Norman Elliott Fenton

• PhD Mathematics (Sheffield University)
• Professor (Full) at Queen Mary University of London

It is crucial to identify the most appropriate hypotheses if one is to apply probabilistic reasoning to evaluate and properly understand the impact of evidence. Subtle changes to the choice of a prosecution hypothesis can result in drastically different posterior probabilities to a defence hypothesis from the same evidence. To illustrate the proble...

It is well known that Bayes’ theorem (with likelihood ratios) can be used to calculate the impact of evidence, such as a ‘match’ of some feature of a person. Typically the feature of interest is the DNA profile, but the method applies in principle to any feature of a person or object, including not just DNA, fingerprints, or footprints, but also mo...

Even before the first trial started in mid-October 2022, Lucy Letby and the Countess of Chester Hospital (CoCH) had dominated the mainstream news and become household names, at least in the United Kingdom. The Royal College of Paediatric and Child Health (RCPCH) invited review report (RCPCH, 2016) and media articles both before and throughout the t...

It is recognised that many studies reporting high efficacy for Covid-19 vaccines suffer from various selection biases. Systematic review identified thirty-nine studies that suffered from one particular and serious form of bias called miscategorisation bias, whereby study participants who have been vaccinated are categorised as unvaccinated up to an...

Efforts to fully exploit the rich potential of Bayesian Networks (BNs) have hitherto not seen a practical approach for development of domain-specific models using large-scale public statistics which have the potential to reduce the time required to develop probability tables and train the model. As a result, the duration of projects seeking to deve...

2 Efforts to fully exploit the rich potential of Bayesian Networks (BNs) have hitherto not seen a practical approach for development of domain-specific models using large-scale public statistics which have the potential to reduce the time required to develop probability tables and train the model. As a result, the duration of projects seeking to de...

Background: Most government efforts to control the COVID-19 pandemic revolved around non-pharmaceutical interventions (NPIs) and vaccination. However, many respiratory diseases show distinctive seasonal trends. In this manuscript, we examined the contribution of these three factors to the progression of the COVID-19 pandemic. Methods: Pearson corre...

Alzheimer’s disease (AD) is a progressively debilitating disease commonly affecting the elderly. Correct diagnosis is important for patients to access suitable therapies and support that can help improve or manage symptoms of the condition. Reports of misdiagnosis and difficulty diagnosing AD highlight existing clinical challenges. Here we propose...

Objectives Globally, demand outstrips capacity in rheumatology services, making Mobile Health (mHealth) attractive, with the potential to improve access, empower patient self-management and save costs. Existing mHealth interventions have poor uptake by end users. This study was designed to understand existing challenges, opportunities and barriers...

Purpose: There remains uncertainty as to which risk factors are important for the development of defaecatory problems as a result of heterogeneity of published evidence. Understanding the impact of risk factors may be important in selecting targets for disease prevention or reversal. The aim of this study was to identify and evaluate risk factors...

We present three experiments using a novel problem in which participants update their estimates of propensities when faced with an uncertain new instance. We examine this using two different causal structures (common cause/common effect) and two different scenarios (agent-based/mechanical). In the first, participants must update their estimate of t...

Background/Aims Rheumatoid arthritis (RA) outcomes have significantly improved with the treat-to-target paradigm, however this necessitates intensive monitoring. Demand outstrips capacity in rheumatology services, making Mobile Health (mHealth) an attractive prospect. However, software developers often design without understanding the needs of ulti...

Background/Aims Rheumatoid arthritis (RA) outcomes have significantly improved with the treat-to-target paradigm, however this necessitates intensive monitoring. Demand outstrips capacity in rheumatology services, making mobile health (mHealth) an attractive prospect. However, software developers often design without understanding the needs of ulti...

Background/Aims Rheumatoid arthritis (RA) outcomes have significantly improved with the treat-to-target paradigm, however, this necessitates intensive monitoring. Demand outstrips capacity in rheumatology services, making Mobile Health (mHealth) an attractive prospect. However, software developers often design without understanding the needs of ult...

Consent to medical intervention is a core legal concept that is ubiquitous and yet continues to frustrate governments, organisations, researchers and the wider community. Most requests for consent incorporate only those elements immediately required to meet ethics review board or organisational definitions, absent a holistic view of all elements th...

Process flow diagrams like caremaps are common in clinical practice guidelines and treatment texts. However, their context is often limited to a single diagnostic or treatment event. While a method has been proposed for creating a health and disease lifecycle called the health condition timeline (HCT), that method is yet to be demonstrated for an e...

In May 2021 The Lancet published a study of the Pfizer covid vaccine on the population of Israel, claiming to show it was 95% effective. On 17 May 2021 we submitted a rapid response 250-word letter explaining why the study was flawed and how the 95% claim was exaggerated. After an initial response saying they would ask the authors for a response to...

In 2021 we presented an interim analysis of reported deaths associated with Covid-19 using data from the Vaccine Adverse Events Reporting System (VAERS). This work applies the same analytical approach used on the original 250 reports from the December 2020 to March 2021 VAERS dataset, to a larger collection containing 1012 reports from the December...

Extensive dataset availability for neurological disease, such as multiple sclerosis (MS), has led to new methods of risk assessment and disease course prediction, such as using machine learning and other statistical methods. However, many of these methods cannot properly capture complex relationships between variables that affect results of odds ra...

The latest ONS vaccine mortality surveillance report for England (for the period 1 Jan 2021 to 31 May 2022) fails to take account various confounding factors in the 'headline' results and can thus be easily misinterpreted. Those seeking evidence that the vaccines are unsafe might point to the overall all-cause mortality rate in the vaccinated (1,36...

In its most recent vaccine mortality surveillance report the UK's Office for National Statistics (ONS) estimated just 8% of adults in England were unvaccinated by the end of May 2022. However, the ONS estimates are based on a special subset of the England population. Other independent estimates for the whole of the population in May were higher: th...

ISO 14971 is the primary standard used for medical device risk management. While it specifies the requirements for medical device risk management, it does not specify a particular method for performing risk management. Hence, medical device manufacturers are free to develop or use any appropriate methods for managing the risk of medical devices. Th...

We study statistical aspects of the case of the British nurse Ben Geen, convicted of 2 counts of murder and 15 of grievous bodily harm following events at Horton General Hospital (in the town of Banbury, Oxfordshire, UK) during December 2013–February 2014. We draw attention to parallels with the cases of nurses Lucia de Berk (the Netherlands) and D...

The partition function Ƶ ${\boldsymbol{Ƶ}}$ is a normalization constant for normalizing all the distributions in probabilistic inference. Ƶ ${\boldsymbol{Ƶ}}$ is closely related to the log probability of evidence (log p ( e ) $\mathrm{log}\unicode{x0200A}p(e)$) for Bayesian networks (BNs), which plays an important role in many applications, such as...

Introduction The influence of risk factors on the development of defaecatory problems is difficult to ascertain due to heterogeneity of published evidence. An understanding of the impact of these risk factors is important in selecting targets for disease prevention. Methods Risk factors for chronic constipation and faecal incontinence were anonymo...

Information visualisation creates visual representations that more easily convey meaningful patterns and trends hidden within large and otherwise abstract datasets. Despite potential benefits for understanding and communicating health data, information visualisation in medicine is underdeveloped. This is especially true in midwifery, where no quali...

Idioms are small, reusable Bayesian network (BN) fragments that represent generic types of uncertain reasoning. This paper shows how idioms can be used to build causal BNs for product safety and risk assessment that use a combination of data and knowledge. We show that the specific product safety idioms that we introduce are sufficient to build ful...

The United Nations Economic Commission for Europe (UN ECE) has developed new aspects of its WP.29 agreement for harmonising vehicle regulations, focusing on the regulation of vehicle manufacturers’ approaches to ensuring vehicle cyber security by requiring implementation of an approved cyber security management system (CSMS). This paper investigate...

A very large trial, whose results were published in Science, carried out in Bangladesh between 2020 and 2021 has been widely acclaimed as providing the most convincing evidence yet that masks work in reducing Covid-19 transmission and infections. However, the media grossly exaggerated the authors' own conclusions, and sceptical researchers have ide...

In December 2020 the law for drone pilots and unmanned aerial vehicle (UAV) use went into a transition phase in preparation for new EU international UAV regulation. That EU regulation comes into full effect as the transition periods defined in the United Kingdom’s Civil Aviation Authority Air Policy CAP722 expire during December 2022 (CAA, 2020). H...

Existing literature review (LR) methods and tools do not comprehensively support the collaborative LR (CLR) analysis and synthesis tasks. This paper presents STaR, a CLR approach that addresses this gap with a framework that support collaborative data collection and synthesis in the CLR process. STaR is a framework that makes use of a mixture of me...

The accuracy of any data purporting to show covid 19 vaccine effectiveness or safety is critically dependent on the accuracy of four measurements: (1) people classified as having the disease; (2) vaccination status; (3) reported deaths; and (4) the population of vaccinated and unvaccinated (the so called 'denominators'). Errors in any of these coul...

Driving is an intuitive task that requires skill, constant alertness and vigilance for unexpected events. The driving task also requires long concentration spans, focusing on the entire task for prolonged periods, and sophisticated negotiation skills with other road users including wild animals. Modern motor vehicles include an array of smart assis...

Artificial intelligence (AI) features are increasingly being embedded in cars and are central to the operation of self-driving cars (SDC). There is little or no effort expended towards understanding and assessing the broad legal and regulatory impact of the decisions made by AI in cars. A comprehensive literature review was conducted to determine t...

Modelling that exploits visual elements and information visualisation are important areas that have contributed immensely to understanding and the computerisation advancements in many domains and yet remain unexplored for the benefit of the law and legal practice. This paper investigates the challenge of modelling and expressing structures and proc...

The risk/benefit of Covid vaccines is arguably most accurately measured by comparing the all-cause mortality rate of vaccinated against unvaccinated, since it not only avoids most confounders relating to case definition but also fulfils the WHO/CDC definition of "vaccine effectiveness" for mortality. We examine two of the most recent UK ONS vaccine...

This paper has been updated and the new version can be found here: Official mortality data for England suggest systematic miscategorisation of vaccine status and uncertain effectiveness of Covid-19 vaccination UPDATED WITH ONS DECEMBER DATA RELEASE & HEALTHY VACCINEE/MORIBUND ANALYSIS http://dx.doi.org/10.13140/RG.2.2.28055.09124 https://www.re...

Introduction: Product risk assessment is the overall process of determining whether a product is judged safe for consumers to use. Among several methods for product risk assessment, RAPEX is the primary one used by regulators in the UK and EU. Despite its widespread use we identify several limitations of RAPEX, including a limited approach to hand...

The likelihood ratio (LR) is a commonly used measure for determining the strength of forensic match evidence. When a forensic expert determines a high LR for DNA found at a crime scene matching the profile of a suspect they typically report that 'this provides strong support for the prosecution hypothesis that the DNA comes from the suspect'. Our o...

Extensive dataset availability for neurological disease, such as multiple sclerosis (MS), has led to new methods of risk assessment and disease course prediction, such as machine learning and other statistical methods. However, many of these methods cannot account for complex relationships between variables that affect results of odds ratios unless...

Aims Gestational diabetes (GDM) is the most common metabolic disorder of pregnancy, requiring complex management and empowerment of those affected. Mobile health (mHealth) applications (Apps) are proposed for streamlining healthcare service delivery, extending care relationships into the community, and empowering those affected by prolonged medical...

UPDATE: A significantly revised version of this report is here:http://www.eecs.qmul.ac.uk/~norman/papers/inconsistencies_vaccine.pdf To determine the overall risk-benefit of Covid-19 vaccines it is crucial to be able to compare the all-cause mortality rates between the vaccinated and unvaccinated in each different age category. However, current pub...

While the laws of probability are rarely disputed, the question of how we should interpret probability judgments is less straightforward. Broadly, there are two ways to conceive of probability—either as an objective feature of the world, or as a subjective measure of our uncertainty. Both notions have their place in science, but it is the latter su...

Given the limitations of the randomized controlled trials (RCTs) for Covid19 vaccines, we must increasingly rely on data from observational studies to determine vaccine effectiveness. But over-simplistic reporting of such data can lead to obviously flawed conclusions due to statistical paradoxes. For example, if we just compare the total number of...

This paper applies the variational methods to learn the parameters and the probability of evidence of directed graphic models (also known as Bayesian networks (BNs)) when data contains missing values. One class of variational methods, the Bethe/Kikuchi approximate algorithm, is combined with Expectation-Maximization (EM) to learn BN model parameter...

Driving is an intuitive task that requires skills, constant alertness and vigilance for unexpected events. The driving task also requires long concentration spans focusing on the entire task for prolonged periods, and sophisticated negotiation skills with other road users, including wild animals. These requirements are particularly important when a...

This is a letter in the American Journal of Therapeutics. It is Open Access and is available here: http://dx.doi.org/10.1097/MJT.0000000000001450 The letter is a summary of a full report that is available here: http://dx.doi.org/10.13140/RG.2.2.19703.75680

An updated version of this paper is here: http://www.eecs.qmul.ac.uk/~norman/papers/Bayesian_Meta_Analysis_of_Ivermectin_Effectiveness_with_sensitivity_analysis_v5.pdf A recent peer reviewed meta-analysis evaluating ivermectin (Bryant et al, 2021) concluded that this antiparasitic drug is a cheap and effective treatment for reducing Covid-19 death...

AN UPDATED VERSION OF THIS ARTICLE IS AVAILABLE: http://dx.doi.org/10.13140/RG.2.2.19703.75680 A recent peer reviewed meta-analysis evaluating ivermectin (Bryant et al, 2021) concluded that this antiparasitic drug is a cheap and effective treatment for reducing Covid-19 deaths. These conclusions were in stark contrast to those of a later study (Ro...

AN UPDATED VERSION OF THIS ARTICLE IS AVAILABLE: http://dx.doi.org/10.13140/RG.2.2.19703.75680 A recent peer reviewed meta-analysis evaluating ivermectin (Bryant et al, 2021) concluded that this antiparasitic drug is a cheap and effective treatment for reducing Covid-19 deaths. These conclusions were in stark contrast to those of a later study (Ro...

No comprehensive review of Bayesian networks (BNs) in healthcare has been published in the past, making it difficult to organize the research contributions in the present and identify challenges and neglected areas that need to be addressed in the future. This unique and novel scoping review of BNs in healthcare provides an analytical framework for...

Clinically trained reviewers have undertaken a detailed analysis of a sample of the early deaths reported in VAERS (250 out of the 1644 deaths recorded up to April 2021). The focus is on the extent to which the reports enable us to understand whether the vaccine genuinely caused or contributed to the deaths. Contrary to claims that most of these re...

The need to update our estimates of probabilities (e.g., the accuracy of a test) given new information is commonplace. Ideally, a new instance (e.g., a correct report) would just be added to the tally, but we are often uncertain whether a new instance has occurred. We present an experiment where participants receive conflicting reports from two ear...

When presenting forensic evidence, such as a DNA match, experts often use the Likelihood ratio (LR) to explain the impact of evidence . The LR measures the probative value of the evidence with respect to a single hypothesis such as 'DNA comes from the suspect', and is defined as the probability of the evidence if the hypothesis is true divided by t...

There has been much research effort expended toward the use of Bayesian networks (BNs) in medical decision-making. However, because of the gap between developing an accurate BN and demonstrating its clinical usefulness, this has not resulted in any widespread BN adoption in clinical practice. This paper investigates this problem with the aim of fin...

This is about the widely publicised claim that "1 in 3 people with Covid-19 have no symptoms".

In the last few decades, the prevalence of multiple sclerosis (MS), a chronic inflammatory disease of the nervous system, has increased, particularly in Northern European countries, the United States, and United Kingdom. The promise of artificial intelligence (AI) and machine learning (ML) as tools to address problems in MS research has attracted i...

The graph of a BN can be machine learned, determined by causal knowledge, or a combination of both. In disciplines like bioinformatics, applying BN structure learning algorithms can reveal new insights that would otherwise remain unknown. However, these algorithms are less effective when the input data are limited in terms of sample size, which is...

The need to update our estimates of probabilities (e.g., the accuracy of a test) given new information is commonplace. Ideally, a new instance (e.g., a correct report) would just be added to the tally, but we are often uncertain whether a new instance has occurred. We present an experiment where participants receive conflicting reports from two ear...

There is a strong push towards standardisation of treatment approaches, care processes and documentation of clinical practice. However, confusion persists regarding terminology and description of many clinical care process specifications which this research seeks to resolve by developing a taxonomic characterisation of clinical care process specifi...

Behavioural change techniques are currently used by many global organisations and public institutions. The amassing evidence base is used to answer practical and scientific questions regarding what cognitive, affective, and environment factors lead to successful behavioural change in the laboratory and in the field. In this piece we show that there...

We discuss statistical issues in cases of serial killer nurses, focussing on the Dutch case of the nurse Lucia de Berk, arrested under suspicion of murder in 2001, convicted to life imprisonment, but declared innocent in 2010; and the case of the English nurse Ben Geen, arrested in 2004, also given a life sentence. At the trial of Ben Geen, a stati...

There has been much discussion about whether statistical analysis alone can establish if there was fraud in the US election. Notable examples include the claims that: 1) Benford's Law proves the Biden count totals were fraudulent (it does not); 2) large batches of votes all for Biden are statistically impossible without fraud (only true if there is...

In absence of the data we need to know what is really happening with COVID-19 infection rates and trends, there are several ways why the increasing proportion of people testing positive for COVID (that is currently observed) could be happening even if there is neither an increase in proportion of cases nor increase in false positive rate

Bayesian networks (BNs) are graphical models that can combine knowledge with data to represent the causal probabilistic relationships between a set of variables and provide insight into the processes underlying disease progression, closely resembling clinical decision-making. This paper describes a BN causal model for the early diagnosis and predic...

In reasoning about situations in which several causes lead to a common effect, a much studied and yet still not well-understood inference is that of explaining away. Assuming that the causes contribute independently to the effect, if we learn that the effect is present, then this increases the probability that one or more of the causes are present....

Whether assessing the accuracy of expert forecasting, the pros and cons of group communication, or the value of evidence in diagnostic or predictive reasoning, dependencies between experts, group members, or evidence have traditionally been seen as a form of redundancy. We demonstrate that this conception of dependence conflates the structure of a...

Modelling that exploits visual elements and information visualisation are important areas that have contributed immensely to understanding and the computerisation advancements in many domains and yet remain unexplored for the benefit of the law and legal practice. This paper investigates the challenge of modelling and expressing structures and proc...

Emerging digital technologies have taken an unprecedented position at the forefront of COVID-19 management. This paper extends a previous Bayesian network designed to predict the probability of COVID-19 infection, based on a patient's profile. The structure and prior probabilities have been amalgamated from the knowledge of peer-reviewed articles....

A need is emerging for individuals to gauge their own risks of coronavirus infection as it becomes apparent that contact tracing to contain the spread of the virus is not working in many societies. This paper presents an extension of an existing Bayesian network model for an application in which people can add their own personal risk factors to cal...

The study of people’s ability to engage in causal probabilistic reasoning has typically used fixed-point estimates for key figures. For example, in the classic taxi-cab problem, where a witness provides evidence on which of two cab companies (the more common ‘green’/less common ‘blue’) were responsible for a hit and run incident, solvers are told t...

Product risk assessment is the overall process of determining whether a product, which could be anything from a type of washing machine to a type of teddy bear, is judged safe for consumers to use. There are several methods used for product risk assessment, including RAPEX, which is the primary method used by regulators in the UK and EU. However, d...

This short paper explains (using a Bayesian analysis) why the UK Government claim of an imminent exponenential increase in number of Covid19 cases that would overwhelm the NHS is not supported by evidence.

Performing efficient inference on high dimensional discrete Bayesian Networks (BNs) is challenging. When using exact inference methods the space complexity can grow exponentially with the tree-width, thus making computation intractable. This paper presents a general purpose approximate inference algorithm, based on a new region belief approximation...

To appear in Trends in Cognitive Science. Abstract: Behavioural change techniques are currently used by many global organisations and public institutions. The amassing evidence base is used to answer practical and scientific questions regarding what cognitive, affective, and environment factors lead to successful behavioural change in the lab and...

The study of people's ability to engage in causal probabilistic reasoning has typically used fixed-point estimates for key figures. For example, in the classic taxi-cab problem, where a witness provides evidence on which of two cab companies (the more common 'green' / less common 'blue') were responsible for a hit and run incident, solvers are told...

The likelihood ratio (LR) is a commonly used measure for determining the strength of forensic match evidence. When a forensic expert determines a high LR for DNA found at a crime scene matching the DNA profile of a suspect they typically report that 'this provides strong support for the prosecution hypothesis that the DNA comes from the suspect'. H...

When analysing Covid-19 death rates by ethnicity in the USA it has been shown that, although the aggregated death rate for whites is higher than for blacks, in each main age subcategory the death rate for blacks is higher than for whites. This apparent statistical anomaly is an example of Simpson's paradox. While the paradox reveals blacks are more...

Concerns about the practicality and effectiveness of using Contact Tracing Apps (CTA) to reduce the spread of COVID19 have been well documented and, in the UK, led to the abandonment of the NHS CTA shortly after its release in May 2020. One of the key non-technical obstacles to widespread adoption of CTA has been concerns about privacy. We present...

Contradictory conclusions have been made about whether unarmed blacks are more likely to be shot by police than unarmed whites using the same data. The problem is that, by relying only on data of 'police encounters', there is the possibility that genuine bias can be hidden. We provide a causal Bayesian network model to explain this bias, which is c...

Contradictory conclusions have been made about whether unarmed blacks are more likely to be shot by police than unarmed whites using the same data. The problem is that, by relying only on data of 'police encounters', there is the possibility that genuine bias can be hidden. We provide a causal Bayesian network model to explain this bias, which is c...

There has been great concern in the UK that people from the BAME (Black And Minority Ethnic) community have a far higher risk of dying from Covid19 than those of other ethnicities. However, the overall fatalities data from the Government's ONS (Office of National Statistics) most recent report on deaths by religion shows that Jews (very few of whom...