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Guillermo Durand committed Dec 18, 2024
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Expand Up @@ -938,7 +938,7 @@ Finally, comparing scenarios 3 & 4 with scenarios 1 & 2, we see that multiplying

In conclusion, we effectively introduced a new algorithm to compute a curve of confidence upper bounds, much faster the previous alternative, with one power of $m$ less in the complexity.

To develop new confidence upper bounds methodology and test them on simulations, it was previously not conceivable to replicate experiments a sufficient number of times while computing whole curves. For instance, in the simulation study of @MR4178188, the number of replications chosen was 10 and the whole curve was not computed, only ten values along the curve were computed, for an `m` set to 12800, that is 0.078% of the curve had been computed. Now, simulation studies with an adequate number of replications become feasible.
To develop new confidence upper bounds methodology and test them on simulations, it was previously not conceivable to replicate experiments a sufficient number of times while computing whole curves. For instance, in the simulation study of @MR4178188, the number of replications chosen was 10 and the whole curve was not computed, only ten values along the curve were computed, for an `m` set to 12800, that is 0.078% of the curve had been computed. Now, simulation studies with an adequate number of replications and 100% of the curve become feasible.

A lot of work remains to be done on the `sanssouci` package. For example, to make the data format of a forest structure $(R_k)_{k\in\cK}$ less convoluted and more user-friendly is an interesting project. Another one would be to implement inside the package the methods of the paper @blain22notip which are currently only available in the Python language [@10.5555/1593511].

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