Why Malerin is Wrong About Bayes Theorem

Ichneumonwasp said:
I'm no mathematician and I have exactly zero training in using Bayes' theorem...
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But aren't you a neurologist (or am I totally mixed up)? Didn't you learn about likelihood ratios, sensitivity, specificity, positive-predictive value, etc. with evidence-based medicine?

My gut tells me we just keep using the posterior probabilities as new prior probabilities and refine our knowledge each time we apply Bayes. Is that correct?
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Yes.

Linda
 
drkitten said:
Better than you, apparently.

The 50/50 is, as has been amply demonstrated, the agnostic probability. The one you hold if you have no information whatsoever.
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Saying that it is "amply demonstrated" doesn't address my point. I accept your argument. The problem is that I don't accept that the "agnostic" position for god is correct. We DO have information.

What is more likely?
  1. A exists.
  2. A does not exist.
Given that there are a finite number of things that exist and an infinite number of things that we could hypothesize that don't exist (like a blind purple people eater living in my basement) then statement #2 is statistically more likely.

The mistake being made is that, from a statistical standpoint, a proposition can be viewed as 50/50 only if you know nothing of the premises.
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We have sufficient information to deduce that the starting point can't be 50/50.
 
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RandFan said:
I can't parse this sentence. You seem to be contradicting yourself. We have evidence there is no god and no evidence that there is a god therefore it's ridiculous to say the probability is less than 0.5?
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Sorry, that sentence made more sense in my head than on paper. I contend it's possible to figure out what I meant, but pretty hard... :D Here it is broken down:

You are presented with a binary proposition R about which you know nothing, whose possible results we label X and Y. Call it W to say that P(R=X) = 0.5. Call it G to say that P(God exists) != 0.5. I am saying that it is incorrect and even silly to claim that G implies W.

RandFan said:
Given zero information I couldn't assign one selection a greater value than another. I also wouldn't assume that it were likely a 50/50 (the world isn't filled with 50/50 propositions) only that my best bet given no information is 50/50. I know it's unintuitive, but then again, it's just mathematics.
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Sounds like we almost agree. Given zero information you must assign a probability of 50/50. For some reason you seem to be saying "oh but the actual, real probability isn't 50/50, it's just that my state of knowledge is 50/50". Well, probability is nothing but a state of knowledge in the Bayesian formulation. A "fair coin" doesn't have some XML tag hanging off of it that says "my probability of landing heads is 0.5". And so your best bet given no information is in fact the probability given your state of knowledge, and there is no universal probability, it's always conditioned on someone's state of knowledge.
 
rocketdodger said:
Yep, this is my sentiment as well. This is also what fls is talking about.

The only question is, are we right?

drkitten and greedyalgorithm are pretty darn smart so if they don't agree then I am not going to be confident in this lol.

EDIT -- upon more thought, maybe this is what they mean by "agnostic?" As in, our knowledge of the existence of things cannot be brought to bare if we are truly agnostic? And in that case 0.5 is the optimal choice since we don't even know what the difference between a binary and "existential" proposition is?
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I've had to say to Dr. Kitten that "I was wrong" before and it could possibly be this time also. :)

I don't let my chance of being wrong take away my conviction of being right so long as I analyize the arguments and seriously consider them. That's the best way to avoid appeals to authority. And it's a damn great way to learn. You really force the brain cells to chew on the problem.

We need to consider ourselves fortunate that there are guys like Dr.Kitten who are willing to even bother with us. And I for one am seriously grateful. I've learned one hell of a lot on this forum.
 
GreedyAlgorithm said:
Sorry, that sentence made more sense in my head than on paper. I contend it's possible to figure out what I meant, but pretty hard... :D Here it is broken down:

You are presented with a binary proposition R about which you know nothing, whose possible results we label X and Y. Call it W to say that P(R=X) = 0.5. Call it G to say that P(God exists) != 0.5. I am saying that it is incorrect and even silly to claim that G implies W.

Sounds like we almost agree. Given zero information you must assign a probability of 50/50. For some reason you seem to be saying "oh but the actual, real probability isn't 50/50, it's just that my state of knowledge is 50/50". Well, probability is nothing but a state of knowledge in the Bayesian formulation. A "fair coin" doesn't have some XML tag hanging off of it that says "my probability of landing heads is 0.5". And so your best bet given no information is in fact the probability given your state of knowledge, and there is no universal probability, it's always conditioned on someone's state of knowledge.
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Yes, I agree.
 
rocketdodger said:
Yep, this is my sentiment as well. This is also what fls is talking about.

The only question is, are we right?

drkitten and greedyalgorithm are pretty darn smart so if they don't agree then I am not going to be confident in this lol.

EDIT -- upon more thought, maybe this is what they mean by "agnostic?" As in, our knowledge of the existence of things cannot be brought to bare if we are truly agnostic? And in that case 0.5 is the optimal choice since we don't even know what the difference between a binary and "existential" proposition is?
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Ah, now I think I understand what you were getting at with your OP. The idea of using an observation in order to begin to be informed about your prior can technically be considered a special case of Bayes Theorem where the p(E) corresponds to the result of the observation. Drkitten even made passing reference to it, I think (will try to find the post later).

In that case, you are right. Hopefully I will have time to go over this later, in greater detail, if necessary.

Linda
 
Dunstan said:
As has been pointed out repeatedly, your equation simply isn't justified by the premises. Instead of asking everyone "what's wrong with saying this," you need to explain why you think that equation is right. Because it's just not a statement that makes any sense.

Maybe try putting into words what it is you think that the equation P(E|H) + P(E|~H) = 1 means?
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I think it means "the chances of a life supporting universe given a creator plus the chances of a life supporting universe given no creator equal one."

So there are two places where I might be wrong. First, I might be wrong about which probabilities I am dealing with. Second, I might be wrong about any probabilities needing to equal 1.

I think I am wrong on the first. What I really want to say is "the sum of all conditional probabilities of E must equal 1," but shouldn't the sum of all conditionals the same as the unconditional? So maybe I want to say P(E) must equal 1?

I guess my confusion is this. I want to say P(E|H1) + P(E|~H1) + P(E|H2) + P(E|~H2) + ... + P(E|Hn) + P(E|~Hn) == 1.0, where n is the number of all possible hypotheses that E could be conditioned on. It seemed to me, at first thought, that with a hypothesis like "a creator exists" no other hypotheses could possibly affect the outcome since ~H encompasses all other hypotheses. I no longer think that might be correct.

Am I right in thinking that the sum of all possible conditionals must equal the unconditional? That is, P(E) can be expanded into the (probably infinite) expression above? If that isn't correct then I am wrong in all possible ways I could be lol.
 
RandFan said:
We need to consider ourselves fortunate that there are guys like Dr.Kitten who are willing to even bother with us. And I for one am seriously grateful. I've learned one hell of a lot on this forum.
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I should add GreedyAlgorithm.
 
RandFan said:
We have sufficient information to deduce that the starting point can't be 50/50.
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(point of reference: IMO you did not in fact make it clear to which things you were objecting up until this post, and if you thought you did, you should update your beliefs to include noisy communication, dim listeners, or something ;))

Now this is an interesting argument! If presented with a binary proposition with unlabeled results, sure, it's 50/50. But what about the specific proposition "A exists." for some unknown A? Your original claim was "finite things exist, infinite things can be described, so P(A exists) < 0.5".

But you're assuming some kind of distribution over possible As here. We can't choose a uniform distribution over all possible As, that doesn't make any sense, there are infinite of them. So some are necessarily more likely than others (see here for example). It's entirely possible that more than 50% of the probability mass is concentrated on things that exist rather than not.

What's certain, though, as you state, is that we definitely have enough information to assign a probability other than 0.5 to the specific proposition "God exists". It might be hard to analyze, but by not doing so we are explicitly throwing away information.
 
fls said:
But aren't you a neurologist (or am I totally mixed up)? Didn't you learn about likelihood ratios, sensitivity, specificity, positive-predictive value, etc. with evidence-based medicine?



Linda
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Shhhhhh. I'm trying to make a point.

OK, I'll come clean. One of the problems I see here is the theist side using a single characteristic to decide "the answer". We all know that the situation is incredibly more complex than that, which is why we all keep saying -- you can't use that prior because we have more knowledge than you are admitting.

I thought by playing dumb it would be more acceptable to see that whatever cj or Malerin want to do with their first run through Bayes, there are many more constraints that we can put on this system. It isn't just "intelligent designer", but that "designer" must have some characteristics, all of which can be analyzed by Bayes. Whatever number we can arrive at through the first run will drop precipitously with all the other information we can have about God or the intelligent designer.

Dualism is one of the big problems with any of these concepts.

The mistake we make is thinking that whatever number is kicked out of the first go -- looking at the probability of life, even with the outrageous restraints placed in the OP of one of those threads (single universe) -- is "the answer". It isn't. It's only a first approximation. We need to take the posterior and subject it to the next set of information that we have. My guess is that, even if we think in terms of a single universe, that number is going to be well below 0.5 and very close to zero.

In other words, we could give cj and Malerin 0.5 as a starting point, but to do the analysis properly, we couldn't just stop at the posterior probablility based on the existence of life, whatever probablilities they come up with in their equation.
 
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GreedyAlgorithm said:
Sounds like we almost agree. Given zero information you must assign a probability of 50/50. For some reason you seem to be saying "oh but the actual, real probability isn't 50/50, it's just that my state of knowledge is 50/50". Well, probability is nothing but a state of knowledge in the Bayesian formulation. A "fair coin" doesn't have some XML tag hanging off of it that says "my probability of landing heads is 0.5". And so your best bet given no information is in fact the probability given your state of knowledge, and there is no universal probability, it's always conditioned on someone's state of knowledge.
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I also agree now.

Thank you for explaining this.

So it is safe to say that 0.5 is the proper agnostic estimate but in reality this likely never occurs because even so much as defining a proposition or event to have any useful meaning whatsoever effectively removes that agnosticism?
 
drkitten said:
The 50/50 is, as has been amply demonstrated, the agnostic probability. The one you hold if you have no information whatsoever.
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Thank you. Defining .5 as the agnostic value was like pulling teeth in another thread.
 
GreedyAlgorithm said:
Now this is an interesting argument! If presented with a binary proposition with unlabeled results, sure, it's 50/50. But what about the specific proposition "A exists." for some unknown A? Your original claim was "finite things exist, infinite things can be described, so P(A exists) < 0.5".

But you're assuming some kind of distribution over possible As here. We can't choose a uniform distribution over all possible As, that doesn't make any sense, there are infinite of them.
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I'm not sure why I can't assume some kind of distribution or an even distribution when discussing the existence of A. I know that false ideas exist (one eyed purple people eaters in my basement) and I know that there are many more false statements than true statements. Whatever the distribution of a finite set in an infinite set is, the mean has to be false (it seems to me).
 
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Linda,

Or another way of putting it is that we could stop all this bickering over the H that Malerin or cj chooses if we realize that we can simply assume complete agnosticism (as they did) and then apply all the other knowledge that we have. We don't have to argue for that knowledge being admitted up front -- just plug the posterior back in and we can build it in from the backside. We'll end up in the same place.

And, yes, I've taken statistics and occasionally use it, but I'm not an academician and not involved in research, so it's not a daily concern. I certainly don't use Bayes on a regular basis.
 
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There is recent speculation that even the brain uses Bayesian methods to classify sensory stimuli and decide on behavioral responses.
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:) At least you admit it's speculation. You know that there is speculation that humans lived with dinosaurs.;)
 
rocketdodger said:
I think I am wrong on the first. What I really want to say is "the sum of all conditional probabilities of E must equal 1," but shouldn't the sum of all conditionals the same as the unconditional? So maybe I want to say P(E) must equal 1?
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Well, saying that P(E) = 1 is probably committing the fallacy that drkitten mentioned earlier, about assuming that just because something did happen, it must have had to happen -- like saying that the probability of rolling a four on a six-sided die is 1 instead of 1/6, because, look, I rolled a four!

But let's put that aside for the moment and move to the next point, which is where I think your real confusion lies:

I guess my confusion is this. I want to say P(E|H1) + P(E|~H1) + P(E|H2) + P(E|~H2) + ... + P(E|Hn) + P(E|~Hn) == 1.0, where n is the number of all possible hypotheses that E could be conditioned on. It seemed to me, at first thought, that with a hypothesis like "a creator exists" no other hypotheses could possibly affect the outcome since ~H encompasses all other hypotheses. I no longer think that might be correct.

Am I right in thinking that the sum of all possible conditionals must equal the unconditional? That is, P(E) can be expanded into the (probably infinite) expression above? If that isn't correct then I am wrong in all possible ways I could be lol.
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Yeah, this is incorrect. There's no basis for concluding that P(E|H1) + .... P(E|Hn) = 1. You could be dealing with an event that was highly likely to happen regardless of which hypothesis is true, or one that was highly unlikely to happen regardless of which hypothesis is true (my "child named Sue" example).
 
RandFan said:
I'm not sure why I can't assume some kind of distribution or an even distribution when discussing the existence of A. I know that false ideas exist (one eyed purple people eaters in my basement) and I know that there are many more false statements than true statements. Whatever the distribution of a finite set in an infinite set is, the mean has to be false (it seems to me).
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Some kind of distribution, certainly. An even distribution, no, it's impossible per the link. Unless you use improper priors, which may be fine.

There are not more false statements than true statements, since every statement has its negation. There may be more nonexistent describable things than existent describable things, but that doesn't mean the priors on them should be flat. As a very simple example, it's more likely that there is a one eyed people eater in your basement than a one eyed purple people eater. I think it's not clear at all how to actually divvy up possibility space.

Of course, this has arbitrarily close to nothing to do with the OP. :)
 
Malerin said:
drkitten said:
The 50/50 is, as has been amply demonstrated, the agnostic probability. The one you hold if you have no information whatsoever.
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Thank you. Defining .5 as the agnostic value was like pulling teeth in another thread.
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But we do have plenty of other information. We know that "God" is not a necessary explanation for anything. We know that the term has been defined in contradictory ways and usually in ways that are internally self-contradictory. We know that most of the characteristics that have historically been attributed to "God" have been found to be naturalistic.

We know that most theists define God as someone who intervenes in all sorts of things, who listens and answers prayers, who reveals future events through prophets, etc. Many theists say their belief in God is based on ancient writings which are known to have errors, inconsistencies, contradictions and downright falsehoods.

Seems like willful ignorance to ignore all that and say that the agnostic value for the probability of God's existence is 0.5.

It would be like playing 3 card monte with a known cheat. You've caught him lying over and over again, yet THIS time you say that the chances of a certain card being the Queen is 1:3.
 
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