2
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Accepted
Computing the posterior distribution in a Bayesian analysis of a normal linear regression model
$\beta \mid \nu, y, X$
We only need to get that by a proportionality factor that is unimportant, i.e., anything not involving $\beta$ is unimportant. In other words, we don't need the "$=$" ...
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Measuring departure between the posterior predictive distribution and the true data generating distribution
Some random remarks:
Statistics questions, unless dealing with heavy probability theory, are probably much better directed at stats.stackexchange.com.
Your question
Suppose, I am trying to measure ...
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