Papers by Anthony Constantinou
In 2015 the British government announced a number of major tax reforms for individual landlords. ... more In 2015 the British government announced a number of major tax reforms for individual landlords. To give landlords time to adjust, some of these tax measures are being introduced gradually from April 2017, with full effect in tax year 2020/21. The changes in taxation have received much media attention since there has been widespread belief that the new measures were sufficiently skewed against landlords that they could signal the end of the Buy-To-Let (BTL) investment era in the UK. This paper assesses the prospective performance of BTL investments in London from the investor’s perspective, and examines the impact of incoming tax reforms using a novel Temporal Bayesian Network model. The model captures uncertainties of interest by simulating the impact of changing circumstances and the interventions available to an investor at various time-steps of a BTL investment portfolio. The simulation results suggest that the new tax reforms are likely to have a detrimental effect on net profits from rental income, and this hits risk-seeking investors who favour leverage much harder than risk-averse investors who do not seek to expand their property portfolio. The impact on net profits also poses substantial risks for lossmaking returns excluding capital gains, especially in the case of rising interest rates. While this makes it less desirable or even non-viable for some to continue being a landlord, based on the current status of all factors taken into consideration for simulation, investment prospects are still likely to remain good within a reasonable range of interest rate and capital growth rate variations. The results also suggest that the recent trend of property prices in London increasing faster than rents will not continue for much longer; either capital growth rates will have to decrease, rental growth rates will have to increase, or we shall observe a combination of the two events.
Despite recent promising developments with large datasets and machine learning, the idea that aut... more Despite recent promising developments with large datasets and machine learning, the idea that automation alone can discover all key relationships between factors of interest remains a challenging task. Indeed, in many real-world domains, experts can often understand and identify key relationships that data alone may fail to discover, no matter how large the dataset. Hence, while pure machine learning provides obvious benefits, these benefits may come at a cost of accuracy. Here we focus on what we call smart-data; a method which supports data
engineering and knowledge engineering approaches that put greater emphasis on applying causal knowledge and real-world ‘facts’ to the process of model development, driven by what data are really required for prediction, rather than by what data are available. We demonstrate
how we exploited knowledge to develop a model that generates accurate predictions of the evolving performance of football teams based on limited data. The model enables us to predict, before a season starts, the total league points a team is expected to accumulate throughout the
season. The results compare favourably against a number of other relevant and different types of models, including some which use far more data. The model results also provide a novel and comprehensive attribution study of the factors most influencing change in team performance, and partly address the cause of the widely accepted favourite-longshot bias observed in bookies odds.
Background: Mental health professionals increasingly carry out risk assessments to prevent future... more Background: Mental health professionals increasingly carry out risk assessments to prevent future violence
by their patients. However, there are problems with accuracy and these assessments do not always
translate into successful risk management.
Objectives: Our aim was to improve the accuracy of assessment and identify risk factors that are causal to
be targeted by clinicians to ensure good risk management. Our objectives were to investigate key risks at the population level, construct new static and dynamic instruments, test validity and construct new models
of risk management using Bayesian networks.
Methods and results: We utilised existing data sets from two national and commissioned a survey to
identify risk factors at the population level. We confirmed that certain mental health factors previously
thought to convey risk were important in future assessments and excluded others from subsequent parts of the study. Using a first-episode psychosis cohort, we constructed a risk assessment instrument for men
and women and showed important sex differences in pathways to violence. We included a 1-year
follow-up of patients discharged from medium secure services and validated a previously developed risk
assessment guide, the Medium Security Recidivism Assessment Guide (MSRAG). We found that it is
essential to combine ratings from static instruments such as the MSRAG with dynamic risk factors. Static
levels of risk have important modifying effects on dynamic risk factors for their effects on violence and we
further demonstrated this using a sample of released prisoners to construct risk assessment instruments for violence, robbery, drugs and acquisitive convictions. We constructed a preliminary instrument including
dynamic risk measures and validated this in a second large data set of released prisoners. Finally, we
incorporated findings from the follow-up of psychiatric patients discharged from medium secure services
and two samples of released prisoners to construct Bayesian models to guide clinicians in risk management.
Conclusions: Risk factors for violence identified at the population level, including paranoid delusions and
anxiety disorder, should be integrated in risk assessments together with established high-risk psychiatric
morbidity such as substance misuse and antisocial personality disorder. The incorporation of dynamic
factors resulted in improved accuracy, especially when combined in assessments using actuarial measures
to obtain levels of risk using static factors. It is important to continue developing dynamic risk and
protective measures with the aim of identifying factors that are causally related to violence. Only causal
factors should be targeted in violence prevention interventions. Bayesian networks show considerable
promise in developing software for clinicians to identify targets for intervention in the field. The Bayesian
models developed in this programme are at the prototypical stage and require further programmer
development into applications for use on tablets. These should be further tested in the field and then
compared with structured professional judgement in a randomised controlled trial in terms of their
effectiveness in preventing future violence.
We show that existing Bayesian network (BN) modelling techniques cannot capture the correct intui... more We show that existing Bayesian network (BN) modelling techniques cannot capture the correct intuitive reasoning in the important case when a set of mutually exclusive events need to be modelled as separate nodes instead of states of a single node. A previously proposed ‘solution’, which introduces a simple constraint node that enforces mutual exclusivity, fails to preserve the prior probabilities of the events, while other proposed solutions involve major changes to the original model. We provide a novel and simple solution to this problem that works in all cases where the mutually exclusive nodes have no common ancestors. Our solution uses a special type of constraint and auxiliary node together with formulas for assigning their necessary conditional probability table values. The solution enforces mutual exclusivity between events and preserves their prior probabilities while leaving all original BN nodes unchanged.
Successful implementation of major projects requires careful management of uncertainty and risk. ... more Successful implementation of major projects requires careful management of uncertainty and risk. Yet such uncertainty is rarely effectively calculated when analysing project costs and benefits. This paper presents a Bayesian network (BN) modelling framework to calculate the costs, benefits, and return on investment of a project over a specified time period, allowing for changing circumstances and trade-offs. The framework uses hybrid and dynamic BNs containing both discrete and continuous variables over multiple time stages. The BN framework calculates costs and benefits based on multiple causal factors including the effects of individual risk factors, budget deficits, and time value discounting, taking account of the parameter uncertainty of all continuous variables. The framework can serve as the basis for various project management assessments and is illustrated using a case study of an agricultural development project.
When developing a causal probabilistic model, i.e. a Bayesian network (BN), it is common to incor... more When developing a causal probabilistic model, i.e. a Bayesian network (BN), it is common to incorporate expert knowledge of factors that are important for decision analysis but where historical data are unavailable or difficult to obtain. This paper focuses on the problem whereby the distribution of some
continuous variable in a BN is known from data, but where we wish to explicitly model the impact of some additional expert variable (for which there is expert judgment but no data). Because the statistical outcomes are already influenced by the causes an expert might identify as variables missing from the dataset, the incentive here is to add the expert factor to the model in such a way that the distribution of the data variable
is preserved when the expert factor remains unobserved. We provide a method for eliciting expert judgment that ensures the expected values of a data variable are preserved under all the known conditions. We show that it is generally neither possible, nor realistic, to preserve the variance of the data variable, but we provide a method towards determining the accuracy of expertise in terms of the extent to which the variability of the
revised empirical distribution is minimised. We also describe how to incorporate the assessment of extremely rare or previously unobserved events.
(1) To develop a rigorous and repeatable method for building effective Bayesian network (BN) mode... more (1) To develop a rigorous and repeatable method for building effective Bayesian network (BN) models for medical decision support from complex, unstructured and incomplete patient questionnaires and interviews that inevitably contain examples of repetitive, redundant and contradictory responses; (2) To exploit expert knowledge in the BN development since further data acquisition is usually not possible; (3) To ensure the BN model can be used for interventional analysis; (4) To demonstrate why using data alone to learn the model structure and parameters is often unsatisfactory even when extensive data is available. The method is based on applying a range of recent BN developments targeted at helping experts build BNs given limited data. While most of the components of the method are based on established work, its novelty is that it provides a rigorous consolidated and generalised framework that addresses the whole life-cycle of BN model development. The method is based on two original and recent validated BN models in forensic psychiatry, known as DSVM-MSS and DSVM-P. When employed with the same datasets, the DSVM-MSS demonstrated competitive to superior predictive performance (AUC scores 0.708 and 0.797) against the state-of-the-art (AUC scores ranging from 0.527 to 0.705), and the DSVM-P demonstrated superior predictive performance (cross-validated AUC score of 0.78) against the state-of-the-art (AUC scores ranging from 0.665 to 0.717). More importantly, the resulting models go beyond improving predictive accuracy and into usefulness for risk management purposes through intervention, and enhanced decision support in terms of answering complex clinical questions that are based on unobserved evidence. This development process is applicable to any application domain which involves large-scale decision analysis based on such complex information, rather than based on data with hard facts, and in conjunction with the incorporation of expert knowledge for decision support via intervention. The novelty extends to challenging the decision scientists to reason about building models based on what information is really required for inference, rather than based on what data is available and hence, forces decision scientists to use available data in a much smarter way.
Decision Support Systems, 2015
The purpose of Medium Secure Services (MSS) is to provide accommodation, support and treatment to... more The purpose of Medium Secure Services (MSS) is to provide accommodation, support and treatment to individuals with enduring mental health problems who usually come into contact with the criminal justice system. These individuals are, therefore, believed to pose a risk of violence to themselves as well as to other individuals. Assessing and managing the risk of violence is considered to be a critical component for discharged decision making in MSS. Methods for violence risk assessment in this area of research are typically based on regression models or checklists with no statistical composition and which naturally demonstrate mediocre predictive performance and, more importantly, without providing genuine decision support. While Bayesian networks have become popular tools for decision support in the medical field over the last couple of decades, they have not been extensively studied in forensic psychiatry. In this paper we describe a decision support system using Bayesian networks, which is mainly parameterised based on questionnaire, interviewing and clinical assessment data, for violence risk assessment and risk management in patients discharged from MSS. The results demonstrate moderate to significant improvements in forecasting capability. More importantly, we demonstrate how decision support is improved over the well-established approaches in this area of research, primarily by incorporating causal interventions and taking advantage of the model's ability in answering complex probabilistic queries for unobserved variables.
Inspired by real-world examples from the forensic medical sciences domain, we seek to determine w... more Inspired by real-world examples from the forensic medical sciences domain, we seek to determine whether a decision about an interventional action could be subject to amendments on the basis of some incomplete information within the model, and whether it would be worthwhile for the decision maker to seek further information prior to suggesting a decision. The method is based on the underlying principle of Value of Information to enhance decision analysis in interventional and counterfactual Bayesian networks. The method is applied to two real-world Bayesian network models (previously developed for decision support in forensic medical sciences) to examine the average gain in terms of both Value of Information (average relative gain ranging from 11.45% and 59.91%) and decision making (potential amendments in decision making ranging from 0% to 86.8%). We have shown how the method becomes useful for decision makers, not only when decision making is subject to amendments on the basis of s...
A gambling market is usually described as being inefficient if there are one or more betting stra... more A gambling market is usually described as being inefficient if there are one or more betting strategies that generate profit, at a consistent rate, as a consequence of exploiting market flaws. This paper evaluates the efficiency of the Association Football betting market. In contrast to earlier studies, we primarily show that: a) the accuracy between bookmakers is extremely consistent and bookmaking accuracy has not improved over the last decade; b) profit margins have been dramatically reduced over the last decade and can be statistically significant between bookmakers; implying that the published odds of one bookmaker cannot be considered as representative of the overall market; c) profit margins per distinct match can be significant even when considering only one bookmaker and one football division; d) there are some arbitrage opportunities; e) both systematic and significant adjustments of published odds occur at least daily. In many cases the changes cannot be explained by rati...
Researchers have witnessed the great success in deterministic and perfect information domains. In... more Researchers have witnessed the great success in deterministic and perfect information domains. Intelligent pruning and evaluation techniques have been proven to be sufficient in providing outstanding intelligent decision making performance. However, processes that model uncertainty and risk for real-life situations have not met the same success. Association Football has been identified as an ideal and exciting application for that matter; it is the world's most popular sport and constitutes the fastest growing gambling market at international level. As a result, summarising the risk and uncertainty when it comes to the outcomes of relevant football match events has been dramatically increased both in importance as well as in challenge. A gambling market is described as being inefficient if there are one or more betting procedures that generate profit, at a consistent rate, as a consequence of exploiting market flaws. This study exhibits evidence of an (intended) inefficient foot...
ABSTRACT A gambling market is usually described as being inefficient if there are one or more bet... more ABSTRACT A gambling market is usually described as being inefficient if there are one or more betting strategies that generate profit, at a consistent rate, as a consequence of exploiting market flaws. This paper examines the online European football gambling market based on 14 European football leagues over a period of seven years, from season 2005/06 to 2011/12 inclusive, and takes into consideration the odds provided by numerous bookmaking firms. Contrary to common misconceptions, we demonstrate that the accuracy of bookmakers' odds has not improved over this period. More importantly, our results question market efficiency by demonstrating high profitability on the basis of consistent odds biases and numerous arbitrage opportunities.
Knowledge-Based Systems, 2012
Despite the massive popularity of probabilistic (association) football forecasting models, and th... more Despite the massive popularity of probabilistic (association) football forecasting models, and the relative simplicity of the outcome of such forecasts (they require only three probability values corresponding to home win, draw, and away win) there is no agreed scoring rule to determine their forecast accuracy. Moreover, the various scoring rules used for validation in previous studies are inadequate since they fail to recognise that football outcomes represent a ranked (ordinal) scale. This raises severe concerns about the validity of conclusions from previous studies. There is a wellestablished generic scoring rule, the Rank Probability Score (RPS), which has been missed by previous researchers, but which properly assesses football forecasting models.
Despite the increasing importance and popularity of association football forecasting systems ther... more Despite the increasing importance and popularity of association football forecasting systems there is no agreed method of evaluating their accuracy. We have classified the evaluators used into two broad categories: those which consider only the prediction for the observed outcome; and those which consider the predictions for the unobserved as well as observed outcome. We highlight fundamental inconsistencies between them and demonstrate that they produce wildly different conclusions about the accuracy of four different forecasting systems (Fink Tank/Castrol Predictor, Bet365, Odds Wizard, and pi-football) based on recent Premier league data. None of the existing evaluators satisfy a set of simple theoretical benchmark criteria. Hence, it is dangerous to assume that any existing evaluator can adequately assess the performance of football forecasting systems and, until evaluators are developed that address all the benchmark criteria, it is best to use multiple types of predictive evaluators (preferably based on posterior validation).
A rating system provides relative measures of superiority between adversaries. We propose a novel... more A rating system provides relative measures of superiority between adversaries. We propose a novel and simple approach, which we call pi-rating, for dynamically rating Association Football teams solely on the basis of the relative discrepancies in scores through relevant match instances. The pi-rating system is applicable to any other sport where the score is considered as a good indicator for prediction purposes, as
well as determining the relative performances between adversaries. In an attempt to examine how well the ratings capture a team’s performance, we have a) assessed them against two recently proposed football ELO rating variants and b) used them as the basis of a football betting strategy against published market odds. The results show that the pi-ratings outperform considerably the widely accepted ELO ratings and, perhaps more importantly, demonstrate profitability over a period of five English Premier League seasons (2007/08 to 2011/12), even allowing for the bookmakers' built-in profit margin. This is the first academic study to demonstrate profitability against market odds using such a relatively simple technique, and the resulting pi-ratings can be incorporated as parameters into other more sophisticated models in an attempt to further enhance forecasting capability.
Objectives: To assess referee bias with respect to fouls and penalty kicks awarded by taking expl... more Objectives: To assess referee bias with respect to fouls and penalty kicks awarded by taking explanatory factors into consideration.
Design: We present a novel Bayesian network model for assessing referee bias with respect to fouls and penalty kicks awarded. The model is applied to the 2011-12 English Premier League season.
Method: Unlike previous studies, the model takes into consideration explanatory factors which, if ignored, can lead to biased assessments of referee bias. For example, a team may be awarded more penalties simply because it attacks more, not because referees are biased in its favour. Hence, we incorporate causal factors such as possession, time spent in the opposition penalty box, etc. prior to estimating the degree of penalty kicks bias.
Results: We found fairly strong referee bias, based on penalty kicks awarded, in favour of certain teams when playing at home. Specifically, the two teams (Manchester City and
Manchester United) who finished first and second appear to have benefited from bias that cannot be fully justified by the explanatory factors. Conversely Arsenal, a team of similar
popularity and wealth and who finished third, benefited least of all 20 teams from referee bias at home with respect to penalty kicks awarded.
Conclusions: Among our conclusions are that, in contrast to many previous studies, being the home team does not in itself result in positive referee bias. More importantly, the model is
able to explain significant discrepancies of penalty kicks bias into non-significant after accounting for the explanatory factors.
Forensic medical practitioners and scientists have for several years sought improved decision sup... more Forensic medical practitioners and scientists have for several years sought improved decision support for
determining and managing care and release of prisoners with mental health problems. Some of these prisoners
can pose a serious threat of violence to society after release. It is, therefore, critical that the risk of violent
reoffending is accurately measured and, more importantly, well managed with causal interventions to reduce
this risk after release. The well-established predictors in this area of research are typically based on regression
models or even some rule-based methods with no statistical composition, and these have proven to be unsuitable
for simulating causal interventions for risk management. In collaboration with the medical practitioners of the
Violence Prevention Research Unit (VPRU), Queen Mary University of London, we have developed a Bayesian
network (BN) model for this purpose, which we call DSVM-P (Decision Support for Violence Management -
Prisoners). The BN model captures the causal relationships between risk factors, interventions and violence and
demonstrates significantly higher accuracy (cross-validated AUC score of 0.78) compared to well-established
predictors (AUC scores ranging from 0.665 to 0.717) within this area of research, with respect to whether a
prisoner is determined suitable for release. Even more important, however, the BN model also allows for
specific risk factors to be targeted for causal intervention for risk management of future re-offending. Hence,
unlike the previous predictors, this makes the model useful in terms of answering complex clinical questions
that are based on unobserved evidence. Clinicians and probation officers who work in these areas would benefit
from a system that takes account of these complex risk management considerations, since these decision support
features are not available in the previous generation of models used by forensic psychiatrists
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Papers by Anthony Constantinou
engineering and knowledge engineering approaches that put greater emphasis on applying causal knowledge and real-world ‘facts’ to the process of model development, driven by what data are really required for prediction, rather than by what data are available. We demonstrate
how we exploited knowledge to develop a model that generates accurate predictions of the evolving performance of football teams based on limited data. The model enables us to predict, before a season starts, the total league points a team is expected to accumulate throughout the
season. The results compare favourably against a number of other relevant and different types of models, including some which use far more data. The model results also provide a novel and comprehensive attribution study of the factors most influencing change in team performance, and partly address the cause of the widely accepted favourite-longshot bias observed in bookies odds.
by their patients. However, there are problems with accuracy and these assessments do not always
translate into successful risk management.
Objectives: Our aim was to improve the accuracy of assessment and identify risk factors that are causal to
be targeted by clinicians to ensure good risk management. Our objectives were to investigate key risks at the population level, construct new static and dynamic instruments, test validity and construct new models
of risk management using Bayesian networks.
Methods and results: We utilised existing data sets from two national and commissioned a survey to
identify risk factors at the population level. We confirmed that certain mental health factors previously
thought to convey risk were important in future assessments and excluded others from subsequent parts of the study. Using a first-episode psychosis cohort, we constructed a risk assessment instrument for men
and women and showed important sex differences in pathways to violence. We included a 1-year
follow-up of patients discharged from medium secure services and validated a previously developed risk
assessment guide, the Medium Security Recidivism Assessment Guide (MSRAG). We found that it is
essential to combine ratings from static instruments such as the MSRAG with dynamic risk factors. Static
levels of risk have important modifying effects on dynamic risk factors for their effects on violence and we
further demonstrated this using a sample of released prisoners to construct risk assessment instruments for violence, robbery, drugs and acquisitive convictions. We constructed a preliminary instrument including
dynamic risk measures and validated this in a second large data set of released prisoners. Finally, we
incorporated findings from the follow-up of psychiatric patients discharged from medium secure services
and two samples of released prisoners to construct Bayesian models to guide clinicians in risk management.
Conclusions: Risk factors for violence identified at the population level, including paranoid delusions and
anxiety disorder, should be integrated in risk assessments together with established high-risk psychiatric
morbidity such as substance misuse and antisocial personality disorder. The incorporation of dynamic
factors resulted in improved accuracy, especially when combined in assessments using actuarial measures
to obtain levels of risk using static factors. It is important to continue developing dynamic risk and
protective measures with the aim of identifying factors that are causally related to violence. Only causal
factors should be targeted in violence prevention interventions. Bayesian networks show considerable
promise in developing software for clinicians to identify targets for intervention in the field. The Bayesian
models developed in this programme are at the prototypical stage and require further programmer
development into applications for use on tablets. These should be further tested in the field and then
compared with structured professional judgement in a randomised controlled trial in terms of their
effectiveness in preventing future violence.
continuous variable in a BN is known from data, but where we wish to explicitly model the impact of some additional expert variable (for which there is expert judgment but no data). Because the statistical outcomes are already influenced by the causes an expert might identify as variables missing from the dataset, the incentive here is to add the expert factor to the model in such a way that the distribution of the data variable
is preserved when the expert factor remains unobserved. We provide a method for eliciting expert judgment that ensures the expected values of a data variable are preserved under all the known conditions. We show that it is generally neither possible, nor realistic, to preserve the variance of the data variable, but we provide a method towards determining the accuracy of expertise in terms of the extent to which the variability of the
revised empirical distribution is minimised. We also describe how to incorporate the assessment of extremely rare or previously unobserved events.
well as determining the relative performances between adversaries. In an attempt to examine how well the ratings capture a team’s performance, we have a) assessed them against two recently proposed football ELO rating variants and b) used them as the basis of a football betting strategy against published market odds. The results show that the pi-ratings outperform considerably the widely accepted ELO ratings and, perhaps more importantly, demonstrate profitability over a period of five English Premier League seasons (2007/08 to 2011/12), even allowing for the bookmakers' built-in profit margin. This is the first academic study to demonstrate profitability against market odds using such a relatively simple technique, and the resulting pi-ratings can be incorporated as parameters into other more sophisticated models in an attempt to further enhance forecasting capability.
Design: We present a novel Bayesian network model for assessing referee bias with respect to fouls and penalty kicks awarded. The model is applied to the 2011-12 English Premier League season.
Method: Unlike previous studies, the model takes into consideration explanatory factors which, if ignored, can lead to biased assessments of referee bias. For example, a team may be awarded more penalties simply because it attacks more, not because referees are biased in its favour. Hence, we incorporate causal factors such as possession, time spent in the opposition penalty box, etc. prior to estimating the degree of penalty kicks bias.
Results: We found fairly strong referee bias, based on penalty kicks awarded, in favour of certain teams when playing at home. Specifically, the two teams (Manchester City and
Manchester United) who finished first and second appear to have benefited from bias that cannot be fully justified by the explanatory factors. Conversely Arsenal, a team of similar
popularity and wealth and who finished third, benefited least of all 20 teams from referee bias at home with respect to penalty kicks awarded.
Conclusions: Among our conclusions are that, in contrast to many previous studies, being the home team does not in itself result in positive referee bias. More importantly, the model is
able to explain significant discrepancies of penalty kicks bias into non-significant after accounting for the explanatory factors.
determining and managing care and release of prisoners with mental health problems. Some of these prisoners
can pose a serious threat of violence to society after release. It is, therefore, critical that the risk of violent
reoffending is accurately measured and, more importantly, well managed with causal interventions to reduce
this risk after release. The well-established predictors in this area of research are typically based on regression
models or even some rule-based methods with no statistical composition, and these have proven to be unsuitable
for simulating causal interventions for risk management. In collaboration with the medical practitioners of the
Violence Prevention Research Unit (VPRU), Queen Mary University of London, we have developed a Bayesian
network (BN) model for this purpose, which we call DSVM-P (Decision Support for Violence Management -
Prisoners). The BN model captures the causal relationships between risk factors, interventions and violence and
demonstrates significantly higher accuracy (cross-validated AUC score of 0.78) compared to well-established
predictors (AUC scores ranging from 0.665 to 0.717) within this area of research, with respect to whether a
prisoner is determined suitable for release. Even more important, however, the BN model also allows for
specific risk factors to be targeted for causal intervention for risk management of future re-offending. Hence,
unlike the previous predictors, this makes the model useful in terms of answering complex clinical questions
that are based on unobserved evidence. Clinicians and probation officers who work in these areas would benefit
from a system that takes account of these complex risk management considerations, since these decision support
features are not available in the previous generation of models used by forensic psychiatrists
engineering and knowledge engineering approaches that put greater emphasis on applying causal knowledge and real-world ‘facts’ to the process of model development, driven by what data are really required for prediction, rather than by what data are available. We demonstrate
how we exploited knowledge to develop a model that generates accurate predictions of the evolving performance of football teams based on limited data. The model enables us to predict, before a season starts, the total league points a team is expected to accumulate throughout the
season. The results compare favourably against a number of other relevant and different types of models, including some which use far more data. The model results also provide a novel and comprehensive attribution study of the factors most influencing change in team performance, and partly address the cause of the widely accepted favourite-longshot bias observed in bookies odds.
by their patients. However, there are problems with accuracy and these assessments do not always
translate into successful risk management.
Objectives: Our aim was to improve the accuracy of assessment and identify risk factors that are causal to
be targeted by clinicians to ensure good risk management. Our objectives were to investigate key risks at the population level, construct new static and dynamic instruments, test validity and construct new models
of risk management using Bayesian networks.
Methods and results: We utilised existing data sets from two national and commissioned a survey to
identify risk factors at the population level. We confirmed that certain mental health factors previously
thought to convey risk were important in future assessments and excluded others from subsequent parts of the study. Using a first-episode psychosis cohort, we constructed a risk assessment instrument for men
and women and showed important sex differences in pathways to violence. We included a 1-year
follow-up of patients discharged from medium secure services and validated a previously developed risk
assessment guide, the Medium Security Recidivism Assessment Guide (MSRAG). We found that it is
essential to combine ratings from static instruments such as the MSRAG with dynamic risk factors. Static
levels of risk have important modifying effects on dynamic risk factors for their effects on violence and we
further demonstrated this using a sample of released prisoners to construct risk assessment instruments for violence, robbery, drugs and acquisitive convictions. We constructed a preliminary instrument including
dynamic risk measures and validated this in a second large data set of released prisoners. Finally, we
incorporated findings from the follow-up of psychiatric patients discharged from medium secure services
and two samples of released prisoners to construct Bayesian models to guide clinicians in risk management.
Conclusions: Risk factors for violence identified at the population level, including paranoid delusions and
anxiety disorder, should be integrated in risk assessments together with established high-risk psychiatric
morbidity such as substance misuse and antisocial personality disorder. The incorporation of dynamic
factors resulted in improved accuracy, especially when combined in assessments using actuarial measures
to obtain levels of risk using static factors. It is important to continue developing dynamic risk and
protective measures with the aim of identifying factors that are causally related to violence. Only causal
factors should be targeted in violence prevention interventions. Bayesian networks show considerable
promise in developing software for clinicians to identify targets for intervention in the field. The Bayesian
models developed in this programme are at the prototypical stage and require further programmer
development into applications for use on tablets. These should be further tested in the field and then
compared with structured professional judgement in a randomised controlled trial in terms of their
effectiveness in preventing future violence.
continuous variable in a BN is known from data, but where we wish to explicitly model the impact of some additional expert variable (for which there is expert judgment but no data). Because the statistical outcomes are already influenced by the causes an expert might identify as variables missing from the dataset, the incentive here is to add the expert factor to the model in such a way that the distribution of the data variable
is preserved when the expert factor remains unobserved. We provide a method for eliciting expert judgment that ensures the expected values of a data variable are preserved under all the known conditions. We show that it is generally neither possible, nor realistic, to preserve the variance of the data variable, but we provide a method towards determining the accuracy of expertise in terms of the extent to which the variability of the
revised empirical distribution is minimised. We also describe how to incorporate the assessment of extremely rare or previously unobserved events.
well as determining the relative performances between adversaries. In an attempt to examine how well the ratings capture a team’s performance, we have a) assessed them against two recently proposed football ELO rating variants and b) used them as the basis of a football betting strategy against published market odds. The results show that the pi-ratings outperform considerably the widely accepted ELO ratings and, perhaps more importantly, demonstrate profitability over a period of five English Premier League seasons (2007/08 to 2011/12), even allowing for the bookmakers' built-in profit margin. This is the first academic study to demonstrate profitability against market odds using such a relatively simple technique, and the resulting pi-ratings can be incorporated as parameters into other more sophisticated models in an attempt to further enhance forecasting capability.
Design: We present a novel Bayesian network model for assessing referee bias with respect to fouls and penalty kicks awarded. The model is applied to the 2011-12 English Premier League season.
Method: Unlike previous studies, the model takes into consideration explanatory factors which, if ignored, can lead to biased assessments of referee bias. For example, a team may be awarded more penalties simply because it attacks more, not because referees are biased in its favour. Hence, we incorporate causal factors such as possession, time spent in the opposition penalty box, etc. prior to estimating the degree of penalty kicks bias.
Results: We found fairly strong referee bias, based on penalty kicks awarded, in favour of certain teams when playing at home. Specifically, the two teams (Manchester City and
Manchester United) who finished first and second appear to have benefited from bias that cannot be fully justified by the explanatory factors. Conversely Arsenal, a team of similar
popularity and wealth and who finished third, benefited least of all 20 teams from referee bias at home with respect to penalty kicks awarded.
Conclusions: Among our conclusions are that, in contrast to many previous studies, being the home team does not in itself result in positive referee bias. More importantly, the model is
able to explain significant discrepancies of penalty kicks bias into non-significant after accounting for the explanatory factors.
determining and managing care and release of prisoners with mental health problems. Some of these prisoners
can pose a serious threat of violence to society after release. It is, therefore, critical that the risk of violent
reoffending is accurately measured and, more importantly, well managed with causal interventions to reduce
this risk after release. The well-established predictors in this area of research are typically based on regression
models or even some rule-based methods with no statistical composition, and these have proven to be unsuitable
for simulating causal interventions for risk management. In collaboration with the medical practitioners of the
Violence Prevention Research Unit (VPRU), Queen Mary University of London, we have developed a Bayesian
network (BN) model for this purpose, which we call DSVM-P (Decision Support for Violence Management -
Prisoners). The BN model captures the causal relationships between risk factors, interventions and violence and
demonstrates significantly higher accuracy (cross-validated AUC score of 0.78) compared to well-established
predictors (AUC scores ranging from 0.665 to 0.717) within this area of research, with respect to whether a
prisoner is determined suitable for release. Even more important, however, the BN model also allows for
specific risk factors to be targeted for causal intervention for risk management of future re-offending. Hence,
unlike the previous predictors, this makes the model useful in terms of answering complex clinical questions
that are based on unobserved evidence. Clinicians and probation officers who work in these areas would benefit
from a system that takes account of these complex risk management considerations, since these decision support
features are not available in the previous generation of models used by forensic psychiatrists