Mixing up of $\Xi$ and $\Psi$ in priors vignette

[mikemc]

The inverse Wishart is first defined with $\Xi$ as the scale matrix parameter, https://github.com/jsilve24/fido/blob/1b33c570e521a52fce2f242d6f78aae51a59c264/vignettes/picking_priors.Rmd#L96 but the subsequent line and equation calls it $\Psi$. Then, starting in the next section, $\Psi$ starts to instead be used for the linear transformation that defines a compositional transformation. So perhaps the first two uses of $\Psi$ are typos for $\Xi$? I think it would help a lot to consistently use $\Xi$ and $\Psi$ to mean distinct matrices - e.g., $\Xi$ for the scale matrix, and $\Psi$ for the transformation matrix. I guess the benefit of $\Psi$ for the scale matrix is that is what is used in Wikipedia (which I'd guess is the source of the original typo).

[jsilve24]

Thanks for finding this! You are correct there were two times where I use \Psi but meant \Xi.

Fixed in: 134076844c38c5cd374d7d9402dc3d1106f21e94

Please let me know if you find any other errors or if I have not found all the typos you were referring to.

If all good, you can go ahead and close the issue.

[mikemc]

I will record some other possible mistakes in this vignette here so that they can be corrected together.

1. The Inverse Wishart is first introduced as having a parameterization with the scale matrix first, then the degrees of freedom parameter. But subsequent lines seem to be using a flipped order, e.g. https://github.com/jsilve24/fido/blob/134076844c38c5cd374d7d9402dc3d1106f21e94/vignettes/picking_priors.Rmd#L117

2. Also in https://github.com/jsilve24/fido/blob/134076844c38c5cd374d7d9402dc3d1106f21e94/vignettes/picking_priors.Rmd#L117 it seems that there is a switch from $\gamma$ to $\upsilon$ that isn't acknowledged/explained - is that a typo?

[jsilve24]

Wonderful! (1) you are correct (2) I think you are write calling this \upsilon would be better. I had distinguished gamma and upsilon only because they are different priors and so I should have really added upsilon = gamma.

Will fix these in a few hours.