HERE IS MY STATISTICAL DEBATE WITH PROFESSOR KRUSCHKE

THIS ITEM WAS RECENTLY PUBLISHED BY JOHN KRUSCHKE ON THE JUNIOR ISBA FACEBOOK PAGE, with a readership of over 1000 Bayesian Statisticians. Fixing seems to be an appropriate word. The 95% HDI later referred to by John may, or may not, have been based upon non-standard assumptions, My understanding, from John's later discussion of 'heavy tails', is that it is much too broad when compared with the standard procedures. The state of the art concerning the Bayesian investigation of hypotheses is described by BASKURT AND EVANS in their recent paper in

*Bayesian Analysis*. In regression situations where there is vague prior knowledge and under appropriate normality assumptions, their procedures are consistent with the usual F, chi-squared, and t-tests, but with weights of evidence which supplement the usual p-values. John seems to be unaware of this.
Fixing the intercept at zero in Bayesian linear regression:

In DBDA2E and in workshops, I present an example of simple linear regression: predicting an adult's weight from his/her height. A participant at a recent workshop suggested that maybe the y-intercept should be fixed at zero, because a person of zero height should have zero weight. I replied that the linear trend is really only intended as a description over the range of reasonable adult heights, not to be extrapolated all the way to a height of zero. Nevertheless, in principle it would be easy to make the restriction in the JAGS model specification. But then it was pointed out to me that the JAGS model specification in DBDA2E standardizes the variables -- to make the MCMC more efficient -- and setting the y intercept of the standardized y to zero is (of course) not the same as setting the y intercept of the raw scale to zero. This blog post shows how to set the y intercept on the raw scale to zero.

In DBDA2E and in workshops, I present an example of simple linear regression: predicting an adult's weight from his/her height. A participant at a recent workshop suggested that maybe the y-intercept should be fixed at zero, because a person of zero height should have zero weight. I replied that the linear trend is really only intended as a description over the range of reasonable adult heights, not to be extrapolated all the way to a height of zero. Nevertheless, in principle it would be easy to make the restriction in the JAGS model specification. But then it was pointed out to me that the JAGS model specification in DBDA2E standardizes the variables -- to make the MCMC more efficient -- and setting the y intercept of the standardized y to zero is (of course) not the same as setting the y intercept of the raw scale to zero. This blog post shows how to set the y intercept on the raw scale to zero.

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