Another probability question, this time with Ravens

[Custom24]

Clearly the Duck race probability thread has shown that my understanding of probability is partial at best.

This isn't the same kind of question, but it's something I've been mulling over for a while and I'd like to see if anyone has any thoughts

I quite like the Hempel Paradox

My question here is not related to the Paradox itself (there is a resolution I am happy with), but rather one of the premises

One of the premises is that a hypothesis is supported by Instance Confirmations. In this case, that every time we see a black raven, it adds evidence for the hypothesis that all ravens are black.

My question is - can this additional evidence be expressed in terms of an increase in probability?

Clearly, if we managed to catalogue every single raven in the world, and they were all black, the probability of the hypothesis being true is 1.00.

But what about a representative 10% sample of all ravens, what about 99%, what about all ravens bar one? At each stage, would it make sense to assign a probability of the hypothesis being true, and if so, what would that probability be?

 

[Levo-Lon]

You lost me at Clearly the Duck

 

[Kestevan]

Clearly, if we managed to catalogue every single raven in the world, and they were all black, the probability of the hypothesis being true is 1.00,

but Nevermore.

 

[ColinJ]

Clearly, if we managed to catalogue every single raven in the world, and they were all black, the probability of the hypothesis being true is 1.00,

but Nevermore.

But how would you know that you had found them all ...?

A million people could help you in a global raven hunt and you could think that between you you had accounted for all of them, but there could still be some sneaky buggers hiding in an inaccessible cave halfway up a sheer rock face in the Andes!

 

[Venod]

But not all ravens are black.

https://www.redbubble.com/people/ravenprints/works/1877692-dare-to-be-different-rare-white-raven

 

[KEEF]

But not all ravens are black.

https://www.redbubble.com/people/ravenprints/works/1877692-dare-to-be-different-rare-white-raven

That's the end of this thread then.

 

[swansonj]

Clearly the Duck race probability thread has shown that my understanding of probability is partial at best.

This isn't the same kind of question, but it's something I've been mulling over for a while and I'd like to see if anyone has any thoughts

I quite like the Hempel Paradox

My question here is not related to the Paradox itself (there is a resolution I am happy with), but rather one of the premises

One of the premises is that a hypothesis is supported by Instance Confirmations. In this case, that every time we see a black raven, it adds evidence for the hypothesis that all ravens are black.

My question is - can this additional evidence be expressed in terms of an increase in probability?

Clearly, if we managed to catalogue every single raven in the world, and they were all black, the probability of the hypothesis being true is 1.00.

But what about a representative 10% sample of all ravens, what about 99%, what about all ravens bar one? At each stage, would it make sense to assign a probability of the hypothesis being true, and if so, what would that probability be?

This is an instance where statistics can't give an unambiguous answer. To perform a statistical calculation, you have to define your hypotheses, and that requires that you bring to the problem judgements or assumptions that are not purely statistical.

To give one specific example: is the alternative to all ravens being black that just one raven in the whole world is white, or that half of all ravens are white, or something in between? If you specify which, a statistician will calculate the probability that the first hundred or thousand ravens you observe will all be black. But the choice of which to test draws on biology rather than statistics (to the extent that is an informed decision at all).

 

[SteveF]

Is this a dirty duck thing?

 

[Julia9054]

But how would you know that you had found them all ...?

A million people could help you in a global raven hunt and you could think that between you you had accounted for all of them, but there could still be some sneaky buggers hiding in an inaccessible cave halfway up a sheer rock face in the Andes!

To estimate the size of a population, a biologist would use a technique called mark - release - recapture.
You capture a certain number of animals within an area and mark them in a harmless way (for a bird, a leg ring would be most suitable). You then release them into the wild and leave a certain amount of time for them to mingle. Return to the area and capture another sample. Count the number of marked individuals within that sample. If you assume that the number of marked individuals within the second sample is proportional to the number of marked individuals in the whole population, an estimate of the total population size can be obtained by :-
Number of animals captured on second visit multiplied by number of animals marked on first, divided by number of marked animals captured on second visit.

 

[ColinJ]

To estimate the size of a population, a biologist would use a technique called mark - release - recapture.
You capture a certain number of animals within an area and mark them in a harmless way (for a bird, a leg ring would be most suitable). You then release them into the wild and leave a certain amount of time for them to mingle. Return to the area and capture another sample. Count the number of marked individuals within that sample. If you assume that the number of marked individuals within the second sample is proportional to the number of marked individuals in the whole population, an estimate of the total population size can be obtained by :-
Number of animals captured on second visit multiplied by number of animals marked on first, divided by number of marked animals captured on second visit.

That would give you a very good idea of the population size, but in order to know that every single bird was one colour you would have to see ALL of them, not MOST of them or even NEARLY ALL of them!

 

[srw]

This is an instance where statistics can't give an unambiguous answer. To perform a statistical calculation, you have to define your hypotheses, and that requires that you bring to the problem judgements or assumptions that are not purely statistical.

To give one specific example: is the alternative to all ravens being black that just one raven in the whole world is white, or that half of all ravens are white, or something in between? If you specify which, a statistician will calculate the probability that the first hundred or thousand ravens you observe will all be black. But the choice of which to test draws on biology rather than statistics (to the extent that is an informed decision at all).

Isn't there an analogy with opinion polling? Sample 1000 ravens, observe 1000 black ones and deduce that as long as your sample is representative 100% of ravens +/- 3% are black.

On a phone so response not entirely coherent.

 

[swansonj]

Isn't there an analogy with opinion polling? Sample 1000 ravens, observe 1000 black ones and deduce that as long as your sample is representative 100% of ravens +/- 3% are black.

On a phone so response not entirely coherent.

I will be happy to charitably blame the phone for the concept that a valid statistical conclusion is that 103% of ravens are black...

 

[Profpointy]

There is quite a good thought experiment concerning how many men's heights you have to measure to be confident that all men are less than 100' tall. It all seems pretty convincing but after measuring 1 million men's heights ranging from maybe 4' to 7'6" you find a 99' high man, which is evidence that supports your hypothesis, isn't it?

 

[ufkacbln]

With Ravens you have to factor in the batteries

As Kete Stewart of U.N.I.T pointed out at the Tower of London...

‘The ravens are looking a bit sluggish. Tell Malcom they need new batteries.’

 

[Custom24]

This is an instance where statistics can't give an unambiguous answer. To perform a statistical calculation, you have to define your hypotheses, and that requires that you bring to the problem judgements or assumptions that are not purely statistical.

To give one specific example: is the alternative to all ravens being black that just one raven in the whole world is white, or that half of all ravens are white, or something in between? If you specify which, a statistician will calculate the probability that the first hundred or thousand ravens you observe will all be black. But the choice of which to test draws on biology rather than statistics (to the extent that is an informed decision at all).

That's what I was thinking, but the Wikipedia article talks about weight of evidence based on Bayesian maths. I need to have another read of it.