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In Bayesian regression context, does it make sense to say things like: “OK, I am going to add the covariate A into my model in order to control for the covariate A”?

My impression is that, since we are treating the regression coefficients to be random quantities, one can no longer control for a certain covariate by adding it into the Bayesian regression model?

Thank you,

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You typically condition on the covariates (i.e. assume them to be given values, rather than also modelling them as some realization of an some underlying process that we also model - which is also possible, but not what you do when you add a variable to a regression equation), it's the regression coefficient that you might interpret in a Bayesian or frequentist manner. That really does not affect whether one wants to adjust for the covariates.

See also this blog post proposing to use "try to adjust".

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