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> And yet nobody seems to be aware of it, and both the popular and scientific press continue with the “where are they?” Fermi paradox headlines. A reasonable e

> And yet nobody seems to be aware of it, and both the popular and scientific press continue with the “where are they?” Fermi paradox headlines. A reasonable explanation here is that the paper is not correct because it relies on unfounded priors, which is generally where most Bayesian work falls flat.

DennisP 3y ago
So your prior is that Bayesian papers are likely to have unfounded priors. Now I'm wondering how well-founded your prior is.
_yb2s 3y ago
You have it backwards- the traditional Drake equation relies on unfounded priors, and by using a Bayesian approach they have avoided that problem. Instead of making up terms from nothing like the Drake equation, they are able to represent only the data we actually have, and leave the rest uncertain. The priors are carefully encoding the actual information they have, and incorporating the extreme lack of prior knowledge as uniform or nearly uniform priors over an extremely wide range for the terms we have no data on. That is the basic takeaway here- with almost no knowledge about a large number of factors (as the Drake equation is constructed), there is an extremely high chance that once of those unknown factors is actually nearly zero, even when your expectation value for each (e.g. what would have been used in the traditional Drake equation) is relatively high. N (number of civilizations) therefore approaches zero, even if there is no single term that you are pretty sure is near zero. The Bayesian approach here allows for a rigorous representation of our (extreme lack of) knowledge and gets to the truth of the matter: civilizations face a huge number of possible bottlenecks, each of which we know almost nothing about the probabilities of. This means, there is a strong chance at least one of those is a massive filter, even if we don't know which.
- vlovich123 3y ago
  While I agree with both the approach and result intuitively, the assumption of uniform unknown priors feels like it could be a huge source of errors
  - adastra22 3y ago
    It is, and that’s what the paper is about. The Drake equation folks aren’t accounting for that huge source of errors. When you do a proper accounting, as the paper does, the number of civilizations approaches N=1 and the paradox dissolves.
  - _yb2s 3y ago
    They are demonstrating a fundamental flaw in the logical reasoning behind the original Drake equation, that is robust to specific choices of distributions, or parameters to include or exclude. Anytime you multiply a large number of uncertain probability distributions, the resulting posterior will have most of the probability mass near zero. This result is not sensitive to which distribution or bounds you choose. The Drake equation is nonsense, because it is effectively assuming certainty about every single term- and that is the only way to produce a result much higher than zero. When you are multiplying seven unknown together, you can be fairly certain that the result is close to zero without knowing the value of any of the terms, unless you have some real information that none of terms can be near zero.
    - jncfhnb 3y ago
      This is some dumb second order Bayesian reasoning. You’re declaring a prior for arbitrary random variables as if their distributions themselves are sampled from a distribution. They are not. You cannot be certain that seven random things multiplied together is close to zero. That statement is very obviously wrong. Further “near zero” is a misleading term at best because it neglects to mention that we are multiplying it by a large number to get an expected value.
      - _yb2s 3y ago
        Please try to keep the discourse civil. You have not understood my argument. What you are dismissing as obviously wrong is a well known mathematical fact [1]. Imagine the “space” of all currently unobserved phenomena that require a series of independent hurdles to be overcome a la the drake equation: observable aliens, etc. This space is infinitely big and the probability of each of the hypothetical phenomena is astronomically low as to not even be worth considering. The ones that are worth considering have some evidence that either they have occurred, or that we think we understand the process by which they come about, and all of the series of independent hurdles are likely to be nonzero. Imagine this simple test: take a random sample of 7+ numbers on [0,1] and multiply them together as the Drake equation does. Repeat this thousands of times to plot a smooth density plot, and you will get a stretched exponential distribution, with the majority of the probability density near zero. This type of causal process with a cascade of independent filters multiplied together that leads to a stretched exponential is common in a lot of domains[1], and almost always makes positive outcomes very rare. For example, the probability that some random new organic molecule will bind to a specific protein target to be an effective drug is similar in this way, and is close to zero. For a molecule to work as a drug it has to pass a lot of hurdles just as a civilization does in the Drake model: be bioavailable, bind to the right target in the right way, not bind to harmful targets, be metabolized at a reasonable rate, etc. [1] https://link.springer.com/article/10.1007/s100510050276 https://link.springer.com/article/10.1007/s100510050276

DennisP 3y ago

So your prior is that Bayesian papers are likely to have unfounded priors. Now I'm wondering how well-founded your prior is.

_yb2s 3y ago

You have it backwards- the traditional Drake equation relies on unfounded priors, and by using a Bayesian approach they have avoided that problem. Instead of making up terms from nothing like the Drake equation, they are able to represent only the data we actually have, and leave the rest uncertain. The priors are carefully encoding the actual information they have, and incorporating the extreme lack of prior knowledge as uniform or nearly uniform priors over an extremely wide range for the terms we have no data on. That is the basic takeaway here- with almost no knowledge about a large number of factors (as the Drake equation is constructed), there is an extremely high chance that once of those unknown factors is actually nearly zero, even when your expectation value for each (e.g. what would have been used in the traditional Drake equation) is relatively high. N (number of civilizations) therefore approaches zero, even if there is no single term that you are pretty sure is near zero. The Bayesian approach here allows for a rigorous representation of our (extreme lack of) knowledge and gets to the truth of the matter: civilizations face a huge number of possible bottlenecks, each of which we know almost nothing about the probabilities of. This means, there is a strong chance at least one of those is a massive filter, even if we don't know which.

vlovich123 3y ago
While I agree with both the approach and result intuitively, the assumption of uniform unknown priors feels like it could be a huge source of errors
- adastra22 3y ago
  It is, and that’s what the paper is about. The Drake equation folks aren’t accounting for that huge source of errors. When you do a proper accounting, as the paper does, the number of civilizations approaches N=1 and the paradox dissolves.
- _yb2s 3y ago
  They are demonstrating a fundamental flaw in the logical reasoning behind the original Drake equation, that is robust to specific choices of distributions, or parameters to include or exclude. Anytime you multiply a large number of uncertain probability distributions, the resulting posterior will have most of the probability mass near zero. This result is not sensitive to which distribution or bounds you choose. The Drake equation is nonsense, because it is effectively assuming certainty about every single term- and that is the only way to produce a result much higher than zero. When you are multiplying seven unknown together, you can be fairly certain that the result is close to zero without knowing the value of any of the terms, unless you have some real information that none of terms can be near zero.
  - jncfhnb 3y ago
    This is some dumb second order Bayesian reasoning. You’re declaring a prior for arbitrary random variables as if their distributions themselves are sampled from a distribution. They are not. You cannot be certain that seven random things multiplied together is close to zero. That statement is very obviously wrong. Further “near zero” is a misleading term at best because it neglects to mention that we are multiplying it by a large number to get an expected value.
    - _yb2s 3y ago
      Please try to keep the discourse civil. You have not understood my argument. What you are dismissing as obviously wrong is a well known mathematical fact [1]. Imagine the “space” of all currently unobserved phenomena that require a series of independent hurdles to be overcome a la the drake equation: observable aliens, etc. This space is infinitely big and the probability of each of the hypothetical phenomena is astronomically low as to not even be worth considering. The ones that are worth considering have some evidence that either they have occurred, or that we think we understand the process by which they come about, and all of the series of independent hurdles are likely to be nonzero. Imagine this simple test: take a random sample of 7+ numbers on [0,1] and multiply them together as the Drake equation does. Repeat this thousands of times to plot a smooth density plot, and you will get a stretched exponential distribution, with the majority of the probability density near zero. This type of causal process with a cascade of independent filters multiplied together that leads to a stretched exponential is common in a lot of domains[1], and almost always makes positive outcomes very rare. For example, the probability that some random new organic molecule will bind to a specific protein target to be an effective drug is similar in this way, and is close to zero. For a molecule to work as a drug it has to pass a lot of hurdles just as a civilization does in the Drake model: be bioavailable, bind to the right target in the right way, not bind to harmful targets, be metabolized at a reasonable rate, etc. [1] https://link.springer.com/article/10.1007/s100510050276 https://link.springer.com/article/10.1007/s100510050276