E not E_θ

[CL-BZH]

Describe the mistake
Formula (9.62) and (9.63a) use E_θ and Cov_θ for the expected value and covariance of Y|X.
I believe it should be E and Cov. That is, not with respect to θ only since Y|X=(Xθ + e)|X with θ and e independent random variables.

Location

1. version: 2019-12-07
2. Chapter: 9
3. page: 312
4. line number/equation number: Formula (9.62) and (9.63a)

Proposed solution
Replace E_θ and Cov_θ by E and Cov respectively.
Furthermore, the conditioning on X should not be dropped.
The formula would be:
(9.62) E[Y | X ] = E[Xθ + e | X] = X E[θ] = X m_0 .
(9.63a) Cov[Y|X ] = Cov[Xθ | X] + Cov[e] = X Cov[θ] X' + σ^2 I

[mpd37]

Here's my suggested fix:

I do want to keep the subscripts in some places to emphasize what the random variables are.

[CL-BZH]

Hi Marc, With the epsilon subscript added it is now correct. Thank you. Chris.

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________________________________ De : Marc Deisenroth <notifications@github.com> Envoyé : mercredi 11 décembre 2019 14:42 À : mml-book/mml-book.github.io <mml-book.github.io@noreply.github.com> Cc : Christophe Louargant <christophe_louargant@hotmail.com>; Author <author@noreply.github.com> Objet : Re: [mml-book/mml-book.github.io] E not E_θ (#454) Here's my suggested fix: [image]<https://user-images.githubusercontent.com/5500569/70631011-57a14600-1be1-11ea-9c25-fff3e640676f.png> I do want to keep the subscripts in some places to emphasize what the random variables are. — You are receiving this because you authored the thread. Reply to this email directly, view it on GitHub<#454?email_source=notifications&email_token=AMHDBSAE42Y7JEBMZJKJHQLQYD355A5CNFSM4JY4C2U2YY3PNVWWK3TUL52HS4DFVREXG43VMVBW63LNMVXHJKTDN5WW2ZLOORPWSZGOEGTL47Y#issuecomment-564575871>, or unsubscribe<https://github.com/notifications/unsubscribe-auth/AMHDBSEROAFPWNLA4P26PYDQYD355ANCNFSM4JY4C2UQ>.