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I am generally not that knowledgeable for math, so if my question is too broad or inaccurate, please let me know.

I am currently reading a paragraph of one paper (https://www.fil.ion.ucl.ac.uk/spm/doc/papers/karl_bayes_dyn.pdf), which is about Bayesian parameter estimation of nonlinear dynamical system. Here is the link for screenshoted paragraph (link).

I have been going through more or less well entire paragraphs but there is one particular transition that I could not figure out, which is about Equation (13). How I can get specified equations for 'parameter covariance' and 'conditional mean parameters given a data' as stated in the paper?

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