Luna 25 lander mission, Russian lander following on from the Soviet-era lunar program Options

[Phil Stooke]

I am starting a new thread for this mission which should fly this year.

Phil

[fredk]

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...

[rlorenz]

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.

[fredk]

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.