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Monday, 6 March 2017

Explaining and predicting football team performance over an entire season


When I was presenting the BBC documentary Climate Changes by Numbers and had to explain the idea of a statistical 'attribution study', I used the analogy of determining which factors most affected the performance of Premiership football teams year on year. Because I had to do it in a hurry I and my colleague Dr Anthony Constantinou did a very crude analysis which focused on a very small number of factors and showed, unsurprisingly, that turnover (i.e. mainly spend on transfer and wages) had the most impact of these. 

We weren't happy with the quality of the study and decided to undertake a much more comprehensive analysis as part of the BAYES-KNOWLEDGE project. This project is all about improved decision-making and risk assessment using a probabilistic technique called Bayesian Networks. In particular, the main objective of the project is to produce useful/accurate predictions and assessments in situations where there is not a lot of data available. In such situations the current fad of 'big data' methods using machine learning techniques do not work; instead we use 'smart-data' -  a method that combines the limited data available with expert causal knowledge and real-world ‘facts’. The idea of predicting Premiership teams' long term performance and identifying the key factors explaining changes was a perfect opportunity to both develop and validate the BAYES-KNOWLEDGE method, especially as we had previously done extensive work in predicting individual premiership match results (see links at bottom).

The results of the study have now been published in one of the premier international AI journals Knowledge Based Systems.

The Bayesian Network model in the paper enables us to predict, before a season starts, the total league points a team is expected to accumulate throughout the season (each team plays 38 games in a season with three points per win and one per draw). The model results compare very favourably against a number of other relevant and different types of models, including some which use far more data. As hoped for the results also provide a novel and comprehensive attribution study of the factors most affecting performance (measured in terms of impact on actual points gained/lost per season). For example, although unsurprisingly, the largest improvements in performance result from massive increases in spending on new players (an 8.49 points gain), an even greater decrease (up to 16.52 points) results from involvement in the European competitions (especially the Europa League) for teams that have previous little experience in such competitions. Also, something  that was very surprising and that possibly confounds bookies - and gives punters good potential for exploiting -  is that promoted teams generate (on average) a staggering increase in performance of 8.34 points, relative to the relegated team they are replacing. The results in the study also partly address/explain the widely accepted 'favourite-longshot bias' observed in bookies odds.

The full reference citation is:
Constantinou, A. C. and Fenton, N. (2017). Towards Smart-Data: Improving predictive accuracy in long-term football team performance. Knowledge-Based Systems, In Press, 2017, http://dx.doi.org/10.1016/j.knosys.2017.03.005
The pre-print version of the paper (pdf) can be found at http://constantinou.info/downloads/papers/smartDataFootball.pdf

We acknowledge the financial support by the European Research Council (ERC) for funding research project, ERC-2013-AdG339182-BAYES_KNOWLEDGE, and Agena Ltd for software support.

See also:

Wednesday, 8 February 2017

Helping US Intelligence Analysts using Bayesian networks


Causal Bayesian networks are at the heart of a major new collaborative research project led by Australian University Monash  - funded by the United States' Intelligence Advanced Research Projects Activity (IARPA). The objective is to help intelligence analysts assess the value of their information. IARPA was set up following the failure of the US intelligence agencies to properly assess the correct levels of threat posed by Al Qaeda in 2001 and Iraq in 2003.

The chief investigator at Monash, Kevin Korb, said in an interview in the Australian:
"..quantitative rather than qualitative methods were crucial in judging the value of intelligence.... more quantitative approaches could have helped contain the ebola epidemic by making authorities appreciate the scale of the problem months earlier. They could also build a better assessment of the likelihood of events like gunfire between vessels in the South China Sea, a substantial devaluation of the Venezuelan currency or a new presidential aspirant in Egypt."
Norman Fenton and Martin Neil (both of Agena and Queen Mary University of London) will be working on the project along with colleagues such as David Lagnado and Ulrike Hahn at UCL.  AgenaRisk will be used throughout the project as the Bayesian network platform.

Further information:

Queen Mary in new £2 million project using Bayesian networks to create intelligent medical decision support systems with real-time monitoring for chronic conditions



UPDATE 9 Feb 2017: Various Research Fellowship and PhD vacancies funded by this project are now advertised. See here.

Queen Mary has been awarded a grant of £1,538,497 (Full economic cost £1,923,122) from the EPSRC towards a major new collaborative project to develop a new generation of intelligent medical decision support systems. The project, called PAMBAYESIAN (Patient Managed Decision-Support using Bayesian Networks) focuses on home-based and wearable real-time monitoring systems for chronic conditions including rheumatoid arthritis, diabetes in pregnancy and atrial fibrillation. It has the potential to improve the well-being of millions of people.

The project team includes researchers from both the School of Electronic Engineering and Computer Science (EECS) and clinical academics from the Barts and the London School of Medicine and Dentistry (SMD). The collaboration is underpinned by extensive research in EECS and SMD, with access to digital health firms that have extensive experience developing patient engagement tools for clinical development (BeMoreDigital, Mediwise, Rescon, SMART Medical, uMotif, IBM UK and Hasiba Medical).

The project is led by Prof Norman Fenton with co-investigators: Dr William Marsh, Prof Paul Curzon, Prof Martin Neil, Dr Akram Alomainy (all EECS) and Dr Dylan Morrissey, Dr David Collier, Professor Graham Hitman, Professor Anita Patel, Dr Frances Humby, Dr Mohammed Huda, Dr Victoria Tzortziou Brown (all SMD). The project will also include four QMUL-funded PhD students.

The three-year project will begin June 2017.

Background

Patients with chronic diseases must take day-to-day decisions about their care and rely on advice from medical staff to do this. However, regular appointments with doctors or nurses are expensive, inconvenient and not necessarily scheduled when needed. Increasingly, we are seeing the use of low cost and highly portable sensors that can measure a wide range of physiological values. Such 'wearable' sensors could improve the way chronic conditions are managed. Patients could have more control over their own care if they wished; doctors and nurses could monitor their patients without the expense and inconvenience of visits, except when they are needed. Remote monitoring of patients is already in use for some conditions but there are barriers to its wider use: it relies too much on clinical staff to interpret the sensor readings; patients, confused by the information presented, may become more dependent on health professionals; remote sensor use may then lead to an increase in medical assistance, rather than reduction.

The project seeks to overcome these barriers by addressing two key weaknesses of the current systems:
  1. Their lack of intelligence. Intelligent systems that can help medical staff in making decisions already exist and can be used for diagnosis, prognosis and advice on treatments. One especially important form of these systems uses belief or Bayesian networks, which show how the relevant factors are related and allow beliefs, such as the presence of a medical condition, to be updated from the available evidence. However, these intelligent systems do not yet work easily with data coming from sensors.
  2. Any mismatch between the design of the technical system and the way the people - patients and professional - interact.
We will work on these two weaknesses together: patients and medical staff will be involved from the start, enabling us to understand what information is needed by each player and how to use the intelligent reasoning to provide it.

The medical work will be centred on three case studies, looking at the management of rheumatoid arthritis, diabetes in pregnancy and atrial fibrillation (irregular heartbeat). These have been chosen both because they are important chronic diseases and because they are investigated by significant research groups in our Medical School, who are partners in the project. This makes them ideal test beds for the technical developments needed to realise our vision and allow patients more autonomy in practice.

To advance the technology, we will design ways to create belief networks for the different intelligent reasoning tasks, derived from an overall model of medical knowledge relevant to the diseases being managed. Then we will investigate how to run the necessary algorithms on the small computers attached to the sensors that gather the data as well as on the systems used by the healthcare team. Finally, we will use the case studies to learn how the technical systems can integrate smoothly into the interactions between patients and health professionals, ensuring that information presented to patients is understandable, useful and reduces demands on the care system while at the same time providing the clinical team with the information they need to ensure that patients are safe.

Further information: www.eecs.qmul.ac.uk/~norman/projects/PAMBAYESIAN/

This project also complements another Bayesian networks based project - the Leverhulme-funded project "CAUSAL-DYNAMICS (Improved Understanding of Causal Models in Dynamic Decision Making)" - starting January 2017. See CAUSAL-DYNAMICS

Sunday, 1 January 2017

The problem with the likelihood ratio for DNA mixture profiles


We have written many times before (see the links below) about use of the Likelihood Ratio (LR) in legal and forensic analysis.

To recap: the LR is a very good and simple method for determining the extent to which some evidence (such as DNA found at the crime scene matching the defendant) supports one hypothesis (such as "defendant is the source of the DNA") over an alternative hypothesis (such as "defendant is not the source of the DNA"). The previous articles discussed the various problems and misinterpretations surrounding the use of the LR. Many of these arise when the hypotheses are not mutually exclusive and exhaustive. This problem is especially pertinent in the case of 'DNA mixture' evidence, i.e. when some DNA sample relevant to a case comes from more than one person. With modern DNA testing techniques it is common to find DNA samples with multiple (but unknown number of) contributors. In such cases there is no obvious 'pair' of hypotheses that are mutually exclusive and exhaustive, since we have individual hypotheses such as:
  • H1: suspect + one unknown
  • H2: suspect + one known other 
  • H3: two unknowns
  • H4: suspect + two unknowns 
  • H5: suspect + one known other + one unknown
  • H6: suspect + two known others
  • H7: three unknowns 
  • H8: one known other + two unknowns
  • H9: two known others + one unknown
  • H10: three known others
  • H11:  suspect + three unknowns 
  • etc.
It is typical in such situations to focus on the 'most likely' number of contributors (say n) and then compare the hypothesis "suspect + (n-1) unknowns" with the hypothesis "n unknowns". For example, if there are likely to be 3 contributors then typically the following hypotheses are compared:
  • H1: suspect + two unknowns
  • H2: three unknowns
Now, to compute the LR we have two compute the likelihood of the particular DNA trace evidence E under each of the hypotheses. Generally both of these are extremely small numbers, i.e. both the probability values P(E | H1) and P( E | H2) are very small numbers. For example, we might get something like
  • P(E | H1) = 0.00000000000000000001  (10 to the minus 20)
  • P(E | H2) = 0.00000000000000000000000001  (10 to the minus 26)
For a statistician, the size of these numbers does not matter – we are only interested in the ratio (that is precisely what the LR is) and in the above example the LR is very large (one million) meaning that the evidence is a million times more likely to have been observed if H1 is true compared to H2. This seems to be overwhelming evidence that the suspect was a contributor. Case closed?

Apart from the communication problem in court of getting across what this all means (defence lawyers can and do exploit the very low probability of E given H1) and how it is computed, there is an underlying statistical problem with small likelihoods for non-exhaustive hypotheses and I will highlight the problem with two scenarios involving a simple urn example. Superficially, the scenarios seem identical. The first scenario causes no problem but the second one does. The concern is that it is not at all obvious that the DNA mixture problem always corresponds more closely to the first scenario than the second.

In both scenarios we assume the following:

There is an urn with 1000 balls – some of which are white. Suppose W is the (unknown) number of white balls. We have 2 hypotheses:
  • H1: W=100
  • H2:  W=90
We can draw a ball as many times as we like, note its colour and replace it (i.e. sample with replacement). We wish to use the evidence of 10,000 such samples.

Scenario 1: We draw 1001 white balls. In this case using standard statistical assumptions we calculate P(E | H1) = 0.013, P(E|H2) = 0.0000036. Both values are small but the LR is large, 3611, strongly favouring H1 over H2.

Scenario 2: We draw 1100 white balls. In this case P(E | H1) = 0.000057, P(E|H2) < 0.00000001. Again both values are very small but the LR is very large, strongly favouring of H1 over H2.

(note: in both cases we could have chosen a much larger sample and got truly tiny likelihoods but these values are sufficient to make the point).

So in what sense are these two scenarios fundamentally different and why is there a problem?

In scenario 1 not only does the conclusion favouring H1 make sense, but the actual number of balls drawn is very close to the expected number we would get if H1 were true (in fact, W=100 is the 'maximum likelihood estimate' for number of balls). So not only does the evidence point to H1 over H2, but also to H1 over any other hypothesis (and there are 1000 different hypotheses W=0, W=1, W=2 etc.).

In scenario 2 the evidence is actually even much more supportive of H1 over H2 than in scenario 1. But it is essentially meaningless because it is virtually certain that BOTH hypotheses are false.

So, returning to the DNA mixture example, it is certainly not sufficient to compare just two hypotheses. The LR of one million in favour of H1 over H2 may be hiding the fact that neither of these hypotheses is true. It is far better to identify as exhaustive a set of hypotheses as is realistically possible and then determine the individual likelihood value of each hypothesis. We can then identify the hypothesis with the highest likelihood value and consider its LR compared to each of the other hypotheses.