a binomial + logit problem like this, to allow binomial p[i] to be a function of the corresponding n[i] or would that amount to using the data in the prior? In other words, in the context of the Seeds example, is r[] the only data or is n[] data as well and therefore not permissible in a prior formulation? I [McLaughlin] currently have a model with a common beta prior for all p[i] but would like to mitigate this commonality (a kind of James-Stein effect) when there are lots of observations for some i. But this seems to feed the data back into the prior. Does it really? It also occurs to me [McLaughlin] that, perhaps, a binomial likelihood is not the one to use here (not flexible enough). My reply: Strictly speaking, “n” is data, and so what you wa
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Introduction: Mike McLaughlin writes: In general, is there any way to do MCMC with a fixed constraint? E.g., suppose I measure the three internal angles of a triangle with errors ~dnorm(0, tau) where tau might be different for the three measurements. This would be an easy BUGS/WinBUGS/JAGS exercise but suppose, in addition, I wanted to include prior information to the effect that the three angles had to total 180 degrees exactly. Is this feasible? Could you point me to any BUGS model in which a constraint of this type is implemented? Note: Even in my own (non-hierarchical) code which tends to be component-wise, random-walk Metropolis with tuned Laplacian proposals, I cannot see how I could incorporate such a constraint. My reply: See page 508 of Bayesian Data Analysis (2nd edition). We have an example of such a model there (from this paper with Bois and Jiang).
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