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Why is centering and standardizing generally recommended in the Bayesian approach (MCMCregress) ?

Does it apply equally for non-informative as well as informative priors?

EDIT: We have been working on a specific example. The following screen shots provide the summary from the R output. Does the centering and standardizing improve the prediction? How will the parameters be interpreted once they have been centered and standardized?

mcmc.logmod <- MCMCregress(log(Salary) ~ AtBat + Hits + HmRun, data = red.hitters,
                           family = gaussian, burnin = 1000, mcmc = 10000, verbose = 0)
summary(mcmc.logmod)
plot(mcmc.logmod, col = "brown")

enter image description here

Centered and standardized:

mcmc.logmod2 <- MCMCregress(salary ~ atbat + hits + hmrun, data = sub.hitters, family = gaussian,
                            burnin = 1000, mcmc = 10000, verbose = 0)
summary(mcmc.logmod2)

enter image description here

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  • $\begingroup$ Why should it be..? $\endgroup$ – Tim Apr 11 '17 at 13:58
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    $\begingroup$ Thats what we have been told in the lecture. I am trying to find out if that is his personal opinion or if there is a legit reason behind that statement? $\endgroup$ – Danka Apr 11 '17 at 14:03
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    $\begingroup$ It is hard to comment without knowing what the actual advice you were given was. However the general answer is no, there is no such recommendations. $\endgroup$ – Tim Apr 11 '17 at 14:15
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    $\begingroup$ Well confidence intervals are shorter because scale of your variables has changed! If instead of transforming to unit variance you would transform your variables to have variance equal to 0.000000001 they would be even shorter but you wouldn't gain any additional precision thanks to such operation... $\endgroup$ – Tim Apr 11 '17 at 14:58
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    $\begingroup$ Would you include effective sample sizes from your 2 runs? I'm anticipating the difference in effective sampling rates will corroborate John Kruschke's answer nicely. $\endgroup$ – David C. Norris Apr 11 '17 at 22:41
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Mean centering or standardizing is done only to improve the efficiency of MCMC sampling (i.e., to reduce autocorrelation in the chains). In principle it is not necessary to mean center (or standardize), but then you'd have to wait around a lot longer for the chains to produce a reasonable effective sample size. (There is no guarantee that mean centering or standardizing will help in all applications, but it tends to help.)

The mean centering or standardizing does not change the parameter estimates. You do, however, have to transform back to the original scale.

Details of this are covered at length in DBDA2E. For linear regression, see Section 17.2.1.1 (p. 485+). For quadratic trend, Section 17.4 (p. 495). For multiple linear regression, Section 18.1.2 (p. 516). For logistic regression, Section 21.1.1 (pp. 624-625).

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