Occam's Razor and WMAP Anomalies

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Discussion Overview

The discussion revolves around the application of Occam's razor to anomalies observed in the WMAP data, particularly focusing on the low quadrupole, the "axis of evil" effect, and the implications for cosmological models such as inflation, dark matter, and dark energy. Participants explore the statistical significance of these anomalies and the methodologies used to assess them.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • Some participants note that the authors of the referenced paper argue that various implementations of Occam's razor undermine claims of anomalies in the WMAP data, particularly the low quadrupole.
  • Others express concern about the reliability of the statistical evidence for non-Gaussianity and the low-l power deficiency, questioning how strong the evidence must be to warrant significant changes in cosmological theories.
  • One participant highlights the importance of understanding the differences in datasets and methodologies used to analyze the WMAP data, indicating that these differences could affect the conclusions drawn.
  • Another participant discusses the various criteria used as razors, such as the Akaike Information Criterion and Bayesian Information Criterion, noting that they sometimes yield conflicting results regarding the anomalies.
  • Some participants suggest that the connection between the low-l power deficiency and the axis of evil may complicate the interpretation of the results, especially if local contamination is a factor.
  • There is a mention of the authors' other research, specifically regarding MOND, which some participants find intriguing but express uncertainty about the clarity of the Occam's razor paper.

Areas of Agreement / Disagreement

Participants express a range of views on the implications of the WMAP anomalies and the application of Occam's razor, with no consensus reached on the strength of the evidence or the validity of the claims made in the paper.

Contextual Notes

Participants note that the statistical significance assessments are complicated by the need to avoid false positives and negatives, which may affect the interpretation of the anomalies. Additionally, the discussion acknowledges that different methodologies yield varying results, contributing to the uncertainty in the findings.

wolram
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http://arxiv.org/abs/astro-ph/0604410

Authors: Joao Magueijo, Rafael D. Sorkin

Using a variety of quantitative implementations of Occam's razor we examine the low quadrupole, the ``axis of evil'' effect and other detections recently made appealing to the excellent WMAP data. We find that some razors {\it fully} demolish the much lauded claims for departures from scale-invariance. They all reduce to pathetic levels the evidence for a low quadrupole (or any other low $\ell$ cut-off), both in the first and third year WMAP releases. The ``axis of evil'' effect is the only anomaly examined here that survives the humiliations of Occam's razor, and even then in the category of ``strong'' rather than ``decisive'' evidence. Statistical considerations aside, differences between the various renditions of the datasets remain worrying.
 
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In "Occam’s razor meets WMAP" the authors are trying their best to find a convincing refutation of the statistical evidence for non-Gaussality, low-l power deficiency, and the 'Axis-of-evil' in the WMAP power spectrum.

However a prior question of the Mainstream model that might be relevant to this approach is: "What does Occam's razor do to Inflation, DM or DE?"

From that paper:
As shown in Table III our evidence for an anomaly is always above H = 3, i.e. “strong evidence”.
But even when different razors agree on an anomaly – such as the axis of evil – one should not trust the result blindly. The issue of systematics remains of paramount importance, as shown by the significant differences in H obtained from the various datasets and methodologies used to deal with the galactic foregrounds. And one should bear in mind that even the most enthusiastic “Ockhamist” would be unlikely to claim for his or her favorite razor a freedom from ambiguity[26] better than H = ±0.3 or so. In addition it’s probably fair to say that the trouble of rewriting cosmology textbooks deserves in itself a penalty factor. This is hard to evaluate but it may translate into the requirement of a higher level of evidence than “strong”, at the phenomenological level. Perhaps the ever improving polarization maps will have a say on the matter and tilt the scales. This issue is currently being very actively investigated.
(emphasis mine)

The question is exactly how 'strong' does the level of evidence have to be before people go to all "the trouble of rewriting cosmology textbooks"?

Perhaps a lesser degree of confidence in the Mainstream model and a greater open-mindedness to other alternatives might not come amiss?

Garth
 
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wolram said:
Statistical considerations aside, differences between the various renditions of the datasets remain worrying.
Could anyone explain what this exactly means? (I have not read the paper)
 
hellfire said:
Could anyone explain what this exactly means? (I have not read the paper)
The paper uses different 'brands' of Occam's razor, using information theory.
The information in the data given the theory is defined as minus the logarithm of the likelihood. But in fact we want to minimize the information in the data and the theory together,that is:
I(D, T ) = I(D|T ) + I(T ) (1)
so that I(T ) is the penalty referred to above.
According to some authorities, strong evidence for a theory over a “base model” requires an improvement in I(D, T ) by at least 3 (see [7, 8]). The title of “decisive evidence” is not normally bestowed unless the improvement exceeds 5.
(Which provides the formal answer to my question above.)

There are different criterion that can be used as razors , the Akaike Information Criterion, AIC, the Bayesian Information Criterion, BIC, and a third described in the text they call the HIC. The desire is for all three to remove the anomalies, and sometimes they do and sometimes they don't. Furthermore, they actually disagree with each other as to which is which and this removes the certainty in their result.

My observations are these:

1. As I have said elsewhere, in statistical significance assessment the desire not to fall into the trap of making a false positive, (e.g. requiring an improvement in I(D, T ) of at least 5 for a decisive result,) i.e. saying the anomalies are there when really they are not, inevitably increases the chance of making a false negative, saying the anomalies are not there when really they are.

2. The paper deals with the low-l power deficiency separately from, and before, the Axis of evil, it concludes that the deficiency disappears after 'shaving' whereas the Axis does not and stubbornly remains. However these anomalies are connected, for if the AoE exists and is caused by local contamination, then the low-l power deficiency becomes even more pronounced and I would guess would actually survive the stringent 'shaving' of this analysis.

Garth
 
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One of the authors is Joao Magueijo.
(of course Bekenstein, the other, is famous for BH temperature and Bekenstein-Hawking BH entropy)

About Magueijo, I really like his recent research. I can't evaluate this Occam WMAP paper but am enthusiastic about this one

http://arxiv.org/abs/hep-th/0509010
MOND habitats within the solar system
Jacob Bekenstein, Joao Magueijo
"MOdified Newtonian Dynamics (MOND) is an interesting alternative to dark matter in extragalactic systems. We here examine the possibility that mild or even strong MOND behavior may become evident well inside the solar system, in particular near saddle points of the total gravitational potential. Whereas in Newtonian theory tidal stresses are finite at saddle points, they are expected to diverge in MOND, and to remain distinctly large inside a sizeable oblate ellipsoid around the saddle point. We work out the MOND effects using the nonrelativistic limit of the TeVeS theory, both in the perturbative nearly Newtonian regime and in the deep MOND regime. While strong MOND behavior would be a spectacular ``backyard'' vindication of the theory, pinpointing the MOND-bubbles in the setting of the realistic solar system may be difficult. Space missions, such as the LISA Pathfinder, equipped with sensitive accelerometers, may be able to explore the larger perturbative region."

Has anyone read "MOND habitats"?

I tend to give this Occam paper benefit of doubt out of respect for the authors. But I fail to get any crisp message from it.
 
Thank you Garth.
 
By Marcus

I tend to give this Occam paper benefit of doubt out of respect for the authors. But I fail to get any crisp message from it.

we do seem to find the odd disturbed pebble, broken twig, but not so much
as a sniff of the prey, it seems to me we desperatly need more dedicated hunters, hounds, maybe only then will we find out which of us is the yeti.
 

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