Table 3.
Probability of discovering a NN model within rank 10 or better (R1–10).
| Neural network model rank1 | Total population of 100 | Total population of 672 | ||
|---|---|---|---|---|
| Markov time as percent of population for rank’s optimal policy2 | Probability of success discovering best ranks within rank3 | Markov time as percent of population for rank’s optimal policy2 | Probability of success discovering best ranks within rank3 | |
| 1 | 37% | 0.3732 | 37% | 0.3703 |
| 2 | 31% | 0.5214 | 29% | 0.5172 |
| 3 | 23% | 0.6057 | 27% | 0.5983 |
| 4 | 21% | 0.6637 | 23% | 0.6507 |
| 5 | 18% | 0.7055 | 20% | 0.6922 |
| 6 | 17% | 0.7373 | 19% | 0.7250 |
| 7 | 17% | 0.7638 | 16% | 0.7476 |
| 8 | 15% | 0.7848 | 16% | 0.7695 |
| 9 | 15% | 0.8015 | 16% | 0.7863 |
| 10 | 14% | 0.8167 | 15% | 0.7990 |
Neural network model ranked by performance; best performing first.
Variability in the Markov Time as Percent of Population for Rank’s Optimal Policy between differing total populations is due to rounding to the nearest integer value (whole, non-fractional number). This occurs due to the nature of the Secretary Problem: the optimal policy for a given Rank may not match the reality of decision making. Such as the optimal policy for selecting Rank 1 is to reject 36.8% of the total population; however, it is not possible to reject 0.8% and interview 0.2% of an applicant, thus integer value rounding must occur.
Similar to table footnote 2, variability is due to rounding to the nearest integer value when the PDF of the modified version Secretary Problem evaluated at each Markov Time variant for each ordinal Rank in ascending order followed by computing the CDF at each Markov Time variant halting at the optimal policy discovered.