Good News for Big Bang theory

Thus spake "John (Liberty) Bell"
Oh No wrote:

Thus spake "John (Liberty) Bell"
Oh No wrote:
Thus spake Oh No
Thus spake Chalky


I still think it is right to take out the
one point beyond 3sigma for the distribution (99.9%)

That sounds reasonable. Which z range does that influence?

The point is a little below z=0.8. The effect of removing it is to allow
the curves to move upward slightly, and curve slight

but I can't really
justify taking out the two others beyond 99%. One might expect two
points beyond that level anyway. Also, when I looked more carefully I
realised that removing one of those points was unfair on Chalky, because
it wasn't beyond 99% from his curve. The result, for 181 data points,
slightly reduces the teleconnection's lead and moves Chalky firmly back
into second place.

Standard Teleconnection Chalky
Chi^2 150.75 148.34 149.78
Omega 0.334 1.997 n/a

Ermmmm. Which data set are we talking about again here? Oh yes, the one
with all the local data around Chalky's ace forbidden.

That struck me too. I have been on to it.


Not, I think, if we concentrate on looking, as well as thinking,
locally, a la Einstein.

Funnily enough, I consider that it is thinking "a la Einstein" which is
the strongest argument for the teleconnection. He always had
reservations about the affine connection, and I found it by pursuing
what I believe are similar lines of thought. He never consider it as a
quantum problem, however. That is critical to making the idea work.

With around 180 points you really want a
difference of about 20 in the value of chi^2 to say anything approaching
conclusive.

OK. Since you have already performed and published, and repeated, a
comparative test with Chalky's ace forbidden, now try a test for that,
alone, as Chalky did, in his blown up graph of 0 z ~ 0.1 (the
original of which was a bit too untidy to publish). That should balance
the ' fairness' stakes quite convincingly.

Ok. For comparison, with 182 points from the gold set with z0.023 the
result was

Standard Teleconnection Chalky
Chi^2 158.75 156.67 158.38
Omega 0.34 2.01 n/a

After removing one outlier

Standard Teleconnection Chalky
Chi^2 150.75 148.34 149.78
Omega 0.334 1.997 n/a


With the entire gold set, including the low z points there were 206 SN.
As previously mentioned, errors are relatively large in the LR sample,
so it makes less difference than one might have thought, but
unfortunately for Chalky, the trend is against him.

Standard Teleconnection Chalky
Chi^2 172.06 169.91 172.58
Omega 0.337 2.01 n/a

After removing the outlier SN01fo (incidentally this is an HZSST point,
one of those also regarded as suspicious in the previously cited paper)
chalky just manages to hold on to second place.

Standard Teleconnection Chalky
Chi^2 164.04 161.57 163.83
Omega 0.328 1.992 n/a

For fair reflection of repetition of local conditions in a larger
subset, you could also look at Snae at the z for the concensus q = ~ 0
, i.e. maximum dimming, at ~ 0.365 z ~ 0.565. That is where God put
Chalky's king, queen, and jack (and the largest concentration of data).
That is why the standard deviations are so small there (in the Wright
analysis).

Are you game?

Truly there are most points there, except for the near set. But I see
little point in binning the data as done by Ned. All three curves are
very close and flat around there. I am not sure whether binning the data
will appear to show a kink, but this is not a feature of any the curves.
There is a suspicion that a kink might be shown because there is a
cluster of 4 HZSST points above the curve, three of which were marked
suspicious in arXiv:astro-ph/0612653. I didn't like that analysis,
because it was based on conformity to a particular model, and I don't
have a good reason to reject individual points apart from the one
genuine outlier.

Funnily enough, although Riess's cleaning up of data has generally
produced tighter fits, this does not appear to be the case with these
HZSST points. They were much closer to the curve in the previous 04
sample. That also might make me suspect a problem with recalibrating the
HZSST data.

Because all the curves are close and flat, if there is still a kink in
the data after binning in the gold set, as well as in the combined set,
it would indicate that the data does not fit any one of them, and it
would be right to conclude that there is indeed a fault in the data, and
to suspect these HZSST points in particular.

It is clear that the HZSST points are by far the least good subset -
they have a much wider scatter than the other sets as well as having
wider error bars. Rather than possibly bias the data by taking out
individual points as suggested by arXiv:astro-ph/0612653, it seems
fairer to try taking out the HZSST points en bloc. Taking out the
individual points would clearly be unfair on chalky, since his curve is
marginally closer to them. The entire subset is a scatter on both sides
of the curves which makes it impossible to predict the result of taking
it out. It is also interesting because if it makes a substantial
difference in the prediction of omega for the teleconnection and
standard models, or dM for every model, that is evidence that the HZSST
data is indeed not fully compatible with the other data.

I haven't given figures for dM. This is the fitting parameter for the
unknown absolute magnitude of a type 1A supernova, offset from some
convenient value chosen by Riess.

For the 181 point set with one HZSST outlier removed I had

Standard Teleconnection Chalky
Chi^2 150.75 148.34 149.78
Omega 0.334 1.997 n/a
dM -0.058 -0.049 0.022

After removing all HZSST points I have a sample of 141, for which I get

Standard Teleconnection Chalky
Chi^2 105.44 104.73 108.51
Omega 0.336 1.985 n/a
dM -.045 -0.033 0.033

Not a huge shift in values of Omega, but a noticeable one in values of
dM. Also a drop of 40-45 in the value of chi^2 is disproportionately
large, which is fairly suggestive that the HZSST data is in tension with
the other sets. I would need to consult a statistician to say more.

The loss of a number of high z points needed to distinguish the
teleconnection from the standard model has noticeably cut the
teleconnection lead, but unfortunately for Chalky, he has started to
trail. Not enough to eliminate his law, but lengthening odds. The
situation would be worse if the low z points were included in this
sample, because there is little change in the difference between values
of dM for his law and the others.


Regards

--
Charles Francis
substitute charles for NotI to email

Oh No wrote:

Thus spake Chalky
Oh No wrote:

Thus spake "John (Liberty) Bell"
Oh No wrote:
Thus spake "John (Liberty) Bell"

Model: Chalky's Law EFE Teleconnection Data points
chi^2 Wright: 383.05 393.49 387.55 292

OK so that IS your chi^2 test of the complete spectrum,

yes.

Finally, by removing the Riess 2004 data too, to just leave the Astier
set, you got:

Model: Chalky's Law EFE Teleconnection No. of Data
Points
chi^2 Astier: 158.38 158.75 156.67 182

No. I didn't run these tests on the original Astier set. This was on the
Riess06 Gold set, in which Riess has recalibrated all his original sets,
compensated for measurement errors which have since been discovered in
the equipment and added in the Astier set as well as 26 new HST
supernovae.

But all this data was _included_ in the already analysed 292 point set
provided by Wright!
All you have done here is remove 110 supernovae from the set, knowing
full well that the vast majority of these are perfectly valid type 1a
supernovae.

As I have said, the relatively few points which are not valid type 1a
supernova have far more influence on chi^2 than the valid ones.

But we are not interested in the trivial absolute value of chi^2. We
are interested in the relative "goodness of fit" for different
theories, over the entire z spectrum.

Compare the full set with 292 points

Standard Teleconnection Chalky
Chi^2 393.49 387.55 383.05
Omega 0.32 1.985 n/a

with the set with 14 outliers removed

Standard Teleconnection Chalky
Chi^2 223.94 219.31 218.73
Omega 0.327 1.997 n/a

Only 14 points out of 292 account for almost half the value of chi^2.
Most of these points are certainly not type 1A, so any effect they have
is meaningless.

Thus is STATISTICS. If they are not type 1A, why the hell should they
preferentially favour Chalky's Law over EFE?

There will be a lot of other non-type 1A SN in the full
sample,

That is speculation

and these will also have a disproportionate effect on the
result. They cannot be picked out by looking at the distribution of
data, because that would bias the results.

Ditto for z 0.023 exclusions.

For a comparative test of a new field equation against an old one, we
need all the data we can get. You only need to supress the evidence
from outliers like this, to defend an older field equation that cannot
adequately cope with the full spectrum of data.

To get an accurate test you have to have accurately typed data, free of
systematic errors and free of tension between the subsamples. That is
why Riess and his team have put a huge amount of effort into analysing
the full experimental results to eliminate false data.

If so, why did they specifically eliminate _true_ data by prohibiting
all observations below z= 0.023?

Incidentally, Ned responded to John at quarter past eight this morning
(California Time) on the 4th.

He provided an update of
http://www.astro.ucla.edu/~wright/sne_cosmology.html, to include the z
range for each binned data point (which we needed for an accurate
graph), and corresponding binned data for the related Gold set, along
with a comment on relative gold/silver merits. This actually resonates
quite well with what you said when you were at your most scientifically
objective, during remorse over slagging me off for no valid reason
earlier. (Your apology is accepted)

Ned also emailed John a particularly astute comment on your debate with
us, which we have decided to keep to ourselves.


Chalky

Oh No wrote:
I am personally very suspicious of the removal of gold SN below some
apparently arbitrary z value.

How would you handle peculiar motions at low z? They can amount to
several hundred km/s. If you had a sample of several hundred low-z SNe
over the whole sky, peculiar motions could be averaged out, but there's
nothing like that available.

Oh No wrote:

Thus spake Chalky
Oh No wrote:

Thus spake "John (Liberty) Bell"
Oh No wrote:
Thus spake "John (Liberty) Bell"

Model: Chalky's Law EFE Teleconnection Data points
chi^2 Wright: 383.05 393.49 387.55 292

OK so that IS your chi^2 test of the complete spectrum,

yes.

Finally, by removing the Riess 2004 data too, to just leave the Astier
set, you got:

Model: Chalky's Law EFE Teleconnection No. of Data
Points
chi^2 Astier: 158.38 158.75 156.67 182

No. I didn't run these tests on the original Astier set. This was on the
Riess06 Gold set, in which Riess has recalibrated all his original sets,
compensated for measurement errors which have since been discovered in
the equipment and added in the Astier set as well as 26 new HST
supernovae.

But all this data was _included_ in the already analysed 292 point set
provided by Wright!
All you have done here is remove 110 supernovae from the set, knowing
full well that the vast majority of these are perfectly valid type 1a
supernovae.

As I have said, the relatively few points which are not valid type 1a
supernova have far more influence on chi^2 than the valid ones.

Compare the full set with 292 points

Standard Teleconnection Chalky
Chi^2 393.49 387.55 383.05
Omega 0.32 1.985 n/a

with the set with 14 outliers removed

Standard Teleconnection Chalky
Chi^2 223.94 219.31 218.73
Omega 0.327 1.997 n/a

Since Ned Wright (http://www.astro.ucla.edu/~wright/intro.html) is a
bona fide UCLA Professor, with a physics background, a Harvard
Astronomy Phd, a very pertinent website, a NASA Exceptional Scientific
Achievement Medal, and a particularly impressive c.v. beyond that, in
the relevant field, I think that Chalky would be well advised to accept
the results of Ned's "robust" statistical analytical method for what
they are, in preference to adopting yours. This is particularly so
because he was kind enogh (and on the ball enough) to provide
comprehensive additional details at the
http://www.astro.ucla.edu/~wright/sne_cosmology.html page, on the same
morning I contacted him over this.

If you study this page, you will see that you have included an obvious
'ringer' in your 292 element set which is absent in Ned's 291 element
set, and which singlehandedly increases the Chi^2 value by 85 points.
Chalky never even used that!

You will also see that your demand for a 20 point Chi^2 improvement
over EFE for Chalky's Law is completely unrealistic and unreasonable.
This is even greater than the Chi^2 difference between the standard
(WMAP) EFE model and the empty (Milne) EFE model, which is used as the
inertial reference standard for this whole programme of research.

You are thus demanding that we show a greater difference between
Chalky's Law and the best fit flat EFE model, which is greater than all
the evidence for accelerating expansion put together.

Consequently, I don't think anyone should take your negative criticisms
too seriously


John Bell.

Professor Wright:

unbinned
Name chi^2/n
best flat 297.7/290

Charles Francis:

unbinned
Name chi^2/n
Best EFE 393.49/292

Diference 1: 95.79/2

Professor Wright:

unbinned
Name chi^2/n
WMAP model 302.6/291

Diference 2 90.89/1


CF Full Analysis - Difference 2:

Model: Chalky's Law Best EFE Telecon. n
chi^2: 292.16 302.60 297.66 291

CF Full Analysis - Difference 1:

Model: Chalky's Law Best EFE Telecon. n
chi^2: 287.26 297.70 291.76 290


Clearly, it would be more scientific if you could simply remove your
obvious ringer from your 292 element set, and run the program again.

If you remove more, you risk throwing the baby out with the bath water.



Chalky

Thus spake "John (Liberty) Bell"
Oh No wrote:


As I have said, the relatively few points which are not valid type 1a
supernova have far more influence on chi^2 than the valid ones.

But we are not interested in the trivial absolute value of chi^2. We
are interested in the relative "goodness of fit" for different
theories, over the entire z spectrum.

Goodness of fit is related to the absolute value of chi^2. If you
compare the relative difference of appalling fits you are not going to
learn very much.

Compare the full set with 292 points

Standard Teleconnection Chalky
Chi^2 393.49 387.55 383.05
Omega 0.32 1.985 n/a

with the set with 14 outliers removed

Standard Teleconnection Chalky
Chi^2 223.94 219.31 218.73
Omega 0.327 1.997 n/a

Only 14 points out of 292 account for almost half the value of chi^2.
Most of these points are certainly not type 1A, so any effect they have
is meaningless.

Thus is STATISTICS.

Of course it is statistics. You have to understand statistics or every
result you get has no meaning.

If they are not type 1A, why the hell should they
preferentially favour Chalky's Law over EFE?

Why not? It's completely random and meaningless.

There will be a lot of other non-type 1A SN in the full
sample,

That is speculation

It is also speculation to say there are not. That is why doubtful points
must be removed before you start.

and these will also have a disproportionate effect on the
result. They cannot be picked out by looking at the distribution of
data, because that would bias the results.

Ditto for z 0.023 exclusions.

Not really. As the fits to teleconnection and standard model showed,
taking these out made no difference. Not so with chalky's law, which
faired better without them.

For a comparative test of a new field equation against an old one, we
need all the data we can get. You only need to supress the evidence
from outliers like this, to defend an older field equation that cannot
adequately cope with the full spectrum of data.

To get an accurate test you have to have accurately typed data, free of
systematic errors and free of tension between the subsamples. That is
why Riess and his team have put a huge amount of effort into analysing
the full experimental results to eliminate false data.

If so, why did they specifically eliminate _true_ data by prohibiting
all observations below z= 0.023?

I don't really know. Someone produced a silly idea which got taken
seriously I think, a "Hubble bubble". But the fits showed no indication
of a Hubble bubble, and nor do I know any reason why there should, or
even could be one.




Regards

--
Charles Francis
substitute charles for NotI to email

Thus spake Steve Willner
Oh No wrote:
I am personally very suspicious of the removal of gold SN below some
apparently arbitrary z value.

How would you handle peculiar motions at low z? They can amount to
several hundred km/s. If you had a sample of several hundred low-z SNe
over the whole sky, peculiar motions could be averaged out, but there's
nothing like that available.

peculiar motions are in the order of 400km/s as I recall. That is

0.0013

which is 1/20th the cutoff they are applying.

In fact what they do is add in an error in magnitude to allow for
peculiar motion. Because of the shape of the curve, this error will be
large for small z, and hence the corresponding value of chi^2 will be
much smaller for low z points. So these points are already weighted to
have less influence on the overall result.

Actually I may have done an injustice when I said the low redshift
sample contained larger errors. Quite possibly these are not measurement
errors, but errors due to peculiar velocity. I would have to calculate
to know.

Anyway, the answer to your question is that this is already handled in
the statistical analysis, or more precisely I should say, it is already
handled in the manner in which the data is tabulated, with the errors
for peculiar motions built in.


Regards

--
Charles Francis
substitute charles for NotI to email

Steve Willner wrote:

Oh No wrote:
I am personally very suspicious of the removal of gold SN below some
apparently arbitrary z value.

How would you handle peculiar motions at low z?

Statistically.

They can amount to
several hundred km/s. If you had a sample of several hundred low-z SNe
over the whole sky, peculiar motions could be averaged out, but there's
nothing like that available.

See comment by Stupendous Man and, hopefully, next week's AAS meeting.

See also http://www.astro.ucla.edu/~wright/sne_cosmology.html . We
already have 22 below z = 0.021, and another 22 below z = 0.04. (You
would only need 8 more for a complete deck of cards.)

In article , Oh No
writes:

Standard Teleconnection Chalky
Chi^2 150.75 148.34 149.78

The question, of course, is whether these differences are significant. A
good test is to randomly remove a data point and recalculate Chi^2.
(Ideally, recalculate it n times where n is the number of data points,
each time removing another one, and take the average.) This gives you a
lower limit on how much Chi^2 can vary just by chance. (Better would be
to remove SQRT(n) points to get an idea of the Poisson noise.) If the
differences in Chi^2 between the different approaches are less than this
"error in Chi^2", then they can't be very significant. (Of course, you
have to scale Chi^2 with the number of data points.)

Thus spake Chalky

Clearly, it would be more scientific if you could simply remove your
obvious ringer from your 292 element set, and run the program again.

If you remove more, you risk throwing the baby out with the bath water.

There is a lot more than one obvious ringer. I made particular remark on
that one in the original post when I ran the test, if you remember. And
removed it and a number of others before getting a result I considered
remotely meaningful. Since the gold set retains 182 properly verified
points, there is not much chance of throwing out any babies here. You
will have observed that the removal of points in the sample which are
essentially random makes little difference to optimum fit values for
Omega in either model that uses it. It makes a lot of difference to
chi^2 and therefore to how meaningful the test is as a test between
models.

I have run a test for comparison with Ned Wright, since it is a good way
to test my program. I have previously reproduced precisely the
predictions and chi^2 values of both Riess and Astier, so I know it is
not fundamentally wrong, but it does appear to reveal something I had
suspected, that I am misinterpreting the way in which the errors are
presented in the new data. As a result it means my values of chi^2 are
systematically high compared to his. This will make little difference to
the overall result, because all three models are affected in exactly the
same way, but I will be rerunning the tests when I have sorted the
problem. Unfortunately I cannot discern exactly is intended here, but
now that I have confirmation of the problem I will ask Ned exactly what
the formula should do.

The following result, and all previous results posted are subject to
revision. They may be compared to each other, but not to the chi^2
values calculated by Ned.

For 291 points
Standard Teleconnection Chalky
Chi^2 348.44 342.88 340.01
Omega 0.317 1.99 n/a

That compares to the previous result for 292 points

Standard Teleconnection Chalky
Chi^2 393.49 387.55 383.05
Omega 0.32 1.985 n/a

So you can see that a noticeable part of chalky's original lead was due
to the single ringer. But I must emphasise, differences in these values
of chi^2 are still primarily due to other, essentially random, data.



Regards

--
Charles Francis
substitute charles for NotI to email