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Utilizing the results of probes sent once a minute to a random node in the network for a random amount (within a reasonable range), we were able to analyze the accuracy of our resulting success probability estimation with various PDFs. For each candidate PDF (as well as other parameters, to be tuned in the coming commits), we used the `min_zero_implies_no_successes` fudge factor in `success_probability` as well as a total probability multiple fudge factor to get both the historical success model and the a priori model to be neither too optimistic nor too pessimistic (as measured by the relative log-loss between succeeding and failing hops in our sample data). We then compared the resulting log-loss for the historical success model and selected the candidate PDF with the lowest log-loss, skipping a few candidates with similar resulting log-loss but with more extreme constants (such as a power of 11 with a higher `min_zero_implies_no_successes` penalty). This resulted in a PDF of `128 * (1/256 + 9*(x - 0.5)^8)` with a `min_zero_implies_no_successes` probability multiplier of 64/78. Thanks to @twood22 for being a sounding board and helping analyze the resulting PDF. |
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