By MIGUEL LÓPEZ RUBIO
“If you are trying to ascertain whether there is a planet behind a star and lack the information to claim its existence with 100% certainty, Bayesian theory allows you to express in mathematical terms how uncertain is your conclusion, whether or not there is a planet there”.
“Bayesian techniques have applications in many fields, such as medicine, for example”.
“We have a dual challenge: to handle large quantities of data, and to see how they vary with time. Statistics on the grand scale”.
Tom Loredo never imagined that he would live surrounded by data. After graduation he thought of concentrating on observation. “I wanted to know the physics behind the stars”. But then, at the request of his thesis advisor he embarked on the project of comparing the theoretical framework of supernovas with a series of findings which seemed promising. Loredo worked for the first time with Bayesian statistics, the discipline which would mark his professional career “ I was hooked” he says.
Loredo, who is a researcher at the University of Cornell (USA) is one of the lecturers at the Winter School number XXVI of the Astrophysics Institute of the Canaries (IAC). The theme of the school is Bayesian inference, which shows how to determine statistically the properties of a population using only a small portion of it. This method allows us to derive conclusions, for example, about all the stars in a galaxy using data taken from a few hundred, always bearing in mind the uncertainty.
Question: Any article which tries to explain Bayesian statistics always includes the term “uncertainty”. Is that the key point?
Answer: In a mathematical problem you try to find a starting point which leads you towards a solution. However in the real world we hardly ever have sufficient information to arrive at an absolutely definite result. We can´t always assume that things are true or false. We admit, therefore, that there is a degree of uncertainty about what is true. Bayesian statistics determines that degree of uncertainty on a scale of 0 to 10 (for example) and from there try to draw conclusions.
Q: So you resort to the Bayesian approximation when you aren´t sure about something…
A: Let´s take as an example that you are trying to ascertain if there is a planet behind a certain star, and you don´t have enough information to confirm its existence with 100% certainty. With Bayesian theory you can express mathematically the degree of uncertainty of your conclusion, of whether or not there is a planet there. Then you have a result which can be extrapolated to other situations via scientific analysis.
Q: And tackle bigger objects, such as galaxies…
A: That´s right, to study their demographics, for example. After analyzing several hundred stars and taking into account that in a galaxy there are hundreds of thousands of millions of stars, what can we say about the galaxy? What you can say about the whole set of stars depends on what you can say about the observations you have made, and in turn what you can say about the hundreds of stars depends on the data obtained from each individual star. Applying Bayesian statistics you can quantify the uncertainty in this approach. The uncertain data from the first measurement are extrapolated to the final conclusion, from one star to all the stars in the galaxy. In the end, it´s a matter of taking the uncertainty to another level. It´s not very different from what you do with opinion polls, for example, in order to determine the intention of the vote.
Q: It may seem a new technique, but the basic theory is a few centuries old.
A: The interesting point about Bayesian theory is that it was the first way to use probability to analyze data. Looking backwards in history astronomers of the quality of Laplace used it to study our own solar system. He used it, for example, to estimate the mass of ´Saturn and his conclusions were confirmed many years later. Laplace made a good deduction, managing the uncertainty. However at the beginning of the XX century another statistical method, now termed frequentist, came to dominate the scene. This method uses variability. The idea is to repeat an observation many times, see what changes, and draw conclusions.
Q: And how did Bayesian statistics become interesting to the scientific community?
A: It occurred in the 1980’s and had a lot to do with advances in computing. As time has passed Bayesian techniques have been applied to fields which without these advances would have remained impossible.
Q: And what of its future?
A: It certainly has a future. At the present time handling large quantities of data, so-called “ big data” has brought statistics into focus. It has applications in many fields, such as medicine, for example. To be sure, until now in frequentist statistics has tended to dominate in big data situations, because it allows many combinations. The challenge is to devise efficient tools which allow us to respond, using Bayesian inference, to complex questions.
Q: Just one personal question “How did Bayesian methods capture you?”
A: From my point of view Bayesian statistics is coherent. If you pose the problem correctly, it will take you methodically to the answer. It has a similar elegance to that which I saw in physics, and which made me, in my early research days, want to be an astrophysicist.
Q: You have applied this technique to one of the questions which arouses most public interest in astrophysics: the search for planets similar to the Earth outside the Solar System.
A: We are on the verge of being able to detect planets similar to the Earth around stars similar to the Sun. We (astronomers) began to identify planets around other stars some 20 years ago, which was revolutionary because until then we had only known our own solar system. It turned out that the first extrasolar planets discovered were very different, they were planets like Jupiter, very massive, orbiting very close to their parent stars, instead of further away as in our own system. They were called “hot Jupiter”. As systems for detecting extrasolar planets have improved, above all NASA’s Kepler mission, we are beginning to discover planets with masses only a little bigger than ours. The main way to detect those planets is to analyze how their presence is affecting their parent star, and there we have problems because the surfaces of stars are always changing. It is there where statistics becomes a very useful tool indeed, especially as we identify smaller and smaller planets
Q: You also collaborate in the development of the LSST, the Large Synoptic Survey Telescope…
A: Historically an astronomer had an idea, went to a telescope, observed, obtained data, and analyzed them. Now with new telescopes, new cameras, and advances in computing, we can observe a significant fraction of the sky in a few nights. This is what is implied in projects such as the LSST although in this particular case instead of providing us with a large quantity of statistical data, we obtain a big stop-motion film. We can collect information form transitional objects which appear and disappear, and see how the objects in the universe change. We are faced with a double challenge: to handle large quantities of data, and to see how they vary with time. This is statistics on a grand scale.
Q: Almost on a Hollywood scale…
A: (laughs) It´s a good way to look at it. It will be a Hollywood-scale public access data base for the whole astronomical community. We expect the LSST to begin operations in about seven years’ time.
Organizing Committee: Andrés Asensio Ramos, Íñigo Arregui, Antonio Aparicio y Rafael Rebolo.
Secretary: Lourdes González.
Contacts: Andrés Asensio Ramos (IAC): aasensio [at] iac.es (aasensio[at]iac[dot]es) y 922605238 Íñigo Arregui (IAC): iarregui [at] iac.es (iarregui[at]iac[dot]es) y 922605465
Press: Carmen del Puerto: prensa [at] iac.es (prensa[at]iac[dot]es) y 922605208
Previous press release: http://www.iac.es/divulgacion.php?op1=16&id=897
Programme of the Winter School: http://www.iac.es/winterschool/2014/pages/about-the-school/timetable.php
Further information: http://www.iac.es/winterschool/2014/