A Bayesian p-value (p) is here defined in terms of the quantile-based (1-p) * 100% credible interval (CRI) that just includes a threshold (Kery and Schaub 2011). By default a p-value of 0.05 indicates that the 95% CRI just includes 0.
References
Kery, M., and Schaub, M. 2011. Bayesian population analysis using WinBUGS: a hierarchical perspective. Academic Press, Boston. Available from https://www.vogelwarte.ch/en/research/population-biology/book-bpa/.
Examples
pvalue(as.numeric(0:100))
#> [1] 0.01960784