Luna 25 lander mission, Russian lander following on from the Soviet-era lunar program |
Luna 25 lander mission, Russian lander following on from the Soviet-era lunar program |
Feb 4 2022, 03:14 AM
Post
#1
|
|
Solar System Cartographer Group: Members Posts: 10191 Joined: 5-April 05 From: Canada Member No.: 227 |
I am starting a new thread for this mission which should fly this year.
Phil -------------------- ... because the Solar System ain't gonna map itself.
Also to be found posting similar content on https://mastodon.social/@PhilStooke Maps for download (free PD: https://upload.wikimedia.org/wikipedia/comm...Cartography.pdf NOTE: everything created by me which I post on UMSF is considered to be in the public domain (NOT CC, public domain) |
|
|
Aug 21 2023, 04:22 AM
Post
#2
|
|
Senior Member Group: Members Posts: 4252 Joined: 17-January 05 Member No.: 152 |
And presumably the "expected success probability" for something like ESA Mars landings needs to be taken with a healthy grain of salt, since there have been no successes...
|
|
|
Aug 22 2023, 01:21 AM
Post
#3
|
|
Member Group: Members Posts: 611 Joined: 23-February 07 From: Occasionally in Columbia, MD Member No.: 1764 |
And presumably the "expected success probability" for something like ESA Mars landings needs to be taken with a healthy grain of salt, since there have been no successes... You miss the whole point of the Cromwell-Laplace estimate (discussed in the supplement to the paper - the success probability estimator of most use may be informally termed the Cromwell‐Laplace estimate, equal to (k+1)/(n+2) where k is the number of successes out of n trials. It essentially encodes the idea that one can never be 100% certain (from Oliver Cromwell’s appeal “I beseech you, in the bowels of Christ, think it possible that you may be mistaken” to the Church of Scotland in 1650). Equivalently, it introduces the possibility that one’s luck could run out and the next trial may fail, even in an otherwise unblemished record so far.) In effect k+1/n+2 dilutes the track record by the prospect that the next attempt could go either way. It embodies the prior that no system is 100% reliable or 100% unreliable, and starts with a 50:50 guess if there is no track record, then asymptotically tends as data accumulate to the frequentist probability k/n. So 'the grain of salt' is baked into the method via Bayes rule. |
|
|
Aug 23 2023, 01:24 AM
Post
#4
|
|
Senior Member Group: Members Posts: 4252 Joined: 17-January 05 Member No.: 152 |
In effect k+1/n+2 dilutes the track record by the prospect that the next attempt could go either way. It embodies the prior that no system is 100% reliable or 100% unreliable, and starts with a 50:50 guess if there is no track record, then asymptotically tends as data accumulate to the frequentist probability k/n. So 'the grain of salt' is baked into the method via Bayes rule. I agree that the Cromwell‐Laplace estimate (aka the "rule of succession") gives the best estimate (expectation of the posterior) of the probability, P, of success for independent trials when we assume a uniform prior on P. My point instead was simply that the variance of the posterior for P gets large for small n. Eg, for ESA Mars landings (k = 0, n = 2) we have mean P = 0.25 but standard deviation of 0.19 (for the beta distribution posterior). In other words, we really can't say much about P in that case except that it's vaguely somewhere between maybe 0.06 and 0.44. That's what I meant by taking P = 0.25 with a grain of salt. Of course the variance gets smaller as n gets larger, so when there are many launches the value of the expectation P is more meaningful. |
|
|
Aug 24 2023, 02:38 AM
Post
#5
|
|
Member Group: Members Posts: 611 Joined: 23-February 07 From: Occasionally in Columbia, MD Member No.: 1764 |
I agree that the Cromwell‐Laplace estimate (aka the "rule of succession") gives the best estimate (expectation of the posterior) of the probability, P, of success for independent trials when we assume a uniform prior on P. My point instead was simply that the variance of the posterior for P gets large for small n. Eg, for ESA Mars landings (k = 0, n = 2) we have mean P = 0.25 but standard deviation of 0.19 (for the beta distribution posterior). In other words, we really can't say much about P in that case except that it's vaguely somewhere between maybe 0.06 and 0.44. That's what I meant by taking P = 0.25 with a grain of salt. Of course the variance gets smaller as n gets larger, so when there are many launches the value of the expectation P is more meaningful. Sure. To put it another way that avoids people having to mess with Beta distributions, you can get an idea of the size of the required salt grain (i.e. some measure of the uncertainty) from the difference between (k/n) and (k+1/n+2), here 0/2 vs 1/4, or 0.25 |
|
|
Lo-Fi Version | Time is now: 13th June 2024 - 04:21 AM |
RULES AND GUIDELINES Please read the Forum Rules and Guidelines before posting. IMAGE COPYRIGHT |
OPINIONS AND MODERATION Opinions expressed on UnmannedSpaceflight.com are those of the individual posters and do not necessarily reflect the opinions of UnmannedSpaceflight.com or The Planetary Society. The all-volunteer UnmannedSpaceflight.com moderation team is wholly independent of The Planetary Society. The Planetary Society has no influence over decisions made by the UnmannedSpaceflight.com moderators. |
SUPPORT THE FORUM Unmannedspaceflight.com is funded by the Planetary Society. Please consider supporting our work and many other projects by donating to the Society or becoming a member. |