JuliaMath / JuliaMath/MeasureTheory.jl

Scaled canonical gaussian likelihoods

Open
#228 5 comments 1 reaction 0 assignees View on GitHub
Mitosis
Dominant language
Julia
Stars
401
Forks
31
PR merge metrics
No merged PRs in 30d

Description

We would like to represent the bounded measure (but not necessarily probability measure) with density

Screen Shot 2022-08-22 at 17 59 17

(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

$$ \propto \exp(-\frac12 (y - A x)' Q^{-1} (y-Ax) )$$

Contributor guide

No contributing guide indexed for this repository

Assessment

This issue has not been assessed yet.

Get new issues in your inbox

A short digest of beginner-friendly GitHub issues.