# How can I make predictions for new samples in the same subject, conditional on one observation?

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?

• That seems to be the point of your model. What is the problem you are facing ? Feb 22 at 14:20
• 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. Feb 22 at 18:02
• That is correct. You do it by applying Bayes rule. Feb 22 at 18:54
• 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). Feb 23 at 8:32