In the debate as to whether or not quasars can be ejected from local active galaxies, the statistics have been hotly debated. Arp has found alignments of quasars across low redshift galaxies. The mainstream responds that these are chance alignments of foreground galaxies with backgroud quasars.

When statistical calculations are made the odds of the assorted alignments being accidental range from 10^-2 to 10^-9 with many of the examples having odds of only 1 in a million of being an accident. The mainstream argues that the statistics are invalid because they are calculated after the alignment is discovered (a posteriori).

For example one older astronomy textbook I have argues that the odds of being dealt a certain combination of cards might be very low, but the odds are meaningless after the fact - after you are actually dealt the cards.

Spaceman Spiff put it this way on the "BigBang busted" thread:

Since this is a central argument the mainstream uses to dismiss Arp’s quasar alignments, I think it is worth a separate thread to explain exactly why this a posteriori argument is a subtle evasion of the issue. I will keep this as short as I can, but it is going to be a lengthy post.

Let’s start with the cards example used by the textbook (Snow 1989). The following questions can be asked:

1. What are the odds of a person being dealt a royal flush? These odds are very low.
2. What are the odds you will be dealt a royal flush tonight. If you play cards tonight, then the odds are still the same very low number. If you don’t play cards tonight the odds are zero.

Lets say you do play cards tonight and against the odds you do get a royal flush. The mainstream now says that to calculate the odds of that is meaningless because it happened:

3. What are the odds that you were dealt a royal flush tonight?

Since you were dealt a royal flush this question is meaningless. The mainstream is correct that this is a worthless a posteriori calculation. But notice how the mainstream’s a posteriori argument subtly shifts the question from one that is relevant to one that is irrelevant.

If tomorrow at work you tell your co-workers about your royal flush, they would likely be impressed with your good fortune because they understand that the odds of getting a royal flush are low:

4. What are the odds that you should have gotten a royal flush?

The fact that you got a royal flush does not make the odds that you should have gotten a royal flush meaningless. What the mainstream has done with the argument is shifted from a relevant question (#4) to an irrelevant question (#3).

If we follow the mainstream a posteriori logic then you should find it unremarkable when you wake up tomorrow and find out that your best friend won tonight’s multi-million dollar lottery. You should not ask about the odds of that happening because you see on the news that it did happen. The odds are meaningless.

But is that the only question you might ask? No – the question you will ask that makes your friend's good fortune remarkable is: “What were the odds of winning that jackpot?” Those odds can be calculated after the winning just as validly as before.

The problem here is that the mainstream is muddling the difference between known/constrained and unknown/unconstrained statistics. If you meet an old friend that you haven’t seen since high school while on a trip to a foreign country, you might find that remarkable. But if you try to calculate the odds of that happening you will get a meaningless result. The statistics of meeting your friend are unknown and unconstrained. How do you quantify the decision-making and timing that led to that coincidence? You can’t –but here is the key: You could not have calculated the odds that you would meet your friend on your trip before you take the trip either. It is an unconstrained statistic and odds before (a priori) are as meaningless as odds after (a posteriori). Spaceman’s licence plate and person being born examples are analogous.

But it is not analogous with the quasar example. The quasar example is like the deck of cards. It is meaningless to calculate the odds that you did get a royal flush after it happens, but it is not meaningless to calculate the odds that you should have gotten the royal flush. The odds that you should have are the same before as after. Just as the odds that your friend should have won the lottery are the same before as after.

The difference is that with the deck of cards we know how many cards are in the deck and can therefore calculate the odds of getting any particular combination of cards. Those odds are the same before and after.

It’s the same with quasars. It is known how many QSO’s are in the various catalogs. It is known how many nearby low redshift galaxies there are. The magnitudes, radio strengths, and redshifts for these objects are known. The odds of a given pair of quasars being within x degrees of any arbitrary point can be calculated - before or after the alignment is discovered. The numbers are constrained by the statistics of the catalogs.

The mainstream’s a posteriori argument subtly tries to shift the question from the relevant one:

What are the odds that this quasar alignment should have happened?

to the irrelevant one:

What are the odds that this quasar alignment did happen?

So when Arp (and others) finds an alignment of QSO’s with a local galaxy that has an odds of 10^-6 of being accidental, the mainstream claims the calculation is after the fact and therefore meaningless and thus effectively evades the issue.

On a final note, there is an even more ridiculous aspect of the a posteriori argument. The mainstream claims the redshift anomalies are accidental alignments. But then when Arp shows just how unlikely that is, the mainstream dismisses the statistics with the false application of the a posteriori argument, and therefore does not allow their claim that it is accidental to be tested or even quantified. If they will not allow the statistical arguments to be considered, then they cannot make the claim that the alignments are accidental.

Well, as astronomer Bill Keel put it....
How many quasars are NOT associated with any galaxies with vastly smaller redshifts? What's the story with THEM?

How many newly formed cosmological objects do NOT have anomalous redshifts?

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Everyone is entitled to his own opinion, but not his own facts.

Who says there are ANY quasars that could not be associated with lower redshift galaxies? For example, Zhu&Chu have shown that the quasar in the direction of Virgo are associated with Virgo galaxies but not with background galaxies at a statistical significance level as high as 7.5 sigma.

You need to be clear about which model you're referring to. In your preferred Big Bang model there are no such things as new cosmological objects because everything was created in the BB.

If your talking about Arp's model then any newly created objects have anomalous redshifts.

In either case neither of your questions have any relevance to the question of the a posteriori argument - which is what this thread is for.

Have you got an example of where the mainstream has used this 'incorrect' argument?

What is much more disturbing is the lack of mainstream interest in validating Arp's statistics. It should be fairly easy, with a reasonable pocket of money, to systematically sort through the Sloan Survey and either validate or invalidate Arp's claims: Simply stating he is rolling crooked dice is an indefensable cheap shot.

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jwj

It's ok not to know. We should try harder to find out.

didn't someone do that with the 2dF survey?

As I noted, Spaceman Spiff used the argument here. Its frequently found in textbook discussions of the issue. Arp discussed the issue in Quasars, Redshifts, and Controversies - which indicates he spent a lot of time dealing with it.

Here is an article that starts off referring to a posteriori statistics. I don't think its a matter of researchers publishing papers with that argument as much as a debate technique and instructional tool for teaching undergraduates that Arp is wrong.

Hawkins did not find evidence for periodicity in the 2dF survey, but Bell finds evidence for periodicity in 44,000 SDSS QSO's. Bell's periodicity formula is different from Arp's and like Hawkins, he finds no evidence for Arp's quantization in the SDSS QSO's.

But periodicity or not, that is a separate phenomenon from the question of whether or not they are local. Hawkins other study did not find evidence for QSO time dilation.

dgruss wrote:
I agree - but isn't the periodicity one of Arp's main evidences for his quasar ejection theory? Also, isn't one of the main points of Hawkins' periodicity paper that Arp (and others) massively overestimated their claimed significances for the periodicity results. This doesn't do Arp's claims much good.

BTW, I think they're different Hawkins'.

No, the alignments themselves are the main evidence. Periodicity would add additional evidence. I think Bell's paper is far more compelling than Arp's periodicity evidence.

That's a good example of where it would be more productive to run the stats themselves rather than just dismiss it all as a posteriori. For example, this paper addresses Arp's statistics and revises downward the significance, but still find a significant result.

dgruss:
I don't quite understand - doesn't Hawkins do exactly what you are asking for? He repeats the previous analysis using the same data but more rigorous statistics and finds that its about a 1sigma effect, if that, rather than the claimed 10sigma effect.
Thats not arguing a posteriori - thats correcting an error.

But what Hawkins did is not what I'm talking about. He's not making the a posteriori claim. Bell found the same thing as Hawkins - the Karlsson formulation for quantization that Arp prefers is not correct. This is shown in Bell's paper. I would suggest that the small 1 sigma effect that Hawkins does find results from the similarity of some of the lower z peaks in Arp's periodicity to Bell's.

In any case, the a posteriori claim has not been made for periodicity. It has been made for the apparent associations between qso's and low z galaxies. In other words, if Arp calculates an arrangement has a probability of only 10^-8 of being accidental, the a posteriori argument is that the statistic is meaningless because its calculated after it was discovered. Here is how it was stated in T. Snows introductory textbook "Exploring the Dynamic Universe" (1988-page 281):

You can also see the quote by Spaceman in the first post above. Same argument.

I agree that the after the a posteriori argument doesn't seem quite right, but that shouldn't be confused with people making valid claims that his calculation of the significances of his alignments are grossly exagerrated. It doesn't help Arp's case when his statistics have been found to be dodgy without any need for an a posteriori claim.

It didn't even occur to me until I read this thread: The supernova Ia researcher are systematically looking for high redshift supernova that support the time dilation hypothesis - in Riess 2004, they even admit that they threw out an apparent Ia because, after correction for time dilation, the light curve was too small to be a redshifted supernova Ia. Bad astronomy!

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jwj

It's ok not to know. We should try harder to find out.