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I have fitted a Bayesian multilevel model. Example:

$$ Y \sim Normal(\mu, \sigma)\\ \mu = \alpha + \beta * time + z_{subject}\\ z_{subject} \sim Normal(\bar{z}, \sigma_z) $$

I have fitted this to some data to get a posterior distribution for $\sigma, \alpha, \beta, \bar{z}$ and $\sigma_z$

I now observe a new Y at time=1 in a subject not related to my original data. Can I make predictions for observations in the same subject at time=2?

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  • $\begingroup$ That seems to be the point of your model. What is the problem you are facing ? $\endgroup$
    – J. Delaney
    Feb 22 at 14:20
  • $\begingroup$ If I make a single observation of Y in a new, I should be able to calculate a distribution of likely values for z for this subject. With this distribution of z and the existing posterior distribution, I should be able to make predictions of Y for this new subject. $\endgroup$
    – JohannesNE
    Feb 22 at 18:02
  • $\begingroup$ That is correct. You do it by applying Bayes rule. $\endgroup$
    – J. Delaney
    Feb 22 at 18:54
  • $\begingroup$ Okay, so if I update the posterior with a single "fake" observation in a subject that is not already present, this will give me a distribution of values for z for this new subject. Can I somehow ensure that this new update will only update z (i use brms). $\endgroup$
    – JohannesNE
    Feb 23 at 8:32

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