JuliaMath / JuliaMath/MeasureTheory.jl
Scaled canonical gaussian likelihoods
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- Julia
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Description
We would like to represent the bounded measure (but not necessarily probability measure) with density

(so `H` (`=Λ` in MT parlance), and `F = Λμ` could be called potential parameter)
For some choice of `c` this *is* a probability measure, but the actual value of `c` itself contains important information about the evidence of a Bayesian model with Gaussian posterior represented in this form)
The likelihood object should pairing with Gaussian priors (giving a Gaussian posterior),
support fusion #229, and pullback
$$\exp(\tilde c + \tilde Fx + x'\tilde Hx) = \int \exp(c + Fy + y' H y) \kappa(x, dy) $$
where
$$\kappa(x) = N(A x + b, Q)$$
is a linear Gaussian kernel, with density
$$ \propto \exp(-\frac12 (y - A x)' Q^{-1} (y-Ax) )$$
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