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The SPRT without draw model, elo model or whatever...
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Michel Van den Bergh



Joined: 28 Sep 2008
Posts: 1907

PostPost subject: The SPRT without draw model, elo model or whatever...    Posted: Tue Sep 01, 2015 7:29 am Reply to topic Reply with quote

A typical implementation of the SPRT (e.g. cutechess) now runs as follows:

(1) Estimate the draw_elo parameter of the BayesElo model from the sample.
(2) Use a "scale" given by a standard formula to convert logistic elo's (input to the SPRT) to Bayes elo's.
(3) Perform the SPRT using the BayesElo model.

This is partially the result of my own suggestion long ago to use the Bayes Elo model for the SPRT.

However I have now come to realize that this procedure is ridiculously circuitous! My suggestion was based on a lack of experience in statistics.

After all a match between two engines just follows a trinomial distribution. Thus we may perform directly a GSPRT(*) for H0:expected_score=score0 against H1:expected_score=score1 with unknown parameter the draw ratio. This is mathematically much cleaner and also much easier to implement....

(*) The GSPRT is a variant on the SPRT when there are unknown parameters. One replaces the log likelihood used in the SPRT by its maximum over the parameter space subject to the conditions H0 and H1. The GSPRT satisfies the same optimality properties as the SPRT, at least asymptotically.
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Subject Author Date/Time
The SPRT without draw model, elo model or whatever... Michel Van den Bergh Tue Sep 01, 2015 7:29 am
      Re: The SPRT without draw model, elo model or whatever... Kai Laskos Tue Sep 01, 2015 9:06 am
            Re: The SPRT without draw model, elo model or whatever... Michel Van den Bergh Tue Sep 01, 2015 11:19 am
                  Re: The SPRT without draw model, elo model or whatever... Ferdinand Mosca Tue Sep 01, 2015 2:35 pm
                        Re: The SPRT without draw model, elo model or whatever... Michel Van den Bergh Tue Sep 01, 2015 2:55 pm
                              Re: The SPRT without draw model, elo model or whatever... Michel Van den Bergh Tue Sep 01, 2015 3:18 pm
                                    Re: The SPRT without draw model, elo model or whatever... Ferdinand Mosca Tue Sep 01, 2015 3:55 pm
                                          Re: The SPRT without draw model, elo model or whatever... Michel Van den Bergh Tue Sep 01, 2015 4:49 pm
                                                Re: The SPRT without draw model, elo model or whatever... Ferdinand Mosca Tue Sep 01, 2015 5:53 pm
                                                      Re: The SPRT without draw model, Elo model or whatever... Jesús Muñoz Tue Sep 01, 2015 6:01 pm
                                                            Re: The SPRT without draw model, Elo model or whatever... Michel Van den Bergh Tue Sep 01, 2015 6:33 pm
                  Re: The SPRT without draw model, elo model or whatever... Ferdinand Mosca Wed Sep 02, 2015 5:53 am
                  Re: The SPRT without draw model, elo model or whatever... Ferdinand Mosca Wed Sep 02, 2015 6:00 pm
                        Re: The SPRT without draw model, elo model or whatever... Michel Van den Bergh Wed Sep 02, 2015 6:12 pm
                              Re: The SPRT without draw model, elo model or whatever... Ferdinand Mosca Wed Sep 02, 2015 6:46 pm
                                    Re: The SPRT without draw model, Elo model or whatever... Jesús Muñoz Wed Sep 02, 2015 7:12 pm
                                          Re: The SPRT without draw model, Elo model or whatever... Ferdinand Mosca Wed Sep 02, 2015 7:27 pm
                              Re: The SPRT without draw model, elo model or whatever... Ferdinand Mosca Wed Sep 02, 2015 10:41 pm
                                    Re: The SPRT without draw model, elo model or whatever... Michel Van den Bergh Thu Aug 18, 2016 3:18 pm
                                          Re: The SPRT without draw model, elo model or whatever... Nicu Ionita Thu Aug 18, 2016 4:39 pm
                                                Re: The SPRT without draw model, elo model or whatever... Michel Van den Bergh Thu Aug 18, 2016 5:15 pm
                                                      Re: The SPRT without draw model, Elo model or whatever... Jesús Muñoz Thu Aug 18, 2016 7:09 pm
                                                            Re: The SPRT without draw model, Elo model or whatever... Michel Van den Bergh Sun Aug 21, 2016 8:35 am
                                                                  Re: The SPRT without draw model, Elo model or whatever... Jesús Muñoz Wed Aug 24, 2016 5:57 pm
                                                                        Re: The SPRT without draw model, Elo model or whatever... Michel Van den Bergh Thu Aug 25, 2016 8:15 am
                                                                              Re: The SPRT without draw model, Elo model or whatever... Michel Van den Bergh Tue Nov 07, 2017 8:21 pm
                                                                                    Re: The SPRT without draw model, Elo model or whatever... Michel Van den Bergh Thu Nov 09, 2017 12:03 am
                                                                              Re: The SPRT without draw model, Elo model or whatever... Isaac Haïk Dunn Thu Nov 09, 2017 9:00 pm
                                                                                    Re: The SPRT without draw model, Elo model or whatever... Richard Delorme Tue Nov 14, 2017 11:40 am
                                                                                          Re: The SPRT without draw model, Elo model or whatever... Álvaro Begué Tue Nov 14, 2017 11:58 am
                                                                                          Re: The SPRT without draw model, Elo model or whatever... Michel Van den Bergh Tue Nov 14, 2017 1:07 pm
                                                      Re: The SPRT without draw model, Elo model or whatever... Jesús Muñoz Fri Aug 19, 2016 6:13 pm
                  Re: SF and Simple SPRT plots Ferdinand Mosca Thu Sep 03, 2015 11:28 am
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