Cosmology and the Born-Again Bayesians!

The other day, via Twitter, I came across an interesting blog post about the relatively recent resurgence of Bayesian reasoning in science. That piece had triggered a discussion about why cosmologists seem to be largely Bayesian in outlook, so I thought I’d share a few thoughts about that. You can find a lot of posts about various aspects of Bayesian reasoning on this blog, e.g. here.

When I was an undergraduate student I didn’t think very much about statistics at all, so when I started my DPhil studies I realized I had a great deal to learn. However, at least to start with, I mainly used frequentist methods. Looking back I think that’s probably because I was working on cosmic microwave background statistics and we didn’t really have any data back in 1985. Or actually we had data, but no firm detections. I was therefore taking models and calculating things in what I would call the forward direction, indicated by the up arrow. What I was trying to do was find statistical descriptors that looked likely to be able to discriminate between different models but I didn’t have the data.

Once measurements started to become available the inverse-reasoning part of the diagram indicated by the downward arrow came to the fore. It was only then that it started to become necessary to make firm statements about which models were favoured by the data and which weren’t. That is what Bayesian methods do best, especially when you have to combine different data sets.

By the early 1990s I was pretty much a confirmed Bayesian – as were quite a few fellow theorists -but I noticed that most observational cosmologists I knew were confirmed frequentists. I put that down to the fact that they preferred to think in “measurement space” rather than “theory space”, the latter requiring the inductive step furnished by Bayesian reasoning indicated by the downward arrow. As cosmology has evolved the separation between theorists and observers in some areas – especially CMB studies – has all but vanished and there’s a huge activity at the interface between theory and measurement.

But my first exposure to Bayesian reasoning came long before that change. I wasn’t aware of its usefulness until 1987, when I returned to Cambridge for a conference called The Post-Recombination Universe organized by Nick Kaiser and Anthony Lasenby. There was an interesting discussion in one session about how to properly state the upper limit on CMB fluctuations arising from a particular experiment, which had been given incorrectly in a paper using a frequentist argument. During the discussion, Nick described Anthony as a “Born-again Bayesian”, a phrase that stuck in my memory though I’m still not sure whether or not it was meant as an insult.

It may be the case for many people that a relatively simple example convinces them of the superiority of a particular method or approach. I had previously found statistical methods – especially frequentist hypothesis-testing – muddled and confusing, but once I’d figured out what Bayesian reasoning was I found it logically compelling. It’s not always easy to do a Bayesian analysis for reasons discussed in the paper to which I linked above, but it least you have a clear idea in your mind what question it is that you are trying to answer!

Anyway, it was only later that I became aware that there were many researchers who had been at Cambridge while I was there as a student who knew all about Bayesian methods: people such as Steve Gull, John Skilling, Mike Hobson, Anthony Lasenby and, of course, one Anthony Garrett. It was only later in my career that I actually got to talk to any of them about any of it!

So I think the resurgence of Bayesian ideas in cosmology owes a very great deal to the Cambridge group which had the expertise necessary to exploit the wave of high quality data that started to come in during the 1990s and the availability of the computing resources needed to handle it.

But looking a bit further back I think there’s an important Cambridge (but not cosmological) figure that preceded them, Sir Harold Jeffreys whose book The Theory of Probability was first published in 1939. I think that book began to turn the tide, and it still makes for interesting reading.

P.S. I have to say I’ve come across more than one scientist who has argued that you can’t apply statistical reasoning in cosmology because there is only one Universe and you can’t use probability theory for unique events. That erroneous point of view has led to many otherwise sensible people embracing the idea of a multiverse, but that’s the subject for another rant.

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Bernard Schutz FRS!

I was idly wondering earlier this week when the annual list of new Fellows elected to the Royal Society would be published, as it is normally around this time of year. Today it finally emerged and can be found here.

I am particularly delighted to see that my erstwhile Cardiff colleague Bernard Schutz (with whom I worked in the Data Innovation Research Institute and the School of Physics & Astronomy) is now an FRS! In fact I have known Bernard for quite a long time – he chaired the Panel that awarded me an SERC Advanced Fellowship in the days before STFC, and even before PPARC, way back in 1993. It just goes to show that even the most eminent scientists do occasionally make mistakes…

Anyway, hearty congratulations to Bernard, whose elevation to the Royal Society follows the award, a couple of years ago, of the Eddington Medal of the Royal Astronomical Society about which I blogged here. The announcement from the Royal Society is rather brief:

Bernard Schutz is honoured for his work driving the field of gravitational wave searches, leading to their direct detection in 2015.

I thought I’d add a bit more detail by repeating what was included in the citation for Bernard’s Eddington Medal which focuses on his invention of a method of measuring the Hubble constant using coalescing binary neutron stars. The idea was first published in September 1986 in a Letter to Nature. Here is the first paragraph:

I report here how gravitational wave observations can be used to determine the Hubble constant, H 0. The nearly monochromatic gravitational waves emitted by the decaying orbit of an ultra–compact, two–neutron–star binary system just before the stars coalesce are very likely to be detected by the kilometre–sized interferometric gravitational wave antennas now being designed1–4. The signal is easily identified and contains enough information to determine the absolute distance to the binary, independently of any assumptions about the masses of the stars. Ten events out to 100 Mpc may suffice to measure the Hubble constant to 3% accuracy.

In this paper, Bernard points out that a binary coalescence — such as the merger of two neutron stars — is a self calibrating `standard candle’, which means that it is possible to infer directly the distance without using the cosmic distance ladder. The key insight is that the rate at which the binary’s frequency changes is directly related to the amplitude of the gravitational waves it produces, i.e. how `loud’ the GW signal is. Just as the observed brightness of a star depends on both its intrinsic luminosity and how far away it is, the strength of the gravitational waves received at LIGO depends on both the intrinsic loudness of the source and how far away it is. By observing the waves with detectors like LIGO and Virgo, we can determine both the intrinsic loudness of the gravitational waves as well as their loudness at the Earth. This allows us to directly determine distance to the source.

It may have taken 31 years to get a measurement, but hopefully it won’t be long before there are enough detections to provide greater precision – and hopefully accuracy! – than the current methods can manage!

Here is a short video of Bernard himself talking about his work:

Once again, congratulations to Bernard on a very well deserved election to a Fellowship of the Royal Society.

UPDATE: a more detailed biography of Bernard is now available on the Royal Society website.

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The 2021 Gruber Prize for Cosmology: Marc Kamionkowski, Uroš Seljak &Matias Zaldarriaga

I’ve just heard via the IAU newsletter that the 2021 Gruber Prize for Cosmology has been awarded to Marc Kamionkowski, Uroš Seljak and Matias Zaldarriaga (from left to right in the picture). Congratulations to them on a well-deserved honour!

In brief the prize is awarded for their contributions to the study of the Cosmic Microwave Background (CMB) and the early Universe. The three recipients of the prize developed techniques to use observations of the CMB to derive information about the early Universe, including some classic work in the 1990s developing the CMBFAST code for calculating properties of the CMB and seminal papers on the polarization of the CMB published in 1997 here and here that did a huge amount to advance that as the important topic it remains this day.

For a fuller description see the press release here.

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Cosmology Talks about the Open Journal of Astrophysics

I have from time to time posted videos from the series of Cosmology Talks curated by Shaun Hotchkiss. These are usually technical talks at the level you might expect for a cosmology seminar, but this time it’s something different. Shaun asked me if I’d like to give a talk about the Open Journal of Astrophysics, so one night last week we recorded this. We ended up chatting about quite a lot of things so it turned out longer than most of the videos in the series, but it’s not a technical talk so I hope you’ll find it bearable!

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Cosmology from Home

Just a quick post to pass on an announcement about the forthcoming Cosmology from Home 2021 conference.

Cosmology from Home is an online cosmology conference with a novel format aimed at bringing the real-world workshop experience into the virtual domain. The format includes the use of pre-recorded talks, and a combination of asynchronous and scheduled live discussions. A freely-navigated virtual office space also facilitates ongoing, organic discussions. The conference will bring together cosmologists from around the world to discuss the current state of cosmology at the interface of theory and observations. For more details see here.

Registration for this event is now open here.

Please note that there will be a limited number of participants so book early!

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The State of the Universe Talk

When I saw the calibre of the other speakers in the Chalonge – De Vega Series organized by Norma Sanchez- including a number of Nobel Laureates – it was with some trepidation that I accepted the invitation to give a Colloquium, but there we are. I’m on the list. If you want to attend the Colloquium (via Zoom) you can register for it here. This series was originally named after Daniel Chalonge but was renamed to honour Hector de Vega, who sadly passed away in 2015.

I used to get invited quite often to the famous Norma Sanchez Schools and Conferences in Paris and Sicily (both Erice and Palermo) but then, about a year ago. I was suddenly stopped receiving invitations. I gather that a number of other colleagues have also been abruptly “cancelled” over the years. Anyway it seems I’m back on the list, at least virtually, possibly owing to some form of administrative error.

I remember one year in Erice at the end of a talk I gave (in the OHP/Transparency era) Norma Sanchez, who was meant to be chairing the questions and discussion started writing on my transparencies, crossing out the word “theory” and replacing it with “model”. That event made quite an impression on the audience who thought it was hilarious and people who were there often remind me of it. Coincidentally, I thought of that event when I wrote Saturday’s post. Since the forthcoming colloquium is via Zoom I think I’ll be safe from any such intervention this time.

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Backwards and Forwards in Science

I spent a few hours today involved with our Open Day at Maynooth University, including – as I mentioned here – giving a presentation about Theoretical Physics to complement one about Experimental Physics followed by a couple of hours of Q&A. It was a bit of a shame to be cooped up inside on such a lovely Spring day but we had a lot of interesting questions and it was all quite enjoyable.

One of the things that I tried to stress in my talk is that while there theorists and experimentalists (or observers), real science is about the interplay between the two, which I’ve illustrated in the above diagram which I use sometimes when talking about cosmology though it applies to other disciplines.

We have theoretical models – normally including a set of free parameters which we don’t know how to fix a priori. What we can do though is calculate the consequences if we did know the values of these parameters. That forward calculation is represented by the upward arrow, using theory to predict the result of a measurement. The backward calculation (inverse reasoning) involves using the measurements to infer values for the free parameters; that’s represented by the downward arrow. There’s usually a considerable amount of back-and-forth between theory space and measurement space as scientific knowledge develops. If one version of a model doesn’t fit we can adjust its parameters until it does, then we might need new data to test this iteration. It is only when the theoretical slack is sufficiently tight and freedom to adjust parameters is eliminated or severely restricted can we really test a theoretical idea definitively.

In cosmology we have only a handful of free parameters and this process has worked pretty well in providing a model in which these parameters are tightly constrained by a host of observational results. This is the standard model and although there a “tensions”, most prominently concerning the Hubble Constant, the model has survived very well. The same situation holds for the standard model of particle physics, though there is tension concerning the muon magnetic moment that I blogged about here.

I’ve written quite a lot on this blog about the inverse reasoning step – partly because I think there are many people (even professional scientists) who don’t understand this part very well and partly because cosmology provides a good example of a model with elements that can’t be calculated from first principles.

It struck me this morning, however, in answering a question about the muon magnetic moment that we often tend to assume that the forward calculation is somehow trivial. In fact the theoretical calculation of (g-2) is nothing of the sort: it requires lengthy supercomputer computations before the theory can make a prediction and there is some doubt over whether the current values of the theoretically expected value of the muon dipole moment are correct within the model.

The same issue arises in cosmology. It is not at all easy to calculate, for example, detailed properties of galaxy clustering in a given cosmological model. The forward calculation here uses huge N-body experiments. This is why a very considerable part of the effort being expended in preparation for the European Space Agency’s Euclid mission is on the simulation side.

Both particle physics and cosmology – and no doubt other fields – are thus limited by how well we can do the forward calculation and that is not going to change very soon. Nevertheless it is the interplay between theory and measurement that has driven the progress so far, and it will continue to do so even if it is the case that the more progress we make the harder it gets to go further.

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Climate Change Research at Maynooth University

Did you know that Maynooth University is Ireland’s leading institution for climate change research and teaching? Researchers are internationally recognized and they are working in areas such as climate modelling, investigating severe weather events and their mitigation, right through to examining the social and economic impacts of climate change.

Here’s a little video about it.

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Theorists and Experimentalists in Physics

Regular readers of his blog (Sid and Doris Bonkers) will know that here at Maynooth University there are two Physics departments, one the Department of Theoretical Physics (of which I am a Faculty member) and the other the Department of Experimental Physics. These two units are in the same building but have so far have been largely separate in terms of teaching and research; Experimental Physics (EP) is somewhat larger in terms of staff and student numbers than Theoretical Physics (TP).

For instance, when students enter on our General Science degree programme they have to choose four subjects in the first year, including Mathematics (much as I did when I did my Natural Sciences degree at Cambridge back in the day). Picking `double physics’ (i.e. Experimental Physics and Theoretical Physics) uses up two of those choices, whereas Physics was a single choice in the first year of my degree. In the second year of this programme students do three subjects so can continue with both Theoretical and Experimental Physics (and another) , as they can in Year 3 where they do two subjects, and in Year 4 where they can do a single Major in either TP or EP or a double Major doing a bit of both.

To confuse matters still further, the Department of Theoretical Physics only changed its name from the Department of Mathematical Physics relatively recently and some of our documentation still carries that title. Quite often I get asked what’s the difference between Theoretical Physics and Mathematical Physics? As far as Maynooth is concerned we basically use those terms interchangeably and, although it might appear a little confusing at first, having both terms scattered around our webpages means that Google searches for both `Mathematical Physics’ and `Theoretical Physics’ will find us.

The Wikipedia page for Theoretical Physics begins

Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain and predict natural phenomena. This is in contrast to experimental physics, which uses experimental tools to probe these phenomena.

This is what Wikipedia says about Experimental Physics:

Experimental physics is the category of disciplines and sub-disciplines in the field of physics that are concerned with the observation of physical phenomena and experiments. Methods vary from discipline to discipline, from simple experiments and observations, such as the Cavendish experiment, to more complicated ones, such as the Large Hadron Collider.

I count myself as a theoretical physicist (that’s what I did in Part II at Cambridge, anyway) though I do work a lot with data and many of the researchers in my discipline (cosmology) actually work at the interface between theory and experiment, so the distinction between theorists and experimentalists is perhaps not a very useful one.

As a matter of fact I think there’s a good case for theoretical physicists to have at least some experience of practical experimental work. There are two reasons for this:

1. to understand about errors in measurement and how to treat them properly using statistical methods;
2. to learn how easy it is to break expensive laboratory equipment.

In the past during Open Days I have asked the audience of prospective physics students if they could name a famous physicist. Most popular among the responses were the names you would have guessed: Einstein, Hawking, Feynman, Dirac, Newton, Schrodinger, and some perhaps less familiar names such as Leonard Susskind and Brian Greene. Every single one of these is (or was) a theorist of some kind. This is confirmed by the fact that many potential students mention similar names in the personal statements they write in support of their university applications. For better or worse, it seems that to some potential students at least Physics largely means Theoretical (or Mathematical) Physics.

Although it is probably good for our recruitment that there are so many high-profile theoretical physicists, it probably says more about how little the general public knows about what physics actually is and how it really works. No doubt there are many prospective students who are primarily drawn to laboratory work just as there are many drawn to theoretical calculations. But there are probably others whose interests encompass both. For me the important thing is the interplay between theory and experiment (or observation), as it is in that aspect where the whole exceeds the sum of the parts.

Anyway, this year we’ve been thinking very hard about bringing about closer cooperation between the two Physics Departments at Maynooth. It remains to be seen precisely what form that closer cooperation will take but I think it’s a good idea in principle. In fact in the Open Day at Maynooth coming up on Saturday 24th April there will, for the first time ever, be a joint talk by the Departments of Theoretical Physics and Experimental Physics. I’m looking forward to seeing how that goes!

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Oh Larmor! Energy in Electromagnetic Waves

This week I started the bit of my Advanced Electromagnetism module that deals with electromagnetic radiation, including deriving the famous Larmor Formula. It reminded me of this little physics riddle, which I thought I’d share again here.

As you all know, electromagnetic radiation consists of oscillating electric and magnetic fields rather like this:

(Graphic stolen from here.) The polarization state of the wave is defined by the direction of the Electric field, in this case vertically upwards.

Now the energy carried by an electromagnetic wave of a given wavelength is proportional to the square of its amplitude, denoted in the Figure by A, so the energy is of the form kA² in this case with k constant. Two separate electromagnetic waves with the same amplitude and wavelength would thus carry an energy = 2kA².

But now consider what happens if you superpose two waves in phase, each having the same wavelength, polarization and amplitude to generate a single wave with amplitude 2A. The energy carried now is k(2A)² = 4kA², which is twice the value obtained for two separate waves.

Where does the extra energy come from?

Answers through the Comments Box please!

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