> Drake equation, which remains a chain of expected value multiplications, which is a bad way to combine probability distributions.
Perhaps the paper wants to say that the problem with the Drake equation is intrinsic to multiplying expected probability, but what they're really doing is laundering their great filter assumptions upwards in the Bayesian hierarchy (ie. into their prior distribution hyperparameters and choice of distribution)
ie. they are still using expected values, they're just using them
This discovery would totally undermine the thesis of this paper. Here's the paper:
> While the analysis above required us to make our own judgment calls about how to represent the state of scientific uncertainty for each of these parameters, our qualitative result is robust to many of these assumptions and can be driven by our claimed uncertainty in f_l alone
This is much less impressive than it sounds. What this means is that if we could verify there is alien life on Venus that independently evolved, then the prior they have for f_l is massively off and their claimed uncertainty is way off. Using a log-uniform + the lowest estimate for f_l they can find in the literature already explains most of their results, not the mere process of multiplying expected probabilities.
> So, you're right, finding life on Venus reduces some uncertainty with $f_l$ and pushes some of the probability mass down the Drake equation, which remains a chain of expected value multiplications, which is a bad way to combine probability distributions.
The only reason they get such a low result is because they push a lot of the probability mass of $f_l$ super super super super far to the left. By their model, the probability that $f_l$ is less than 0.0001 is something like 42%... if we discovered independently evolved life on venus that would shift extremely far to the right and change their results completely.
Perhaps the paper wants to say that the problem with the Drake equation is intrinsic to multiplying expected probability, but what they're really doing is laundering their great filter assumptions upwards in the Bayesian hierarchy (ie. into their prior distribution hyperparameters and choice of distribution)
ie. they are still using expected values, they're just using them
This discovery would totally undermine the thesis of this paper. Here's the paper:
> While the analysis above required us to make our own judgment calls about how to represent the state of scientific uncertainty for each of these parameters, our qualitative result is robust to many of these assumptions and can be driven by our claimed uncertainty in f_l alone
This is much less impressive than it sounds. What this means is that if we could verify there is alien life on Venus that independently evolved, then the prior they have for f_l is massively off and their claimed uncertainty is way off. Using a log-uniform + the lowest estimate for f_l they can find in the literature already explains most of their results, not the mere process of multiplying expected probabilities.
> So, you're right, finding life on Venus reduces some uncertainty with $f_l$ and pushes some of the probability mass down the Drake equation, which remains a chain of expected value multiplications, which is a bad way to combine probability distributions.
The only reason they get such a low result is because they push a lot of the probability mass of $f_l$ super super super super far to the left. By their model, the probability that $f_l$ is less than 0.0001 is something like 42%... if we discovered independently evolved life on venus that would shift extremely far to the right and change their results completely.