[karpierz]

> 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.

[_yb2s]

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]

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

[_yb2s]

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]

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.

[mjburgess]

Distributions are sampled from distributions -- it is this problem which makes global scepticism an even minimally interesting problem.

When faced with "global, recursive" epistemic problems one arrives at an extremely power-law asymmetric distribution where the "bayesian value" of almost all evidence is near zero.

We live our entire lives in this "nero zero" range, and i'd suppose, this makes a "pure bayesian" solution to the problem of knowledge deficient. Since we succeed in knowing, so we succeed in making hyperfine determinations.

This sort of "hyperfine epistemology" works globally to allow us to "know at all", but as you're sensing here -- it's pretty much useless for any local problem.

Perhaps this is just the single up-side of the bayesian approach to the drake eqn: it shows how impossible it is to state such an eqn, let alone evaluate it. We cannot, a priori, make such hyperfine determiniations on such circumstantial matters.

[jncfhnb]

This post is full of fancy word nonsense.

“Distributions are sampled from distributions” is meaningless because you cannot define the meta distribution. But more importantly, the Drake equation is not a RANDOM SAMPLE from a population of distributions. So the idea of sampling distributions is irrelevant even if true. The naive math of multiplying them together is invalid.

[_yb2s]

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

[jncfhnb]

No, this is nonsense.

You’re implying that there are many things that could go wrong, and that if we took a random sample of “things” that we would probably find some joint distribution that is small. This is true in the sense that an incalculably small proportion of conceivable things happen.

But this particular thing is not a random sample of things. You don’t get to appeal to the unknown distribution of distributions. Your claim that it “ almost always makes positive outcomes very rare” is completely irrelevant to non randomly chosen and defined processes.

You can’t insert steps into a Bayesian inference until your priors match a desired outcome. It’s as fallacious as inserting an infinite number of steps that are highly likely but technically possible to not be the case as a way to reduce any given prior from basically guaranteed to basically never expected to happen.

Your argument reduces to “I don’t know what decides the probability of alien life but I think the chance is small” which is a fine opinion, but your mathemagics have not strengthened your argument.

Suppose we play a game called “the four game” in which case you have to guess if I’m thinking of the number 4. By your reasoning you would probably guess 0% because you don’t know the rules of generation and there are infinite conceivable ways I could draw numbers from and 1 out of infinite draws will be exactly 4. But when I play the four game I always think of 4. The imagined sampling of unknown distributions is irrelevant because the game itself is not random.

Now, look, the Drake equation tries to do it all, and that’s probably bad. Let’s re imagine it as a function that simply identifies a probability of alien life, by now, on a randomly chosen planet, multiplied by the total number of planets out there right now (let’s ignore the detectable part). Is the probability part really small? Well yeah almost certainly. No math required. Is it small enough that we can provide any confidence on the order of magnitude of the expected value? Nope. The only interesting question, imo, is whether that expected value is greater than or less than one.

The drug example you have provided is a case of exploring a new space. This is not comparable to life appearing on a planet. Because like a novel drug development, we have an example of life originating on a planet. It’s not a random sample either but it’s sufficient to observe that the process to make this happen exists and has happened. Unlike the drug development which largely a test of whether the pattern exists or not.

[adastra22]

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.

[DennisP]

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