Picture this

You can’t help but be amazed at the recent release of the first ever genuine image of a black hole. The picture itself, and the knowledge of what it represents, are extraordinary enough, but the sheer feat of human endeavour that led to this image is equally breathtaking.

Now, as far as I can see from the list of collaborators that are credited with the image, actual designated statisticians didn’t really contribute. But, from what I’ve read about the process of the image’s creation, Statistics is central to the underlying methodology. I don’t understand the details, but the outline is something like this…

Although black holes are extremely big, they’re also a long way away. This one, for example, has a diameter that’s bigger than our entire solar system. But it’s also at the heart of the Messier 87 galaxy, some 55 million light years away from Earth. Which means that when looking towards it from Earth, it occupies a very small part of space. The analogy that’s been given is that capturing the black hole’s image in space would be equivalent to trying to photograph a piece of fruit on the surface of the moon. And the laws of optics imply this would require a telescope the size of our whole planet.

To get round this limitation, the Event Horizon Telescope (EHT) program uses simultaneous signals collected from a network of eight powerful telescopes stationed around the Earth. However, the result, naturally, is a sparse grid of signals rather than a complete image. The rotation of the earth means that with repeat measurements this grid gets filled-out a little. But still, there’s a lot of blank space that needs to be filled-in to complete the image. So, how is that done?

In principle, the idea is simple enough. This video was made some years ago by Katie Bouman, who’s now got worldwide fame for leading the EHT program to produce the black hole image:

The point of the video is that to recognise the song, you don’t need the whole keyboard to be functioning. You just need a few of the keys to be working – and they don’t even have to be 100% precise – to be able to identify the whole song. I have to admit that the efficacy of this video was offset for me by the fact that I got the song wrong, but in the YouTube description of the video, Katie explains this is a common mistake, and uses the point to illustrate that with insufficient data you might get the wrong answer. (I got the wrong answer with complete data though!)

In the case of the music video, it’s our brain that fills in the gaps to give us the whole tune. In the case of the black hole data, it’s sophisticated and clever picture imaging techniques, that rely on the known physics of light transmission and a library of the patterns found in images of many different types. From this combination of physics and library of image templates, it’s possible to extrapolate from the observed data to build proposal images, and for each one find a score of how plausible that image is. The final image is then the one that has the greatest plausibility score. Engineers call this image reconstruction; but the algorithm is fundamentally statistical.

At least, that’s how I understood things. But here’s Katie again giving a much  better explanation in a Ted talk:

Ok, so much for black holes. Now, think of:

  1. Telescopes as football matches;
  2. Image data as match results;
  3. The black hole as a picture that contains information about how good football teams really are;
  4. Astrophysics as the rules by which football matches are played;
  5. The templates that describe how an image changes from one pixel to the next as a rule for saying how team performances might change from one game to the next.

And you can maybe see that in a very general sense, the problem of reconstructing an image of a black hole has the same elements as that of estimating the abilities of football teams. Admittedly, our football models are rather less sophisticated, and we don’t need to wait for the end of the Antarctic winter to ship half a tonne of hard drives containing data back to the lab for processing. But the principles of Statistics are generally the same in all applications, from black hole imaging to sports modelling, and everything in between.

It’s just not cricket

I’ve written a couple of posts now – here and here – where I’ve mentioned the Duckworth-Lewis method. As I explained in the first of those posts, this is a  statistical approach to the problem of setting runs targets in cricket matches that are interrupted by rain. And at some point, I might write a post discussing a little about the detail of this method.

But you don’t want me to spoil your post-xmas-party hangover with some heavy statistics, right? You’d much prefer it if I spoilt it with some terrible music.

So, ladies and gentleman, I give you…

The Duckworth Lewis method (band)


If you follow the link to their webpage you will find details of past tours as well as their recent album, Sticky Wickets, which I presume is a cricket-based play on words referring to the Rolling Stones’s Sticky Fingers. The comparison stops there though!

As you might have guessed from both the name of the band and their album title, their songs are mostly – if not all – cricket-related. So if you’re feeling especially brave, and promise not to hold me responsible, try the following.

It’s just not cricket…


Enjoy the universe while you can


I’ve mentioned in the past that one of the great things about Statistics is the way it’s a very connected subject. A technique learnt for one type of application often turns out to be relevant for something completely different. But sometimes the connections are just for fun.

Here’s a case in point. A while back I wrote a post making fun of Professor Brian Cox, world renowned astrophysicist, who seemed to be struggling to get to grips with the intricacies of the Duckworth-Lewis method for adjusting runs targets in cricket matches that have been shortened due to poor weather conditions. You probably know, but I forgot to mention, that in his younger days Brian was the keyboard player for D:Ream. You’ll have heard their music even if you don’t recognise the name. Try this for example:


Anyway, shortly after preparing that earlier post, I received the following in my twitter feed:

I very much doubt it’s true, but I love the idea that the original version of

Things can only get better

was going to be

Things inexorably get worse, there’s a statistical certainty that the universe will fall to bits and die

Might not have had the same musical finesse, but is perhaps a better statement on the times we live in. Or as Professor Cox put it in his reply: