# Deciphering Prior Concentration for Bayesian Contingency Tables

I'm having some trouble in wrapping my mind about the prior concentration parameter when calculating a Bayes factor for contingency tables.

Specifically, the parameter prior concentration for package bf_contingency_tab in r refers to the "a" parameter in "Gunel & Dickey, 1974" which I do not have access too.

The only text I can find regarding the prior concentration is from Jamil, Ly, Morey, Love, Marsman & Wagenmakers (2017) and state:

For the matrix of prior parameters a ∗∗ (i.e., the gamma shape parameters of the Poisson rates for the cell counts, see below), a default value is obtained when each a r c =a=1 – in the multinomial case, this indicates that every combination of parameter values is equally likely a priori. Higher values of a bring the predictions of H1 closer to those of H0 ; the prior distribution under a=10, for instance, may be thought of as an uninformative a=1 prior distribution that has been updated using 9 hypothetical observations in each cell of the table. For the data in Table 1, y ..=34, y ∗.=(18,16) a vector of row totals, and y.∗=(11,23) a vector of column totals. When a=1 then a ∗.=(2,2) and a.∗=(2,2). Consequently, ξ ∗. is a vector of ones of length R, the number of rows, ξ.∗ is a vector of ones of length C, the number of columns, and ξ ..=3 . Finally, D() is a Dirichlet function defined in Eq. 5j (Albert 2007; Gunel and Dickey 1974).

What I'm getting from this is that a larger prior concentration lowers the prior belief that h1 is different than h0, is that a correct interpretation?

Further, how would I apply this prior concentration with real data?

For example: If I were to have a contingency table of car accident fatalities when it is and is not raining, and I also had prior proof that fatal accidents are 5 times more likely to occur when it is raining (OR = 5). How would I apply this info to the prior concentration parameter?