I had glossed over this difference, and so it would be confusing
to understand why my equations for VAR and COV are incorrect for
samples. I distinguished between the two and gave the correct
computations for each.
Pointed out that height of students probably has two means if the
population includes males and females. Did not go into Gaussian
mixtures or conditioning of the data.
Thought I had this fixed, not sure why it came back. Had to add
\normalem to template file to force \emph to be italics, which is
the default. Not sure why it has been doing underlining recently.
I moved the conversion of the multivariate equations to univariate
equations to the supporting textbook. It's not terribly necessary,
especially since I converted the univariate equations to look like
the multivariate ones.
Some equations used \\ without a gathered or aligned block.
They render fine in the notebook, not not in the PDF.
Also, switched back my ill chosen use of \overline for \bar.
I've derived the x + Ky form for the univariate kalman filter.
I completely reordered material, cutting about 10 pages (pdf)
of material. I made the connection between the bayesian form
and orthogonal form more explicit.
Probably there are a lot of grammatical errors, but I wanted to get
these checked in.
I also altered the css - mainly the font.
Added the likelihood equations/form from the discrete bayes
chapter to better tie in that form of reasoning. then I converted
the 1d equations to the orthogonal projection form to show how
the Kalman gain is computed and where the residual comes from
computationally. This should make the full KF equations much more
approachable.
All my code in this chapter hard coded the computation of the
likelihood inside the update() function, where it had no business.
Also, my treatment of the likelihood was rather hand wavey. By
pulling it out of update() and maing it explicit I have created
a firm foundation for the rest of the book.
It rendered fine in the notebook, but \text{foo_bar} was causing
an error in the pdf generation. Switching to \mathtt{foo\_bar}
mostly fixes it (though in the notebook it renders as -, not _.
Oye.
I was using a bunch of variable names that weren't consistent
with the rest of the book (but perhaps are more consistent with
the literature). It just made everything more challenging than
it needed to be, so instead of \mu and \sigma (e.g.) I use
\bar x and \bar P.
I also am in the middle of rewriting some sections for clarity,
but that work is not completed.
I added titles so you can see where in the processing the
graph is.
This surfaced a bug in matplotlib 1.5 (#5399) so I added
some code to work around that.
* integrals should have "du", etc. (right??)
* $\mathit{VAR}$ gives better spacing than $VAR$
* I find "within $1\sigma$" to be ambiguous; "within $\pm1sigma$" much more clear
* Changed dashes in text from hyphens to em-dashes
* Changed (some) straight quotation marks to curly ones (and removed single quotes in favour of double ones)
* Improved "°C" to just use a text symbol
* Assorted random typos, etc., but avoided rewording anything except for one particularly difficult sentence
Roger Labbe
Gluttton
Will Robertson