## Journal Club – Theory constraint

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According to Wikipedia, a journal club is a group of individuals who meet regularly to critically evaluate recent articles in the scientific literature. And of course, the first rule of Journal Club is… don’t talk about Journal Club.

So, without further ado – today’s journal article is about how new data are limiting the theoretical options available to explain the observed accelerating expansion of the universe.

**Today’s article:**

Zhang et al Testing modified gravity models with recent cosmological observations..

Theorists can develop some pretty ‘out there’ ideas when using limited data sets. But with the advent of new technologies, or new ways to measure things, or even new things to measure – new data becomes available that then constrains the capacity of various theories to explain what we have measured.

Mind you, when new data conflicts with theory, the first question should always be whether the theory is wrong or the data is wrong – and it may take some time to decide which. A case in point is the Gran Sasso faster-than-light neutrino data. This finding conflicts with a range of well established theories which explain a mountain of other data very well. But to confirm that the neutrino data are wrong, we will need to reproduce the test – perhaps with different equipment under different conditions. This might establish an appropriate level of confidence that the data are really wrong – or otherwise that we need to revise the entire theoretical framework of modern physics.

Zhang et al seek to replicate this sort of evidence-based thinking using Bayesian and also Akaike statistics to test whether the latest available data on the expansion of the universe alters the likelihood of existing theories being able to explain that expansion.

These latest available data include:

- the SNLS3 SN1a data set (of 472 Type 1a supernovae);
- the Wilkinson Microwave Anisotropy Probe (WMAP) 7 year observations;
- Baryonic acoustic oscillation results for the Sloan Digital Sky Survey release 7; and
- the latest Hubble constant measures from the Wide Field Camera 3 on the Hubble Space telescope.

The authors run a type of chi-squared analysis to see how the standard Lambda Cold Dark Matter (CDM) model and a total of five different modified gravity (MG models) fit against both the earlier data and now this latest data. Or in their words ‘we constrain the parameter space of these MG models and compare them with the Lambda CDM model’.

It turns out that the latest data best fit the Lambda CDM model, fit less well with most MG models and at least one of the MG models is ‘strongly disfavored’.

They caveat their findings by noting that this analysis only indicates how things stand currently and yet more new data may change the picture again.

And not surprisingly, the paper concludes by determining that what we really need is more new data. Amen to that.

So… comments? Are Bayesian statistics just a fad or a genuinely smarter way to test a hypothesis? Are the first two paragraphs of the paper’s introduction confusing – since Lambda is traditionally placed on ‘the left side of the Einstein equation’? Does anyone feel constrained to suggest an article for the next edition of Journal Club?

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Bayes’ rule or Bayesian statistics “rules.” Bayes rule is the most general way to work with statistics. Bayes’s rule is

P(A)P(B|A) = P(B)P(A|B),

written here in a symmetrical form. To compute the conditional probability P(A|B) then P(A) is the prior probability (an estimate or data input) so that

P(A|B) = P(B|A)P(A)/P(B).

P(A|B) is the posterior probability of A given the data on B and the conditional probability divided by the post probability P(B|A)/P(B) is the probability support for A given B.

This has been around since the 18th century, and there really has been no significant mathematical improvement on this. There have been of course advancement with Bayes’s rule, such as regression analysis.

LC

OK

Bayesian statistics is not the end all on the subject, but I think it is the most logically reasonable. As one increases the data about a system this narrows errors on prior estimates. The world is then a sort of 20-questions system, where the accumulation of information updates one computation of the posterior probability.

Frequentism is not wrong in a strictly mathematical sense. However, it really is most applicable if one has either an infinite sample space or if that sample space is completely known in a finite case. In the infinite case frequentism and Bayes rule tend to converge in some sense.

Statistics is an empirical branch of mathematics. As a result it is somewhat outside the axiomatic-theorem approach of the rest of mathematics. What constitutes “truth” is not hard, but more in line with Popper’s notion of contingent truth in empirical science.

LC

I don’t think anyone here has a problem with Bayesian statistics in itself. The question is whether this is the right tool for this paper.

I would say that this is good thing to do. Astronomical data is expensive. The old supernova datasets are a good set of well-known priors, and the new supernova datasets look like a good test data set. If we aren’t writing all the knowledge we can out of the data we have, then we ought to be.

The devil is always in the details. If new data was gathered by looking at exactly the same region of sky with the same equipment and the same techniques then it would work. Or, if you split your data in half at random; deliberately formulated your theories having only seen one half the data; then try the fit with the other half. If you are doing statistics on the efficacy of drugs, then you have to be very careful about any sources of experimenter bias: I recommend Ben Goldacre’s ‘Bad Science’ for a nice introduction on how hard that sort of thing is to do. Here, there is a bias because the prior results were actually obtained prior to the test data. This is almost inevitable, but it isn’t good.

The authors have considered this. This isn’t one of those ‘oh crap we haven’t enough points, lets use a fancy stats package I found on the net’ paper. Unless there is something flat wrong that we haven’t spotted, I feel they have probably done as good a job as the data allows.

I have only at this stage looked at the paper. They do test f(R) theories, of which Gauss-Bonnet theory is an example of. This is of interest, and I wrote a paper on such a theory where the deviation from the Einstein-Hilbert action is due to string correction.

It is interesting that the DGP model seems to fail the most. In that model gravity “leaks” off the D3-brane as Type IIA-B and Het strings are closed and not attached to the brane by open endpoints or Chan-Paton factors. This has the troubling implication that quantum information leaks out of the universe and such information in the “bulk” would diffuse in.

LC

Maybe similar to how a black hole evaporates from the event horison. Could it be that we are living on the eventhorizon of a higher order part of the universe?

Maldacena demonstrated how a spacetime called the anti-de Sitter spacetime has isometries or symmetries which are dual to a conformal field theory on the boundary. The boundary is conformally flat, which can include a de Sitter spacetime that models inflationary cosmology. The boundary is similar to an event horizon.

LC

Now you are confusing me. BH evaporation is explicitly unitary (no loss of observable information), isn’t it? Maybe not locally but globally, or Hawking wouldn’t have lost his bet.

Or maybe you meant the rest, which may be an analogy for all I know. If holography is correct it would if I understand it and BH correctly, but then again you would have problems with what is “the universe” above in order to preserve unitarity.

Yes i know there would be problems, and im not suggesting this to be the case (no evidence whatsoever).

As a response question to LC’s: “This has the troubling implication that quantum information leaks out of the universe and such information in the “bulk” would diffuse in.” im just pondering the possibility that our universe (3D+T+maybe 6H) is wrapped around a higher order brane giving it some analogy to an event horizon. Quantum states leaking out of that brane (then implying a higher order bulk of the universe) might then be analogous to quantum states leaking off the event horizon of a black hole. Just pondering the possibility.

GR doesnt support my analogy, but then at this end of things GR is replaced by QM or in the future some new better theory (string theory perhaps, or something else).

There are some relationships between even and odd dimensional Dp-branes, p = dimension, that have holographic content. The boundary of an anti-de Sitter spacetime is a conformal field in one dimension lower. This boundary is not an event horizon however. This does also have a bearing on the structure of compactified spaces, which are called Calabi-Yau spaces.

I thought for a bit about how much I should write about this. This is awfully tough mathematical physics. I decided to defer on that, for I think it is too advanced a topic for this blog.

LC

Yes, the natural laws of this universe seems to be in direct relation and requirement upon the number of dimensions (assuming stringtheory being close to correct).

But it could also be the opposite, that we have the natural laws we have, because the number of dimensions available are set, which then only allow a certain set of waveforms (in probability space) to be stable. The requirement upon a higher dimension then would be that at the limit to our ‘universe’ the rules transform into what we observe. The argument could then be repeated upwards towards an infinity of dimension, but would leave observability and thus become pure speculation.

I would be going off the deep end here in my speculations, so i think I better stop.

The columns here are getting too narrow for me to write much. I wrote here at UT in early January a proof for why the universe has these extra dimensions. If the topic is more commensurates with the blog entry I might rewrite that.

LC

Comments engine still a bit unpredictable.

Bayesian statistics is not the end all on the subject, but I think it is the most logically reasonable. As one increases the data about a system this narrows errors on prior estimates. The world is then a sort of 20-questions system, where the accumulation of information updates one computation of the posterior probability.

Frequentism is not wrong in a strictly mathematical sense. However, it really is most applicable if one has either an infinite sample space or if that sample space is completely known in a finite case. In the infinite case frequentism and Bayes rule tend to converge in some sense.

Statistics is an empirical branch of mathematics. As a result it is somewhat outside the axiomatic-theorem approach of the rest of mathematics. What constitutes “truth” is not hard, but more in line with Popper’s notion of contingent truth in empirical science.

LC

Thanks – I am just throwing comment provoking statements around. Actually I quite like the Bayesian approach – though I agree with Richard Kirk’s analysis that it only ‘sort of’ fits this context.

Bayesian statistics permits a regression that is similar to a game of 20 questions. In this process your prior estimates are made more precise. This is why we have a “sort of fits.” At this time of course our observations of the universe are preliminary, and we are stuck on this one planet looking out over billions of light years.

I read the paper by Zhang and the rest of the Chinese investigators. It is interesting that the ?CDM came out on top, and the Braney theory the worst. The string/brane physics I think has some bearing on the nature of reality. This acts as a sort of framework that I think is more general than other attempts at quantum supergravity. However, I think it does not permit us to understand the universe completely. I think there is some missing ingredient, which as I see it involves quantum phase structure.

LC

No worries. Bayesian statistics can be applied to _anything_.

Hah – I was refering to my random OK comment above, although it fitted the comment stream for a while there.

Bayesian rules – OK

I’ll take “Bayesian statistics” for 100 site cookies, Steve:

Bayesian probabilities can become a lot of things depending on context.

1 If used in a general sense bayesian probabilities are a form of betting, which falls under success criteria of game strategies but are not regular likelihoods (probabilities).

2 If used as here bayesian probabilities are judging parsimony.

2.1 Here bayesian probabilities are used for comparing, but not safely excluding, theories.

2.2 This may be inspired by the use of bayesian probabilities within a theory like standard cosmology to constrain parameters from these various data sources based on parsimony. Another example would be the SETI Drake equation. These parameter regions are then tested with the hypothesis.

2.3 Bayesian probabilities can further be used to propose by parsimony a set of hypotheses to be tested. This is how these methods have found good use in biology to propose phylogenies. It is similar use as in 2.1 and 2.2.

2.4 Or bayesians can try parsimony over hypotheses and parameters both, I believe I have seen that suggested. However, as in ordinary optimization the many degrees of freedom implodes the use what I know of it.

Akin to how “a theory that predicts everything predicts nothing”. It is the heuristics of the bayesian heresy. =D

3 Hidden Markov Models use bayesian probabilities for modeling. Those would be ordinary observable (frequentist) probabilities, AFAIU.

And here is 2 of my site cookies back FWIW:

It is not a fad and it is not a way to do testing.

It is a more general way to do parsimony than “number of parameters”, for one. HMMs makes it stay, everything else alike. Biologists love their bayesian methods, I don’t think you can do reasonable phylogenetic work without it.

I just wish bayesians didn’t call it “probabilities” or “statistics” then clearly it isn’t most of the time.* It diminishes the strength of using of those terms. It’s a little like calling fishes “water animals”. Yes, but what about those other animals living in water, or fishes like us that lives on land today?

———————

* I know the history of the field, and the problems how to define observable probabilities, made it a start and a tempting continuation. And unfortunately there are philosophers of science pushing their ideas onto the area.

Maybe one day, when and if they discover that they can’t subsume all of probability theory and statistics alike, they would call it “bayesities” and “bayesics”. Because those grand posteriors would still inflate the ego of the bayesian user.

Hi Torbjorn…

quoting you – //It’s a little like calling fishes “water animals”. //

Plural of Fish is “Fish” (no es at the end)… I feel like IvanMan …

Probably one of the extremely rare occasions I have been able to correct you on something – Now if I can just catch you out with an astrophysics boo-boo 😉

Wezley

ps. nice discussion here – Haven’t been reading UT much lately but looking forward to more great articles and discussion.

Well, new data? It seems like buttloads of new data. 😀

Bayesian seems dumb, but it says something.