Arp objects, QSOs, Statistics

[BeAChooser]

Take ten hands of poker (five card no draw) dealt, returned, shuffled and dealt again.

The individual odds of a royal flush hearts are (1/52)⁵=2.63 v 10^-9
Now does this mean that out of ten hands you should expect:

10 x 2.63 x10^-9=2.63 x 10^-8
and therefore if the royal flush hearts appears twice its actual probability of occurenceis

(2.63 x 10^-8)² and therefore if it did happen it means that the shuffle was not random?

But the difference between this example David, and the problem being studied is that that we don't know FOR A FACT that the mainstream model is correct. We know exactly what a deck of cards contains assuming we just took it out of the box. We aren't trying to deduce from our observations what that deck of cards might contain. But in the problem at hand, we are trying to deduce from observations the nature of that deck of cards. Say you didn't know that a deck of cards had 52 different cards. You just had a model where you assumed it does. And you start dealing hands, getting 4 four of a kind in a row again and again. Might you not reasonably suspect that the deck has a completely different set of cards in it than you modeled or was shuffled in a different manner than you assumed. And if you continued to get hands like that which were at variance with your original assumed model, then at some point shouldn't you actually reevaluate that model and revise it so it better fits the actual data?

 

[Reality Check]

BeAChooser. Your probability calculations for your mixed mainstream/non mainstream model (e.g. uniform distribution + Karlsson values) may be correct or incorrect. But what model are you comparing it against?

You do not do statistics (the subject of this topic) by just calculating probabilities. You need to compare hypotheses:
Null Hypothesis: Quasars are distributed uniformly and their position is not related to galaxies.
Test Hypothesis: Quasars are not distributed uniformly and their position is related to some galaxies.

Pease state your null and test hypotheses.

 

[sol invictus]

No no no.

I don't have time to post now - I will in the next few days if you haven't figured this out yet.

Just take 10 random data points - or take them to be evenly distributed, it doesn't matter - and aaply your formula to the case I suggested (one Karlsson peak at z=.5, z from 0 to 1). you will get P~.00001, when you should get P~.5.

Just try it.

Sol, will you admit that the probability of seeing a given observation, given the assumptions behind the mainstream model with respect to quasar redshift, is the same regardless of when the data I'm asking that we study was gathered? That probability is implicit in the model itself, independent of the specific observation having been made or not. That probability is what we would EXPECT to see in that case given the model assumptions and nothing else. Right? Likewise, the total of observable quasars that the mainstream seems to think are in the sky is (for all intents and purposes) independent of these specific observations too. Right? And so is the distribution of quasars with respect to low redshift galaxies. That is (for all intents and purposes) independent of when these observations were made or when I do these calculations. Right?

And will you admit that the answer to what the probability is of seeing a given observation, given the model assumptions, is of more than passing interest if the answers turn out to be very low probabilities? Our interest here is in checking whether the assumptions in the mainstream model are correct. Suppose the calculated probability of seeing each of these observations came out to be 10^-100, assuming we'd examined every possible observable quasar/galaxy association in the sky? Wouldn't that be telling us that the model is wrong if we'd then already seen 5 such observations? Sure, there is a very small probability that one could see those observations but wouldn't the better bet be that the model itself is defective in some important way? Of course it would.

Scientists (and engineers) build models all the time and then test those models against data they encounter to ensure the model works. This is no different. The argument about this being a meaningless or improper calculation because it uses a posteriori statistics is a smokescreen for ignoring legitimate indications of a possible problem with the model.



It's not wrong. Not for the reason you've stated (or any reason I can see). 2*deltaz had better be less than 1 because it's a probability that goes from 0 to 1, as deltaz increases from 0 to half the width of the range (in your example). Perhaps you have misunderstood what I meant by deltaz? It's not the width of the zone in which a quasar lies centered about the Karlsson value. It's the distance of that specific data point z from the Karlsson value ... so it's one-half the zone width.

We can check that my formula is right for one data point by looking at the answer in your example if we let deltaz for a given quasar equal half the possible range (i.e., deltaz = 1/2 of 1). Then the probability is 2*deltaz1 = 1 of that quasar being within 1/2 of the midpoint. As it should be. The probability of finding a quasar that lies between 0 and 1 being somewhere between 0 and 1 is indeed 1. And if you have 10 QSO's that all have z within 0.5 (i.e., deltaz = 0.5) of a Karlsson value that is at the midpoint of the range 0 to 1, then the probability of finding that case is in fact 1 * 1 * 1 * etc. = 1.0 (assuming quasars are independent).



What's wrong with that? The probability of each quasar in that case being within deltaz = 0.25 (note that 2*deltaz = 1/2 means deltaz equals 0.25) of the midpoint in the range 0 to 1 is 0.5. And since each data point is independent, the probability of all of them being within 0.25 of the midpoint must be .5¹⁰ = 0.000977 = 0.001. Again, I think you've misunderstood what I deltaz means.



And why shouldn't the product be dominated by the lowest probability data points if the data points are independent. Say we have 2 QSOs in your example instead of 10. One QSO has a deltaz of 0.5 so the probability of finding it is 1. One QSO has a deltaz of 0.001 so the probability of finding it, assuming quasars are randomly drawn from the range 0 to 1, is .002. The joint (multiplicative) probability is 1 * 0.002 = 0.002. That's the correct answer for finding both data points if they are independent events ... and it is indeed dominated by the lowest probability data point.



Sure you can. Say we are talking about your 1 Karlsson value case with 2 quasars. The quasars are independent of one another. Correct? According to the mainstream model there is not supposed to be any physical connection between two quasars in a given viewing field and the value of z for each is supposed to be independent of one another ... just come from the same overall distribution. The probability of quasar1 being within deltaz1 of a given Karlsson value is known (based on the above) and independent of the probability of quasar2 being within deltaz2 of that same Karlsson value, which is also known. Since they are independent, the joint probability of there being 2 quasars within those two specific distances of the same Karlsson value is the product of the probability of each quasar being within it's specified deltaz. Right? So there's nothing wrong with the equation for 1 Karlsson value and 2 quasars. Adding more quasars doesn't change any of the above logic either. So the new formula is correct for 1 Karlsson value and any number of quasars.

If there is more than 1 Karlsson value in the total z range, then things get a little more complicated. But just a little. Let's again look at the case of 2 quasars. Say I find a deltaz to the nearest Karlsson value for the first quasar. Call it deltaz_nearest. The probability of that quasar being within deltaz_nearest of that Karlsson value is 2*deltaz_nearest. Now if the other Karlsson value can be anywhere in the 0 to 1 range, the probability of that quasar being within 2*deltaz_nearest of that Karlsson value is also at most 2*deltaz_nearest. So at the very least, I'm conservative in estimating the probability of it being within deltaz_nearest of both Karlsson values as twice the probability of it being within deltaz_nearest of the nearest one. And I can do the same for the other quasar, independent of the first, using its own different deltaz_nearest. And since they are independent quasars, I can multiply the two probabilities I've obtained to get the joint probability of both quasars being within their respective deltaz of both Karlsson values. Which is exactly what my new equation does. And again, adding more quasars doesn't change to validity of any of the above logic, nor does adding more Karlsson values. So I think you are wrong about your conclusion that this formula doesn't work for the purpose at hand.

I probably should modify the equation so there is no confusion and future misuse of it, however. It should read:

P <= ((2*n_k)/3)^r * (deltaz₁ * deltaz₂ * ... * deltaz_i=r)

where

n_k is the number of Karlsson values in the range 0-3,

r is the number of quasars,

and deltaz_i is the distance to the NEAREST Karlsson value of the ith quasar,

assuming the distribution of quasar z is uniform in the range 0-3.

With regard to that last condition, z is not exactly uniform over the whole range as I noted in my earlier posts. Do you have any suggestions, sol, on how to accurately incorporate that fact into the analysis ... assuming we can agree on everything else above? I previously tried a power law weighting where each of the deltaz_i would be raised to a weight that is the ratio of the value of frequency of that z in the real distribution compared to what the value would be were the distribution uniform and the overall area under the frequency distribution were the same as in the real distribution. Do you think that a valid approach? Are the weights in that case meaningful? Note that the result, depending on the specific case, may either raise or lower the final probability.

 

[Dancing David]

But the difference between this example David, and the problem being studied is that that we don't know FOR A FACT that the mainstream model is correct. We know exactly what a deck of cards contains assuming we just took it out of the box. We aren't trying to deduce from our observations what that deck of cards might contain. But in the problem at hand, we are trying to deduce from observations the nature of that deck of cards. Say you didn't know that a deck of cards had 52 different cards. You just had a model where you assumed it does. And you start dealing hands, getting 4 four of a kind in a row again and again. Might you not reasonably suspect that the deck has a completely different set of cards in it than you modeled or was shuffled in a different manner than you assumed. And if you continued to get hands like that which were at variance with your original assumed model, then at some point shouldn't you actually reevaluate that model and revise it so it better fits the actual data?

Um, i don't think that it has been demonstrated that you are getting "4 four of a kind in a row again and again", which is why I would recomend the gathering of representative samples of 'normative' galaxies and random points in the sky. then as the size of the samples rises you have something to comare Arp's data to.

I am not sure that what Arp found was as likely as 'four od a kind' as we don't know what the frequencies of occurance are.

You are assuming that it is a four of a kind without a notion of what the commonality of occurance is. It could just be getting a garbage hand over and over. Or it could be a deck of 52 cards that only has four different face values so 'four of a kind' would be common.

You have yet to demonstrate how Arp's method can tell a causal from a random placement, which is what i have asked for.

How does Arp's or your methods determine the difference bwteen a random and a causal relationship?

I am not assuming the mainstream anything, I am saying that the best way to know what the random occurance of an event is, is to measure it.

Arps does not have a way of determining what the random occurance of an event is, nor does your method.

 

[DeiRenDopa]

Sol, will you admit that the probability of seeing a given observation, given the assumptions behind the mainstream model with respect to quasar redshift, is the same regardless of when the data I'm asking that we study was gathered? That probability is implicit in the model itself, independent of the specific observation having been made or not. That probability is what we would EXPECT to see in that case given the model assumptions and nothing else. Right? Likewise, the total of observable quasars that the mainstream seems to think are in the sky is (for all intents and purposes) independent of these specific observations too. Right? And so is the distribution of quasars with respect to low redshift galaxies. That is (for all intents and purposes) independent of when these observations were made or when I do these calculations. Right?

And will you admit that the answer to what the probability is of seeing a given observation, given the model assumptions, is of more than passing interest if the answers turn out to be very low probabilities? Our interest here is in checking whether the assumptions in the mainstream model are correct. Suppose the calculated probability of seeing each of these observations came out to be 10^-100, assuming we'd examined every possible observable quasar/galaxy association in the sky? Wouldn't that be telling us that the model is wrong if we'd then already seen 5 such observations? Sure, there is a very small probability that one could see those observations but wouldn't the better bet be that the model itself is defective in some important way? Of course it would.

Scientists (and engineers) build models all the time and then test those models against data they encounter to ensure the model works. This is no different. The argument about this being a meaningless or improper calculation because it uses a posteriori statistics is a smokescreen for ignoring legitimate indications of a possible problem with the model.



It's not wrong. Not for the reason you've stated (or any reason I can see). 2*deltaz had better be less than 1 because it's a probability that goes from 0 to 1, as deltaz increases from 0 to half the width of the range (in your example). Perhaps you have misunderstood what I meant by deltaz? It's not the width of the zone in which a quasar lies centered about the Karlsson value. It's the distance of that specific data point z from the Karlsson value ... so it's one-half the zone width.

We can check that my formula is right for one data point by looking at the answer in your example if we let deltaz for a given quasar equal half the possible range (i.e., deltaz = 1/2 of 1). Then the probability is 2*deltaz1 = 1 of that quasar being within 1/2 of the midpoint. As it should be. The probability of finding a quasar that lies between 0 and 1 being somewhere between 0 and 1 is indeed 1. And if you have 10 QSO's that all have z within 0.5 (i.e., deltaz = 0.5) of a Karlsson value that is at the midpoint of the range 0 to 1, then the probability of finding that case is in fact 1 * 1 * 1 * etc. = 1.0 (assuming quasars are independent).



What's wrong with that? The probability of each quasar in that case being within deltaz = 0.25 (note that 2*deltaz = 1/2 means deltaz equals 0.25) of the midpoint in the range 0 to 1 is 0.5. And since each data point is independent, the probability of all of them being within 0.25 of the midpoint must be .5¹⁰ = 0.000977 = 0.001. Again, I think you've misunderstood what I deltaz means.



And why shouldn't the product be dominated by the lowest probability data points if the data points are independent. Say we have 2 QSOs in your example instead of 10. One QSO has a deltaz of 0.5 so the probability of finding it is 1. One QSO has a deltaz of 0.001 so the probability of finding it, assuming quasars are randomly drawn from the range 0 to 1, is .002. The joint (multiplicative) probability is 1 * 0.002 = 0.002. That's the correct answer for finding both data points if they are independent events ... and it is indeed dominated by the lowest probability data point.



Sure you can. Say we are talking about your 1 Karlsson value case with 2 quasars. The quasars are independent of one another. Correct? According to the mainstream model there is not supposed to be any physical connection between two quasars in a given viewing field and the value of z for each is supposed to be independent of one another ... just come from the same overall distribution. The probability of quasar1 being within deltaz1 of a given Karlsson value is known (based on the above) and independent of the probability of quasar2 being within deltaz2 of that same Karlsson value, which is also known. Since they are independent, the joint probability of there being 2 quasars within those two specific distances of the same Karlsson value is the product of the probability of each quasar being within it's specified deltaz. Right? So there's nothing wrong with the equation for 1 Karlsson value and 2 quasars. Adding more quasars doesn't change any of the above logic either. So the new formula is correct for 1 Karlsson value and any number of quasars.

If there is more than 1 Karlsson value in the total z range, then things get a little more complicated. But just a little. Let's again look at the case of 2 quasars. Say I find a deltaz to the nearest Karlsson value for the first quasar. Call it deltaz_nearest. The probability of that quasar being within deltaz_nearest of that Karlsson value is 2*deltaz_nearest. Now if the other Karlsson value can be anywhere in the 0 to 1 range, the probability of that quasar being within 2*deltaz_nearest of that Karlsson value is also at most 2*deltaz_nearest. So at the very least, I'm conservative in estimating the probability of it being within deltaz_nearest of both Karlsson values as twice the probability of it being within deltaz_nearest of the nearest one. And I can do the same for the other quasar, independent of the first, using its own different deltaz_nearest. And since they are independent quasars, I can multiply the two probabilities I've obtained to get the joint probability of both quasars being within their respective deltaz of both Karlsson values. Which is exactly what my new equation does. And again, adding more quasars doesn't change to validity of any of the above logic, nor does adding more Karlsson values. So I think you are wrong about your conclusion that this formula doesn't work for the purpose at hand.

I probably should modify the equation so there is no confusion and future misuse of it, however. It should read:

P <= ((2*n_k)/3)^r * (deltaz₁ * deltaz₂ * ... * deltaz_i=r)

where

n_k is the number of Karlsson values in the range 0-3,

r is the number of quasars,

and deltaz_i is the distance to the NEAREST Karlsson value of the ith quasar,

assuming the distribution of quasar z is uniform in the range 0-3.

With regard to that last condition, z is not exactly uniform over the whole range as I noted in my earlier posts. Do you have any suggestions, sol, on how to accurately incorporate that fact into the analysis ... assuming we can agree on everything else above? I previously tried a power law weighting where each of the deltaz_i would be raised to a weight that is the ratio of the value of frequency of that z in the real distribution compared to what the value would be were the distribution uniform and the overall area under the frequency distribution were the same as in the real distribution. Do you think that a valid approach? Are the weights in that case meaningful? Note that the result, depending on the specific case, may either raise or lower the final probability.

.

BAC, we have been over the core ("mainstream") part of this, again and again, and six different ways to Sunday. Somehow, you are still not getting it.

Let's just go over one, tiny, little aspect again, shall we?

Neither galaxies nor AGNs (which are the nuclei of galaxies) are distributed randomly on the sky; in no "mainstream" theory/model/assumption/whatever (that I know of) has such a parody/strawman existed.

Astronomers have been studying the non-random distribution of galaxies and AGNs, both on the sky and in 3D, for many decades now.

One powerful way to do this kind of study is to calculate (cross-)correlations.

The astronomical literature is chock-a-block full of papers reporting the results of various (cross-)correlation studies.

Many very interesting things have been discovered from correlation studies, from weak gravitational lensing (e.g. magnification), to the way the deviation from average density of the universe changes as the scale over which that density is measured increases ("P(k)", to be technical), to the detection of a clear BAO signal (baryon acoustic oscillation).

One of the particularly neat results is that the large-scale structure estimated by such correlation studies matches extremely well with the results of CMB observations such as WMAP.

To repeat: if you want to test whether some particular, observed configuration (or distribution), on the sky, of 'quasars' and low redshift galaxies is consistent with "mainstream assumptions/theory/models/whatever", then you need to start with such assumptions/theory/models/whatever!

(and not make stuff up).

And, to repeat, again, once more: central to any such work will be a clear, quantitative, unambiguous definition of 'quasar'.

 

[Dancing David]

Once more I will write a post and BAC can choose to ignore it as he wishes.

Averages vs. normative distribution.

In an earlier post I have said that BAC assumes that the QSOs are distribut6ed evenly when making calculations. This shows one of the errors of using an average when dealing with population studies.

Say that we say a square of 10 nicks by 10 nicks has and average of 3 bots per sq. nick. What does this mean, does it mean that we should expect an even distribution? One where there are 3 bots per sq. nk. ? That is the average after all, but is it reasonable to assume that is the distribution of bots in a square of 100 sq. nk. ?

That is one possible way to get an average of 3 bots/sq. nk. , but if we posit a field of 1000 x 1000 nicks and we start examining fields of 10 x 10 nicks, what might we find?

First the overall number of bots in the super field is 3,000,000 and the total of sq. nks is 1,000,000 to give us our average of 3 bt./sq. nk..

But if we examine small fields (squares) of 10 x 10 what might we find? We might find

-a square with two sq. nk that have 120 bots each and that there are 78 sq. nk that are empty and that the other 20 sq. nicks have 3 bots each. Average is 3bts/ sq. nk.


In fact any arrangement of 300 bots in a square of 10x10 is going to give us the average of 3 bt./sq.nk.

So if we just start looking at individual square nicks and say “hey this sq. nick has ten bots in it, that is more than three times the average” and “here is another sq. nick that has 60 bots in it and that is twenty times the average”, what has this sample of two squares actually said?

How can you tell what the distribution of bots is?

Can you just say, well there are 3,000,000 bots and 1,000,000 sq. nicks so it should be 3 bt./sq.nk.!

Or would it be better to look at say 1,000 or 10,000 or 100,000 of the sq. nk. , randomly chosen. And then determine what the distribution actually looks like? Then you can look at the samples and how the bots are distributed in them, you might find high peaks and low valleys that occur regularly, you might find that there really are three bots in 99% of the sample squares and wonder where the empty ones are for the two high ones you found.

But the best way that you can use to determine what is an abnormal value is to actually measure the distribution through representative sampling of randomly chosen sq. nk. , the higher the sample size the better the representation you might have.

 

[Dancing David]

.

BAC, we have been over the core ("mainstream") part of this, again and again, and six different ways to Sunday. Somehow, you are still not getting it.

Let's just go over one, tiny, little aspect again, shall we?

Neither galaxies nor AGNs (which are the nuclei of galaxies) are distributed randomly on the sky; in no "mainstream" theory/model/assumption/whatever (that I know of) has such a parody/strawman existed.

Astronomers have been studying the non-random distribution of galaxies and AGNs, both on the sky and in 3D, for many decades now.

One powerful way to do this kind of study is to calculate (cross-)correlations.

The astronomical literature is chock-a-block full of papers reporting the results of various (cross-)correlation studies.

Many very interesting things have been discovered from correlation studies, from weak gravitational lensing (e.g. magnification), to the way the deviation from average density of the universe changes as the scale over which that density is measured increases ("P(k)", to be technical), to the detection of a clear BAO signal (baryon acoustic oscillation).

One of the particularly neat results is that the large-scale structure estimated by such correlation studies matches extremely well with the results of CMB observations such as WMAP.

To repeat: if you want to test whether some particular, observed configuration (or distribution), on the sky, of 'quasars' and low redshift galaxies is consistent with "mainstream assumptions/theory/models/whatever", then you need to start with such assumptions/theory/models/whatever!

(and not make stuff up).

And, to repeat, again, once more: central to any such work will be a clear, quantitative, unambiguous definition of 'quasar'.

Cool!


i am the one who might have started the random distribution statements, so Arp's model needs to show exactly what i have said all along.

that the QSOs/Arp galaxy association rises above the level of what is already present and is not consistent with the frequencies that sampling of large sets would show.

 

[Tubbythin]

Yes. Isn't nice to finally meet someone around here who is able to admit when he's wrong? Unlike so many that one meets around here.

Well you do seem to give yourself more opportunity than most people do.

The folks who show no interest whatsoever in calculating the probability of seeing certain observations, given the mainstream assumptions about quasar numbers, quasar distribution with respect to low-redshift galaxies and quasar redshift?

I think most 'mainstream proponents' are unsure of the null and test hypothesise (is that the correct plural?) that you want 'us' to test.
But that is by-the-by. Time and again your statistics have been shown to be faulty. You're the one trying to dispute the mainstream. Therefore the ball is firmly in your caught. The burden of proof is on you.

I've asked and asked for one of the mainstream proponents to tell us what they think is the probability of seeing the observations I've noted. And none of them will. The only answer I seem able to get from them is a probability of 1, because we've seen one. But that's not an answer to the question I posed and you know it. It's an evasion.

Process X has a large number of possible outcomes, n. Eg dealing a pack of shuffled cards, tossing a coin 1000 times, throwing a dice 4,000,000 times. Whatever.
Null hypothesis: all outcomes of process X are equi-probable.
Observe process X with data set 0: result is outcome x1.
But under the null hypothesis P(X=x1) = 1/n and since n is large, P(X=x1) is small. So I've just observed a possible outcome which has a very low probability of occurring. Can I conclude the null hypothesis is wrong? Of course not! How could I test the null hypothesis? Come up with a test hypothesis. E.g. P(X=x1)>1/n. Then take measurements to create more data sets. Call them sets 1,2,3,4... Then look to see if x1 occurs more frequently than one would expect.
What shouldn't I do? Calculate P(X=x1) for data set 0. Why? because thats like asking "given that I've thrown a six, what is the probability that I've thrown a six?"
It is not an evasion.

 

[BeAChooser]

BeAChooser. Your probability calculations for your mixed mainstream/non mainstream model (e.g. uniform distribution + Karlsson values) may be correct or incorrect. But what model are you comparing it against?

I'm not sure what you mean. All my calculation asks is the probability (likelihood) of the quasar z values in a given observation all being *that* close to a specific set of values that just happen () to be the values Karlsson identified back in the 1970s. The only model being tested, per se, is the mainstream model. That model has a set of assumptions regarding the distribution of z of quasars that might be observed in a given field of view. The field of view in this case just happens () to be the region near low redshift galaxies where there are lots of quasars. And the result is simply a measure of our expectation that we will encounter that observation in a single trial. I then multiply that by what I estimate to be the total number of trials that could occur if we sampled every single observable quasar/galaxy association out there. Now if that probability is very low, we should rightly be a little suspicious if we find not just one but a whole string of observations like that. And then keep in mind that we haven't actually sampled all the possible quasar/galaxy associations. The probability of encountering the observations will go down in direct proportion to the fraction of the total population we have sampled (and by sample I mean looked at a case close enough to detect a curious confluence of quasars near a low redshift galaxy and note their redshifts relative to Karlsson values). If we've only sampled 1/100th of the total (and I'm not sure what the number is but I think it's quite small), the expectation that we'd see the observations will be a hundred times smaller than calculated. At some point you have to question the model assumptions on which the number is based ... either the assumption regarding the distribution of redshifts, the number of quasars or their distribution.

You need to compare hypotheses:
Null Hypothesis: Quasars are distributed uniformly and their position is not related to galaxies.
Test Hypothesis: Quasars are not distributed uniformly and their position is related to some galaxies.

Actually, I'm not really making a statement about quasar position being related to galaxies. I'm accepting (for the time being) the mainstream's estimate for the number of quasars. I'm accepting that there are a lot of low redshift galaxies out there. I'm allowing quasars to "clump" in areas where there is no low redshift galaxy. I am only assuming that half the quasars are near low redshift galaxies. And I think that is a conservative assumption that INCREASES the probability of detecting the given observations. I'm assuming a distribution of those quasars that are near galaxies in terms of their number. Again, one I think is conservative.

 

[Dancing David]

Actually, I'm not really making a statement about quasar position being related to galaxies. I'm accepting (for the time being) the mainstream's estimate for the number of quasars. I'm accepting that there are a lot of low redshift galaxies out there. I'm allowing quasars to "clump" in areas where there is no low redshift galaxy. I am only assuming that half the quasars are near low redshift galaxies. And I think that is a conservative assumption that INCREASES the probability of detecting the given observations. I'm assuming a distribution of those quasars that are near galaxies in terms of their number. Again, one I think is conservative.

Hmm, that is interesting, what about the posts where you do mention the close proximity of QSOs to Arp galaxies and galactic features. That is the contetion which you made in many posts.

Do you still say that those events support the Arp theory of anamalous redshift?

What is your hypothesis that we can test or observe? Or short of that what is your hypothsis.

the mainstraem model is in error is sort of a hypothesis.

But ejected QSOs don't seem likely at this point.

 

[BeAChooser]

Just take 10 random data points - or take them to be evenly distributed, it doesn't matter - and aaply your formula to the case I suggested (one Karlsson peak at z=.5, z from 0 to 1). you will get P~.00001, when you should get P~.5.

Each quasar has a probability of being near the Karlsson peak that is independent of the others. Hence the individual probability of each quasar can be multiplied together to get the probability that all of them will be within a certain distance of the Karlsson value. Now you said 2*deltaz = 0.5 . That means deltaz = 0.25 . If the length of the line between 0 and 1 is 1, the probability that a randomly placed quasar will be within 0.25 of the Karlsson value at the midpoint of that line will be 0.5. So if we have 10 randomly place quasars on the 0 to 1 line, the probability that ALL of them will be within 0.25 of that Karlsson value at the midpoint is 0.5¹⁰ = 0.000977 = 0.001 . As I said.

 

[Dancing David]

Gee, I suppose I can't ask you if every red shift or just some redshifts are suspect can i BAC, since you refused to answer the last time i asked, and you got all rude as well.

But here you are repeating or making claims about the association of QSOs and galaxies or galactic features, this does not involve the Karlson peaks all the time.

http://www.internationalskeptics.com/forums/showpost.php?p=2913550&postcount=90

(It is kind of funny reading the old threads how you just keep asserting "Peratt's" model explains galaxy rotation curves, but nowehere do you mention how he gets from a 10 cm plasma in a 4.5 gauss field to a galxy size object. And again I note very early I asked you for evidence of Perrat's model being scaled up to a galaxy. Which you still haven't answered.)

More associations of QSOs and galaxies here:
http://www.internationalskeptics.com/forums/showpost.php?p=2916730&postcount=99 (lloks like about seven)

http://www.internationalskeptics.com/forums/showpost.php?p=2917518&postcount=102 (the QSO in the galaxy)

And i am sure there are others in that thread.

So do you still believe that there is an association betwen high z QSOs and low z galaxies?

If not why aren't you talking about it in this thread.

You also keep saying that this chews a hole in the big bang theory.

yet the only evidence from tehse posts seems to be that there is an association of high z and low z objects.

So please clarify BAC:

1. What is your hypothesis, and what are they?
2. Do you still hold that there is a problem for the big bang because there is an association between low z galaxies and high z QSOs.
3. How do you determine that the associations of QSOs with galaxies is not just at the 'noise' level of placement and that it is a significant correlation between QSOs and Arps galaxies.
4. Are all redshifts intrinsic or are some consmological?

 

[sol invictus]

So if we have 10 randomly place quasars on the 0 to 1 line, the probability that ALL of them will be within 0.25 of that Karlsson value at the midpoint is 0.5¹⁰ = 0.000977 = 0.001 . As I said.

BAC - that's true, but that's NOT what you're doing. Stop for a moment and think. You're using a different deltaz for each data point, and that's wrong.

I'll do it for you:

In[18]:= data = Table[Random[], {n, 1, 10}]

Out[18]= {0.284105, 0.943911, 0.518192, 0.817081, 0.33991, 0.726244, \
0.516348, 0.388008, 0.687381, 0.828992}

Those are 10 random values between 0 and 1. Now I'm going to apply your method to those 10 random points - so I take a value, find the closest Karlsson peak (always z=.5, since that's the only peak in this toy example), compute the distance deltaz_n = .5 - z_n, and then take the product of 2*deltaz_n over n from 1 to 10 (so over all the data points). Here it is:

In[19]:= P = Product[2 (.5 - data[[n]]), {n, 1, 10}]

Out[19]= -2.31416*10^-6

(The minus sign is meaningless - I should have taken the absolute value.) So this particular random sample gives P=.000002. According to you, the chance that this data set occurred by chance is around 2 in a million - obviously that's wrong, unless I'm really, really, really lucky. The problem, as I keep telling you, is that you cannot pick a different deltaz for each data point like that - it's just plain wrong.

Here's another run:

In[21]:= data = Table[Random[], {n, 1, 10}]

Out[21]= {0.410318, 0.494959, 0.583798, 0.38408, 0.818009, 0.591804, \
0.417665, 0.864703, 0.718926, 0.888689}

In[22]:= P = Product[2 (.5 - data[[n]]), {n, 1, 10}]

Out[22]= 3.35444*10^-7

And another:

In[23]:= data = Table[Random[], {n, 1, 10}]

Out[23]= {0.248059, 0.444437, 0.823192, 0.165249, 0.963953, 0.500526, \
0.305, 0.348169, 0.624043, 0.774282}

In[24]:= P = Product[2 (.5 - data[[n]]), {n, 1, 10}]

Out[24]= -3.81054*10^-7

And another:

In[25]:= data = Table[Random[], {n, 1, 10}]

Out[25]= {0.788652, 0.96016, 0.936662, 0.945289, 0.378333, 0.465201, \
0.352864, 0.561209, 0.560324, 0.873396}

In[26]:= P = Product[2 (.5 - data[[n]]), {n, 1, 10}]

Out[26]= -0.0000227146

OK?

 

[DeiRenDopa]

I'm not sure what you mean. All my calculation asks is the probability (likelihood) of the quasar z values in a given observation all being *that* close to a specific set of values that just happen () to be the values Karlsson identified back in the 1970s.

... snip ...

.

Um, er, ... surely you also need to take a stab at estimating the probability of 'the quasar z values in a given observation all being' close to every other "specific set of values"? And then you would have 'probabilities' for every one of those sets!

In particular, by taking a number of 'random' specific sets, you would be able to see what the probabilities are (of the z values being close to several random sets), and could compare them with your (non-null) hypothesis.

If you don't do this (or something like it), you have no basis for concluding anything from the 'probability' that you calculate ... or have I misunderstood (yet again)?

 

[Reality Check]

I'm not sure what you mean. All my calculation asks is the probability (likelihood) of the quasar z values in a given observation all being *that* close to a specific set of values that just happen () to be the values Karlsson identified back in the 1970s. The only model being tested, per se, is the mainstream model. That model has a set of assumptions regarding the distribution of z of quasars that might be observed in a given field of view. The field of view in this case just happens () to be the region near low redshift galaxies where there are lots of quasars. And the result is simply a measure of our expectation that we will encounter that observation in a single trial. I then multiply that by what I estimate to be the total number of trials that could occur if we sampled every single observable quasar/galaxy association out there. Now if that probability is very low, we should rightly be a little suspicious if we find not just one but a whole string of observations like that. And then keep in mind that we haven't actually sampled all the possible quasar/galaxy associations. The probability of encountering the observations will go down in direct proportion to the fraction of the total population we have sampled (and by sample I mean looked at a case close enough to detect a curious confluence of quasars near a low redshift galaxy and note their redshifts relative to Karlsson values). If we've only sampled 1/100th of the total (and I'm not sure what the number is but I think it's quite small), the expectation that we'd see the observations will be a hundred times smaller than calculated. At some point you have to question the model assumptions on which the number is based ... either the assumption regarding the distribution of redshifts, the number of quasars or their distribution.

Actually, I'm not really making a statement about quasar position being related to galaxies. I'm accepting (for the time being) the mainstream's estimate for the number of quasars. I'm accepting that there are a lot of low redshift galaxies out there. I'm allowing quasars to "clump" in areas where there is no low redshift galaxy. I am only assuming that half the quasars are near low redshift galaxies. And I think that is a conservative assumption that INCREASES the probability of detecting the given observations. I'm assuming a distribution of those quasars that are near galaxies in terms of their number. Again, one I think is conservative.

Are you stating that Karlsson values are part of mainstream astronomy and so are catered for in all measurements of quasar redshifts by all astronomers? Or are they used in a majority of measurements of quasar redshifts by majority of astronomers?

You are still just doing probability calculations. These are a step in statistics calculations not the entire calculation. At some stage you will want to compare the expected results from the model to the observed results. If the observed results are significantly different to the expected results then your ("mainstream") model is refuted.
You may want to find out how the statistics of your mainstream model (uniform distribution of quasars and low red shift galaxies + Karlsson "clumping" if you want) differ from the statistics of the Arp model

As an example: Someone hands you a pair of dice and you want to know if they are fair or not. To test this you throw the dice multiple times and record the results. Now you want to find out whether the results support the null hypothesis that the dice are fair or whether the results refute the null hypothesis (i.e. support the alternative hypothesis that the dice are not fair). In this case a chi-square test may be used.

 

[Dancing David]

Hi,

Set 1 was a random set (X,X) with X randomly generated 1-100. (random.org integer generator)

Set 2 was weighted (X, Yx20+Z) with X being 1-100, Y being 1-4 and Z being -5 to -5 so with repeated samples it would have become very apparent that there were areas that the second value was not appearing. 0-14, 26-34, 46-54, 66-74, 86-100 , however this would not have been noticable until at least the third trial, although it was very heavily weighted and it would be apparent rather quickly.

I haven't done the math yet but i think that a probability derviation by reciprocal distance from the mean would not have said that Set 2 was the weighted set.


BAC I am still waiting for a decent explanation of how Arps' method of finding QSO/galaxy associations can determine random from causal placements.

 

[Tubbythin]

Process X has a large number of possible outcomes, n. Eg dealing a pack of shuffled cards, tossing a coin 1000 times, throwing a dice 4,000,000 times. Whatever.
Null hypothesis: all outcomes of process X are equi-probable.
Observe process X with data set 0: result is outcome x1.
But under the null hypothesis P(X=x1) = 1/n and since n is large, P(X=x1) is small. So I've just observed a possible outcome which has a very low probability of occurring. Can I conclude the null hypothesis is wrong? Of course not! How could I test the null hypothesis? Come up with a test hypothesis. E.g. P(X=x1)>1/n. Then take measurements to create more data sets. Call them sets 1,2,3,4... Then look to see if x1 occurs more frequently than one would expect.
What shouldn't I do? Calculate P(X=x1) for data set 0. Why? because thats like asking "given that I've thrown a six, what is the probability that I've thrown a six?"
It is not an evasion.

Oops. That's really shoddy nomenclature. I changed the naming of my data sets and didn't think to change the naming of my outcome. That is to say, the result of X with data set 0 should (if we're being consistent) be x0.
Still not convinced their isn't better nomenclature for this whole thing mind.

 

[DeiRenDopa]

One, and only one, possible null BeAChooser hypothesis:

* the distribution of 'quasars'
-> (however defined, as long as it's consistent)
-> around random points on the sky (so long as they are not in the ZoA or other special parts) and
-> in random directions
will be different, in a statistically significant sense, from the distribution of 'quasars' around 'Arpian' galaxies (however defined).

Of course we already know that there will be a difference (as shown by Scranton et al. 2005, for example), and this would need to be built into what constitutes 'statistically significant'.

A variant: instead of random points on the sky, choose (bright) stars, and instead of random directions, choose the scan direction of SDSS (and orthogonal to that direction).

One serious problem (among many) with the BeAChooser approach, as presented so far (and insofar as I understand it, which I don't), is that there is no way to understand or interpret the significance of the result of the calculation ... if only because there's nothing to compare it to.

 

[BeAChooser]

Originally Posted by BeAChooser
So if we have 10 randomly place quasars on the 0 to 1 line, the probability that ALL of them will be within 0.25 of that Karlsson value at the midpoint is 0.510 = 0.000977 = 0.001 . As I said.

BAC - that's true,

I'm glad you agree because this is for the example that YOU posed where there are 10 QSO all with the same deltaz (0.25) Maybe I misunderstood but I believe you said the overall probability was 0.5. That's wrong. It's 0.001, as I showed.

but that's NOT what you're doing. Stop for a moment and think. You're using a different deltaz for each data point, and that's wrong.

It's not wrong to use different deltaz.

Isn't it a fact that the probability for each QSO, by itself, can be determined individually as 2*deltaz. Just like in the above 1 QSO example. Correct?

And isn't it a fact that the placement of each QSO is independent of the placement of any other. They are independent phenomena ... under the assumptions of mainstream theory. And given that the placement of the QSOs are independent of one another, isn't the joint probability the product of the probabilities of the individual placements? That's a fundamental rule. Here: http://www.mathgoodies.com/lessons/vol6/independent_events.html "When two events, A and B, are independent, the probability of both occurring is:*P(A and B) = P(A) · P(B)". Correct?

So the result is inescapable, even when the deltaz of each QSO is different. It's just simple math. I'm not wrong in this case, sol. The formula is correct for 1 "quasi-Karlsson" value and 10 quasars each a different distance from that "quasi-Karlsson" value.

The random number cases you cited resulted in small probabilities, but that's as one would expect when the probability for any given point being within that points deltax from the "quasi-Karlsson" value is < 1. From the set of calculations you did, it would appear that the average probability you will get in that case is around 10^-6 to 10^-7 from random samples ... assuming the distribution they are drawn from is uniform across the total range. But what probability would you get if the set of QSOs you observed were are all fairly close to the midpoint ... say within 0.1? Why 10^-10. A thousand orders of magnitude less. So the real measure of whether the QSOs are inordinately close is how small the probability is to that average probability you get if you assume a random placement.

If time and time again, you get probabilities that are many, many orders of magnitude smaller than what you expect to get on average, that might be an indication of a problem in your assumptions about the distribution of z. And what if the total number of cases with 10 QSO is limited ... as in the real situation? What if there are only 1000 such cases possible, yet you find case after case showing up where the deltaz are such that you get probabilities that when multiplied by that 1000 are still << 1? Yet there you are with multiple cases. Doesn't that suggest that the process creating those quasar z values is not uniform as you assumed?

I've never suggested that the single sample probability in my calculations isn't going to be a small value even if the distribution from which the z come is really uniform and not quantized. But it's hard to evaluate what that small probability means, one way or the other, with just that alone. What's important is the final probability accounting for the maximum possible number of cases there could be with r quasars or even better, the number of cases actually examined to find the observations you have that contain those r quasar low probabilities cases. If you multiply the single sample probability by the total number of cases that might possibly exist, and you still end up with probabilities much less than one, and you have found numerous such cases, then perhaps it is time to reevaluate your assumption about the distribution of z in the total interval. OK?

 

[BeAChooser]

Are you stating that Karlsson values are part of mainstream astronomy

Of course not. Where did you get that idea? As I've said repeatedly now, the mainstream says the assertion that quasar redshifts have a tendency towards Karlsson's values (or any other values, for that matter, other than what I described earlier in this thread) is an illusion. My calculation, however, demonstrates quite clearly that it might not be an illusion after all.

At some stage you will want to compare the expected results from the model to the observed results.

But I do that. First I calculate the probability that a given observation would be seen if the mainstream assumptions about quasar z distribution were correct and we were able, hypothetically, to examine every possible observable quasar/galaxy association in the sky. And then I compare that probability to the fact that we've already seen such a case and add in the fact that we've seen not just one such case but several others ... which suggests that probability should be somewhere near 1, not 0.000something.

If the probability I get in such a calculation were anywhere close to 1, I'd have to admit that perhaps its just luck that those observations turned up. I acknowledge that. But if the calculated probabilities are far less than 1 ... say 0.000something, then isn't it prudent to wonder whether the assumption made about quasar z distribution in the calculation is correct ... especially in light of the fact that several renown scientists have said they've found evidence of "quantization"?

You may want to find out how the statistics of your mainstream model (uniform distribution of quasars and low red shift galaxies + Karlsson "clumping" if you want) differ from the statistics of the Arp model

I'm not arguing Arp's model at this point, RC. I've decided to back up a step and simply challenge the mainstream assumption that quasar z has no tendency towards specific values and that quasar location is unrelated to specific features (such as minor axes). If we can agree I'm right, then we can look at the options vis a vis revising the mainstream model. Fair enough?