In CollinErickson/GauPro: Gaussian Process Fitting

Here I will derive the best unbiased linear predictors for Gaussian Process regression models.

Let $X$ be the $n$ by $d$ matrix whose $n$ rows are $d$ dimensional vectors from the input space where the output has been measured. Let $Y$ be the measured values.

Let $x$ be a new design point, with output $y(x)$.

What is a BLUP?

The best linear unbiased predictor (BLUP) is a predictor of $y(x)$ with three properties: Linear: It is a linear combination of $Y$. Unbiased: Its expectation is the true value. * Best: Of all linear and unbiased predictors, it has the minimum variance.

Mean 0

If

knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)

Vignettes are long form documentation commonly included in packages. Because they are part of the distribution of the package, they need to be as compact as possible. The html_vignette output type provides a custom style sheet (and tweaks some options) to ensure that the resulting html is as small as possible. The html_vignette format:

• Never uses retina figures
• Has a smaller default figure size
• Uses a custom CSS stylesheet instead of the default Twitter Bootstrap style

Vignette Info

Note the various macros within the vignette section of the metadata block above. These are required in order to instruct R how to build the vignette. Note that you should change the title field and the \VignetteIndexEntry to match the title of your vignette.

Styles

The html_vignette template includes a basic CSS theme. To override this theme you can specify your own CSS in the document metadata as follows:

output: 
  rmarkdown::html_vignette:
    css: mystyles.css

Figures

The figure sizes have been customised so that you can easily put two images side-by-side.

plot(1:10)
plot(10:1)

You can enable figure captions by fig_caption: yes in YAML:

output:
  rmarkdown::html_vignette:
    fig_caption: yes

Then you can use the chunk option fig.cap = "Your figure caption." in knitr.

More Examples

You can write math expressions, e.g. $Y = X\beta + \epsilon$, footnotes^[A footnote here.], and tables, e.g. using knitr::kable().

knitr::kable(head(mtcars, 10))

Also a quote using >:

"He who gives up [code] safety for [code] speed deserves neither." (via)

CollinErickson/GauPro documentation built on March 25, 2024, 11:20 p.m.