wanted the post to focus specifically upon how difficult it seems to avoid the conclusion of prioritizing animal welfare in neartermism
I wasn’t familiar with these other calculations you mention. I thought you were just relying on the RP studies which seemed flimsy. This extra context makes the case much stronger.
Sadly, I don’t think that approach is correct. The 5th percentile of a product of random variables is not the product of the 5th percentiles—in fact, in general, it’s going to be a product of much higher percentiles (20+).
I don’t think that’s true either.
If you’re multiplying noramlly distributed distributions, the general rule is that you add the percentage variances in quadrature.
Which I don’t think converges to a specific percentile like 20+. As more and more uncertainties cancel out the relative contribution of any given uncertainty goes to zero.
IDK. I did explicitly say that my calculation wasn’t correct. And with the information on hand I can’t see how I could’ve done better. Maybe I should’ve fudged it down by one OOD.
On the percentile of a product of normal distributions, I wrote this Python script which shows that the 5th percentile of a product of normally distributed random variables will in general be a product of much higher percentiles (in this case, the 16th percentile):
import random
MU = 100
SIGMA = 10
N_SAMPLES = 10 ** 6
TARGET_QUANTILE = 0.05
INDIVIDUAL_QUANTILE = 83.55146375 # From Google Sheets NORMINV(0.05,100,10)
samples = []
for _ in range(N_SAMPLES):
r1 = random.gauss(MU, SIGMA)
r2 = random.gauss(MU, SIGMA)
r3 = random.gauss(MU, SIGMA)
sample = r1 * r2 * r3
samples.append(sample)
samples.sort()
# The sampled 5th percentile product
product_quantile = samples[int(N_SAMPLES * TARGET_QUANTILE)]
implied_individual_quantile = product_quantile ** (1/3)
implied_individual_quantile # ~90, which is the *16th* percentile by the empirical rule
I apologize for overstating the degree to which this reversion occurs in my original reply (which claimed an individual percentile of 20+ to get a product percentile of 5), but I hope this Python snippet shows that my point stands.
I did explicitly say that my calculation wasn’t correct. And with the information on hand I can’t see how I could’ve done better.
This is completely fair, and I’m sorry if my previous reply seemed accusatory or like it was piling on. If I were you, I’d probably caveat your analysis’s conclusion to something more like “Under RP’s 5th percentile weights, the cost-effectiveness of cage-free campaigns would probably be lower than that of the best global health interventions”.
I wasn’t familiar with these other calculations you mention. I thought you were just relying on the RP studies which seemed flimsy. This extra context makes the case much stronger.
I don’t think that’s true either.
If you’re multiplying noramlly distributed distributions, the general rule is that you add the percentage variances in quadrature.
Which I don’t think converges to a specific percentile like 20+. As more and more uncertainties cancel out the relative contribution of any given uncertainty goes to zero.
IDK. I did explicitly say that my calculation wasn’t correct. And with the information on hand I can’t see how I could’ve done better. Maybe I should’ve fudged it down by one OOD.
Thanks for being charitable :)
On the percentile of a product of normal distributions, I wrote this Python script which shows that the 5th percentile of a product of normally distributed random variables will in general be a product of much higher percentiles (in this case, the 16th percentile):
I apologize for overstating the degree to which this reversion occurs in my original reply (which claimed an individual percentile of 20+ to get a product percentile of 5), but I hope this Python snippet shows that my point stands.
This is completely fair, and I’m sorry if my previous reply seemed accusatory or like it was piling on. If I were you, I’d probably caveat your analysis’s conclusion to something more like “Under RP’s 5th percentile weights, the cost-effectiveness of cage-free campaigns would probably be lower than that of the best global health interventions”.