Marginal & Conditional for the Multivariate Normal | Full Derivation

The Multivariate Normal allows for many analytical computations that are infeasible with other (joint) distributions.

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Timestamps:
00:00 Introduction
01:25 What partitioning means for the parameters
02:39 Marginal
04:06 Marginal: Visualization for Bivariate Normal
08:26 Conditional: Bayes' Theorem
09:43 Conditional: Idea for Derivation
10:02 Conditional: Recap Multivariate Normal
10:47 Conditional: Precision Matrix
11:45 Conditional: Inserting Subdivision
19:46 Conditional: Ignoring terms
22:32 Conditional: Completing the Square
27:43 Conditional: Discussion on mu
28:08 Conditional: Preliminary Solution
20:33 Conditional: Schur Complement
37:28 Summary
40:19 Outro

[fahadrizvi]

Thank you so much for explaining every step, I'm sure there was a part of you that wanted to skip over the expansions.

[maurocomi]

Thank you for explaining this step by step! I also like that you provide nice visualisations along with the explanation, since I can understand things much better when I can see them

[josephgonzalez]

This video is so useful, it deserves much more views

[philippvetter]

This video was really helpful for me. Thank you for explaining this step by step!

[parkdavid]

Truly appreciated all of your great contents! Just to clarify, in the summary session, you wrote "Sigma a|b = Sigma aa + Sigma ab * Sigma bb inverse * Sigma ba". Shouldn't it be "Sigma a|b = Sigma aa - Sigma ab * Sigma bb inverse * Sigma ba.", minus in between? In any case, I am truly impressed, and enjoy your thoughtful step-by-step detailed lectured! Thanks!

[tvogfilmtelia]

Thanks a lot for this video! You are awesome :)

[wryltxw]

Can we look at Gaussian Process for a future video given the connection with this video.

[orjihvy]

Just trying to see when something like this can be useful to apply.

[creationwithsas]

Sir please add one practical question related this topic