This paper presents a new algorithm (and an additional trick) that allows to compute fastly an entire curve of post hoc bounds for the False Discovery Proportion when the underlying bound $V^*\_{ \mathfrak{ R}}$ construction is based on a reference family $\mathfrak{ R}$ with a forest structure { \`a} la Durand et al. (2020). By an entire curve, we mean the values $V^*\_{ \mathfrak{ R}}(S\_1),\dotsc,V^*\_{ \mathfrak{ R}}(S\_m)$ computed on a path of increasing selection sets $S\_1\subsetneq\dotsb\subsetneq S\_m$, $|S\_t|=t$. The new algorithm leverages the fact that going from $S\_t$ to $S\_{ t+1}$ is done by adding only one hypothesis. Compared to a more naive approach, the new algorithm has a complexity in $O(|\mathcal K|m)$ instead of $O(|\mathcal K|m^2)$, where $|\mathcal K|$ is the cardinality of the family.
Categories: math.ST stat.CO stat.ME stat.TH