What does Veeky Forums think about absence of evidence?

Depends on your definition of evidence

en.wikipedia.org/wiki/Raven_paradox

>Definition: If there is evidence for X, then the probability of X is greater than if there weren't.
>Theorem: If there is no evidence for X, then the probability of X is smaller than if there were.
Bayesianists are retarded.

>P(B|A) > P(B|~A) 1 - P(~B|A) > 1 - P(~B|~A)
lol

>A = null
No, that would mean that no possible event could be evidence. Absence of evidence on the other hand is that the possible event that would be evidence did not occur.

For example, an intelligent radio signal from outer space would be evidence of alien life, but this signal is currently absent. Saying that evidence of alien life = null is to say that the probability space does not contain the event of receiving an alien radio signal.

>The "evidence" in Bayes theorem is the event in the conditional
This ignores that the phrase refers to specific evidence for an event. A conditional is not evidence for all events.

>and so "not A" being placed there means there is in fact evidence being considered.
Which is correct since the absence of evidence for one thing is evidence for something else.

Mmm well I would say it's a bit stronger than that. You don't necessarily need to look for evidence to have it. It could just fall into your lap. As long as that possibility exists, its absence is evidence of absence.

Conditional probabilities and Bayes' Theorem don't work if the conditioning probability is 1 or 0 since in this case you are using both A and A*.

Evidence either exists somewhere or it doesn't. P(A) = 1 or 0, nothing inbetween. As others have said, this means A* is the null set.

You can't just fix this by saying 0 < P(A) < 1, because what does that mean?

>using a frequentist interpretation of probability with bayes' theorem
lelllllllllllllllllllll

>Evidence either exists somewhere or it doesn't. P(A) = 1 or 0
Wew lad, nice bait.

Right, since "either it exists or it doesn't" means P(A) = 0.5 obviously.

No, it doesn't necessarily mean that either. It might mean that in certain cases. For example if you flip a fair coin then the chance it landed heads is 0.5 before you look at the result. Not "1 or 0." But again this is clearly bait as anyone who has passing knowledge of what a probability is would know this.

Not baiting. If you think I'm wrong about what the probability of A is, come up with a definition of A is - what does it represent - that doesn't contradict the manipulations that supposedly follow.

Suppose P(A) = 0.4. What does this mean? 40% chance of evidence existing? That's a meaningless statement. 40% of finding evidence given that it exists? That's just kicking the can down the road; how would you evaluate such a probability without presupposing the conclusion the argument?

You assumed your conclusion in Definition 1. People who say that phrase do not use it when Definition 1 applies.

nice. too bad evidence is more than one probability being greater than the other.

there's no evidence of your dick. therefore you have no dick.

>If you think I'm wrong about what the probability of A is, come up with a definition of A is - what does it represent - that doesn't contradict the manipulations that supposedly follow.
The entire definition is right there. A is an event which increases the probability of B when true.

>Suppose P(A) = 0.4. What does this mean? 40% chance of evidence existing?
Does "evidence existing" mean that the chance of B increases? If yes, then yes it means that.

>40% of finding evidence given that it exists?
I don't see what this has to do with the problem. Where do you see the conditional "given that it exists"?

As far as I can make out, it's just mincing words. Logical negation is not a good representation of what "absence" means.

>what is the likelihood we'd see ten heads in a row, given the coin is fair
>what is the likelihood the coin is fair, given we saw ten heads in a row
what oh what could it all mean, I guess everything is either P(X) = 1 or P(X) = 0 because we talk personally to god who has the ultimate set of tools, how does he even deal with the absence of tails it's truly a puzzler

>we have no evidence of aliens existing
Have you looked?

A) Yes. Then absence of evidence is evidence of absence.
B) No. Then look you fucking idiot.

>people actually take a class to learn this

how do you know if you've fully looked

>>we have no evidence of aliens existing
Who are you quoting?

>Have you looked?
What exactly does this mean in mathematical terms?

>too bad evidence is more than one probability being greater than the other.
Such as?

It means P(A) > 0

I'm presenting a scenario and using the greentext to highlight a different voice in a hypothetical conversation.

>It means P(A) > 0
Then why does "A) Yes. Then absence of evidence is evidence of absence" follow?

The pic in the OP explains that.

You don't, which is why it's a question of probability.

Evidence should be defined as P(B|A) > P(~B|A). The way you write it, P(B|A) could be 0.00001 and A could still be considered evidence for B.

So you can't have evidence that an unlikely event happened?

>As far as I can make out, it's just mincing words. Logical negation is not a good representation of what "absence" means.
This. The pic in OP seems to be mixing up "absence of evidence" and "having complementary evidence".

You're completely and utterly missing the point. Of course that's how probability works, in terms of events. The problem is there's no way to map an event occurring to the question of existence/absence in this way. That's why I asked what A refers to, not about its implicit mathematical definition in the inequality that follows.

If P(b|a) > P(b| not a) then doesn't that mean a is by definition evidence, and so can not be an absence of evidence?

also on this point, wouldn't it make more sense for the "absence of evidence" to be the union of all events (not A) such that P(B|A)>P(B|not A)?

It's pretty simple. Either evidence is present and increases the chance of B, or it is absent. That's exactly how it is defined in the OP. Either present a counterargument or accept it.

>Either evidence is present and increases the chance of B, or it is absent.
What does that mean mathematically? The evidence being used are just events (sets), what does it mean for a set to be "present" or "absent"?

By that logic there is no such thing as an "absence of evidence," since absence of evidence for B is evidence against B.

>By that logic there is no such thing as an "absence of evidence," since absence of evidence for B is evidence against B.
Why does absence of evidence for B being evidence against B mean that absence of evidence doesn't exist?

>What does that mean mathematically?
Again, it's written mathematically in the OP. Why are you asking questions that have already been answered?

>The evidence being used are just events (sets), what does it mean for a set to be "present" or "absent"?
Again it's clearly defined in the OP. Evidence is present when the event defined as the condition which increases the chance of B occurs. It is absent when the event does not occur.

Definitions 2 and 3 are conflicting.

>It is absent when the event does not occur.
So how do you distinguish when A "does not occur" and when not A occurs?

Why are you asking me to explain your own argument?

>If P(b|a) > P(b| not a) then doesn't that mean a is by definition evidence, and so can not be an absence of evidence?

Any event a which is an absence of evidence for B is evidence for b. Thus there cannot be an absence of both evidence for B and evidence for b.

Wrong.

A better definition for absence of evidence for B would be an event A such that P(B|A) = P(B).

Why do you think they need to be distinguished?

The Absence of Evidence is just Unfalsifiability

>Why do you think they need to be distinguished?
Because they are two separate cases.

>Why are you asking me to explain your own argument?
I'm not, you're the one who made the claim.

That would mean that the presence of evidence against B is the presence of evidence for B.

Why?

I don't follow, can you elaborate?

Did you read the post before responding?

Let event C be the presence of evidence against B such that it decreases the chance of B.

If the absence of evidence for B would be an event A such that P(B|A) = P(B), then event C occurring means that there is not an absence of evidence for B, since it violates the definition.

Thus C means that evidence against B is present and it means that evidence for B is not absent, i.e. evidence for B is present.

>Did you read the post before responding?
Yes, you wrote "By that logic there is no such thing as an "absence of evidence," since absence of evidence for B is evidence against B." and I asked you "Why does absence of evidence for B being evidence against B mean that absence of evidence doesn't exist?". What part of that was my own argument?

I don't see any reference to the last post you were responding to. Did you read it?

>I don't see any reference to the last post you were responding to. Did you read it?
Yes, I quoted it in full.

>Why?
For example, the probability of the throw of a die giving 6 is different than the probability of the throw of a die giving 6 given you rolled an odd number.

but probability of B given A is not higher then probability of B given negative A.B is independent of A.
i dont think whoever wrote that took\understood his probability course .

>If the absence of evidence for B would be an event A such that P(B|A) = P(B), then event C occurring means that there is not an absence of evidence for B, since it violates the definition.
Can you rephrase this part? It's not clear to me what you're trying to say. What exactly is violating which definition?

No you didn't. Read in full before responding.

I don't see what that has to do with distinguishing A not occurring and not A occuring. Are you saying they are mutually exclusive?

>I don't see what that has to do with distinguishing A not occurring and not A occuring.
" the probability of the throw of a die giving 6" and "the probability of the throw of a die giving 6 given you rolled an odd number" are two different probabilities, and so it makes sense to distinguish them.

>Are you saying they are mutually exclusive?
No.

>No you didn't.
Which part did I not include in the quote?

>but probability of B given A is not higher then probability of B given negative A.B is independent of A.
By definition B is dependent on A. I don't think you have ever passed a probability course.

P(B|C) =/= P(B) therefore C is not an absence of evidence of B.

Nothing you quoted was even in that post. Just stop posting.

>P(B|C) =/= P(B) therefore C is not an absence of evidence of B.
Why is that an issue? Not everything has to be an absence of evidence of B.

>Nothing you quoted was even in that post.
Which part did I not include in the quote?

youtube.com/watch?v=_w5JqQLqqTc

The non-absence evidence of B is the presence of evidence of B.

>The non-absence evidence
How is this defined?

I dont get it. So | is NAND? P(B|A) > P(B|notA) is true for values only true for second option: A=0, B=1, right: 10 01 00 11. Then P(B|A) > P(B|notA) mean 1|0 > 1|1 and is true for those values, right? Then everything that goes along is inconsistent because 1-1 is not bigger then 1-1. Explain these things for me, i see this P() thing for the first time

The non-absence of evidence for B is the presence of evidence for B.

>The non-absence of evidence for B is the presence of evidence for B.
So what does this have to do with not everything having to be an absence of evidence of B? I just don't see why some definition is apparently being violated

en.wikipedia.org/wiki/Conditional_probability

If P(B|C) =/= P(B) then C occurring means evidence for B is present. But C is the presence of evidence against B. Thus we have a contradiction that invalidates your definition

>If P(B|C) =/= P(B) then C occurring means evidence for B is present.
Yes.

>But C is the presence of evidence against B.
Why does this follow?

>Yes.
By this I mean either C or not C is evidence for B.

C was defined as such from the beginning...

Absence of evidence is evidence of absence, it just isn't proof of it.

>C was defined as such from the beginning...
If C is defined to be evidence against B then why does it matter if C is not absence of evidence for B?

The non-absence of evidence for B is its presence. Whatever you define as the absence of evidence for B, its complement is presence of evidence for B. Since your definition does not include evidence against B, it falls.

Because if it's not absence it's presence. Absence and presence of something are mutually exclusive and collectively exhaustive.

>Whatever you define as the absence of evidence for B, its complement is presence of evidence for B.
Can you elaborate?

>Since your definition does not include evidence against B, it falls.
What do you mean by "it falls"?

See

>See
That doesn't explain why "Whatever you define as the absence of evidence for B, its complement is presence of evidence for B". Obviously your statement is only true if whatever you've defined as the absence of evidence for B is the complement of presence of evidence for B. Why is it so?

>Because if it's not absence it's presence.
If what is not absence then it's presence?

You mean why can't something be both present and absent? It follows from the definitions of absence and presence.

C.

>You mean why can't something be both present and absent?
No, I asked why the definitions must be the way you said they must be.

>C.
What does it mean for C to be presence? I thought C was evidence.