Scaled inverse-chi-square priors specification

sherloconan

Hello, Dr. Wagenmakers and Dr. Morey.

I am reading one of your papers,

@article{rouder2017bayesian,
  title={Bayesian analysis of factorial designs.},
  author={Rouder, Jeffrey N and Morey, Richard D and Verhagen, Josine and Swagman, April R and Wagenmakers, Eric-Jan},
  journal={Psychological Methods},
  volume={22},
  number={2},
  pages={304},
  year={2017},
  publisher={American Psychological Association}
}

My concerns are whether there are some typos in this paper (or already discussed):

(1) On Page 309, "a scaled inverse $\chi^2$ distribution with a single degree of freedom (Zellner & Siow, 1980). The density of this prior is $f(g;h)=\frac{h^2}{2g^{3/2}\Gamma{1/2}}\text{exp}(h^2/2g)$, ..."

This expression does not seem to be correct.

(2) On Page 311, "$g_d\sim\text{Inv }\chi^2(1,h_d)$, ..."

This expression is inconsistent with other $g$-priors in the paper, e.g., $g_d\sim\text{Inv }\chi^2(1,h^2)$ on Page 309. Hence, I am not sure the default values ($h=0.5$ for rscaleFixed and $h=1$ for rscaleRandom ) are specified on $h$ or $h^2$.

Thank you for your comments.

jeff

Sorry for confusion. The prior setting is on h and not h^2. It is the scale of effect size and not effect size squared. The scale of the inverse chi-square is square of the h. Clear?

sherloconan

Thank you, Dr. Rouder.