Here is the next chart set, on priors.

We discussed the highly correlated case that we discussed earlier, and gave a better solution, using exact simulation via a Cholesky decomposition of the matrix that describes the problem.

We briefly noted how somewhat similar problems could be attacked using proposal distributions that have fatter tails than a normal, for example a “t” distribution with a low degree-of-freedom, with a description matrix derived from the corresponding Laplace approximation.

We then discussed matrix methods for studying multivariate linear models.

Then, we looked at how the conjugate priors for a normal linear model can be used to produce a model in that class of models. The means end up being an “average” of what the data tells us and what the prior information tells us.

Finally, we talked about “posterior prediction”. The idea here is that we want to hit some target (e.g., sending a rocket to Mars), and want to know the prediction of where the rocket will end up. Or even, what the *observations* that we will observe will look like. We talked about the Dirac “delta function” and its uses under an integral sign.

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