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Rose Baker

University of Salford, College of Business and Law Salford Business School, Emerita

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I started off as a theoretical physicist, and did a PhD in bubble-chamber physics. Subsequently I spent a year in India, at I.I.T. Powai, before moving to Rutherford High Energy Laboratory in 1974. When funds began drying up in
big physics, I moved to Salford University, where I have been
a computing officer, senior computing officer, lecturer,
reader and Professor of Statistics. I'm now retired, a Prof. Emeritus, doing a lot of research, now that I no longer have to inflict Statistics lectures on students.
Supervisors: the cat next door has listened patiently to my thoughts.

less

University of Cambridge

Aslı SUNER (KARAKÜLAH)

Ege University

Imperial College London

University of Hertfordshire

École Normale Supérieure de Lyon

Prof.Amjad Al-Nasser

Yarmouk University

Michael J. Gonzalez

Universidad de Puerto Rico Rio

Hungarian Academy of Sciences

Universitas Syiah Kuala Banda Aceh

Jose Luis Vicente Villardon

University of Salamanca

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Papers by Rose Baker

ARMA Model Identification

The Statistician, 1994

Library of Congress Cataloging-in-Publication Data Choi, ByoungSeon ARMA model identification p. ... more

New survival distributions that quantify the gain from eliminating flawed components

Reliability Engineering & System Safety, May 1, 2019

fr e ely a v ail a bl e o nli n e a n d c a n b e r e a d , d o w nlo a d e d a n d c o pi e d fo... more fr e ely a v ail a bl e o nli n e a n d c a n b e r e a d , d o w nlo a d e d a n d c o pi e d fo r n o nc o m m e r ci al p riv a t e s t u dy o r r e s e a r c h p u r p o s e s . Pl e a s e c h e c k t h e m a n u s c ri p t fo r a n y fu r t h e r c o py ri g h t r e s t ri c tio n s. Fo r m o r e info r m a tio n, in cl u di n g o u r p olicy a n d s u b mi s sio n p r o c e d u r e , pl e a s e c o n t a c t t h e R e p o si to ry Te a m a t: u si r@ s alfo r d. a c. u k .

Copulas from Order Statistics

arXiv (Cornell University), Dec 2, 2014

A new class of copulas based on order statistics was introduced by Baker ( ). Here, further prope... more A new class of copulas based on order statistics was introduced by Baker ( ). Here, further properties of the bivariate and multivariate copulas are described, such as that of likelihood ratio dominance (LRD), and further bivariate copulas are introduced that generalize the earlier work. One of the new copulas is an integral of a product of Bessel functions of imaginary argument, and can attain the Fréchet bound. The use of these copulas for fitting data is described, and illustrated with examples. It was found empirically that the multivariate copulas previously proposed are not flexible enough to be generally useful in data fitting, and further development is needed in this area.

A useful family of fat-tailed distributions

arXiv (Cornell University), Feb 4, 2022

It is argued that there is a need for fat-tailed distributions that become thin in the extreme ta... more It is argued that there is a need for fat-tailed distributions that become thin in the extreme tail. A 3-parameter distribution is introduced that visually resembles the t-distribution and interpolates between the normal distribution and the Cauchy distribution. It is fat-tailed, but has all moments finite, and the moment-generating function exists. It would be useful as an alternative to the t-distribution for a sensitivity analysis to check the robustness of results or for computations where finite moments are needed, such as in option-pricing. It can be motivated probabilistically in at least two ways, either as the random thinning of a long-tailed distribution, or as random variation of the variance of a normal distribution. Its properties are described, algorithms for random-number generation are provided, and examples of its use in data-fitting given. Some related distributions are also discussed, including asymmetric and multivariate distributions.

Blue dye for identification of sentinel nodes in breast cancer and malignant melanoma: a systematic review and meta-analysis

Future Oncology, Feb 1, 2017

The combined technique (radioisotope and blue dye) is the gold standard for sentinel lymph node b... more The combined technique (radioisotope and blue dye) is the gold standard for sentinel lymph node biopsy (SLNB) and there is wide variation in techniques and blue dyes used. We performed a systematic review to assess the need for radioisotope and the optimal blue dye for SLNB. A total of 21 studies were included. The SLNB identification rates are high with all the commonly used blue dyes. Furthermore, methylene blue is superior to iso-sulphan blue and Patent Blue V with respect to false negative rates. The combined technique remains the most accurate and effective technique for SLNB. In order to standardise the SLNB technique, comparative trials to determine the most effective blue dye and national guidelines are required.

Creating new distributions by blunting cusps

Statistics & Probability Letters, May 1, 2017

A simple method is proposed for 'blunting' cusped distributions, i.e. removing the cusp. No addit... more A simple method is proposed for 'blunting' cusped distributions, i.e. removing the cusp. No additional parameters are required. The method is applied to the asymmetric Laplace distribution, to the van Dorp and Kotz double-sided power distribution, and to the double-sided asymmetric Pareto distribution, and some properties of the blunted distributions are derived. An example of fitting the blunted asymmetric Pareto distribution to data is given.

Axillary dissection versus axillary observation for low risk, clinically node-negative invasive breast cancer: a systematic review and meta-analysis

Breast Cancer, Jul 9, 2021

Purpose 1. To systematically analyse studies comparing survival outcomes between axillary lymph-n... more Purpose 1. To systematically analyse studies comparing survival outcomes between axillary lymph-node dissection (ALND) and axilla observation (Obs), in women with low-risk, clinically node-negative breast cancer. 2. To consider results in the context of current axillary surgery de-escalation trials and studies. Methods 9 eligible studies were identified, 6 RCTs and 3 non-randomized studies (4236 women in total). Outcomes assessed: overall survival (OS) and disease-free survival (DFS). The logged (ln) hazard ratio (HR) was calculated and used as the statistic of interest. Data was grouped by follow-up. Results Meta-analyses found no significant difference in OS at 5, 10 and 25-years follow-up (5-year ln HR = 0.08, 95% CI -0.09, 0.25, 10-year ln HR = 0.33, 95% CI -0.07, 0.72, 25-year ln HR = 0.00, 95% CI -0.18, 0.19). ALND caused improvement in DFS at 5-years follow-up (ln HR = 0.16, 95% CI 0.03, 0.29), this was not demonstrated at 10 and 25-years follow-up (10-year ln HR = 0.07, 95% CI -0.09, 0.23, 25-year ln HR = -0.03, 95% CI -0.21, 0.16). Studies supporting ALND for DFS at 5-years follow-up had greater relative chemotherapy use in the ALND cohort. Conclusion ALND does not cause a significant improvement in OS in women with clinically node-negative breast cancer. ALND may improve DFS in the short term by tailoring a proportion of patients towards chemotherapy. Our evidence suggests that when the administration of systemic therapy is balanced between the two arms, axillary de-escalation studies will likely find no difference in OS or DFS.

New order-statistics-based ranking models and faster computation of outcome probabilities

Ima Journal of Management Mathematics, Feb 8, 2019

In sport, order-statistics-based models such as Henery's gamma model and the Thurstone-Mosteller ... more In sport, order-statistics-based models such as Henery's gamma model and the Thurstone-Mosteller type V model are useful in estimating competitor strengths from observed performance of players in competitions between 2 or more players. They can also be applied in many other areas, such as analysis of consumer preference data, which would be useful to marketing management. Two new families of such models derived from the exponentiated exponential and Pareto distributions are introduced. Use of order statistics-based models when there are more than 2 competitors has been hampered by lack of an efficient method of computation of outcome probabilities as a function of competitor strengths, and a fast method of computation of outcome probabilities is presented, that exploits the fact that the integral to be evaluated is an iterated integral.

Mathematical models of confirmation bias

arXiv (Cornell University), Feb 7, 2022

Confirmation bias is a cognitive bias that adversely affects management decisions, and mathematic... more Confirmation bias is a cognitive bias that adversely affects management decisions, and mathematical modelling is an aid to its detailed understanding. Bias in opinion update about the value of a parameter is modelled here assuming that observations are discounted depending on their distance from prior opinion. The models allow belief persistence, attitude polarization, and the irrational primacy effect to be explored. A general framework for exploring large-sample properties of these models is given, and an attempt made to classify the models. An interesting result is that in some models the influence of an observation always increases with distance from the prior opinion, whereas in others observations greatly at odds with prior opinion are given very little weight. The models could be useful to those exploring these phenomena in detail.

A new generalization of the beta distribution

arXiv (Cornell University), Dec 16, 2016

The beta distribution is the best-known distribution for modelling doubly-bounded data, e.g. perc... more The beta distribution is the best-known distribution for modelling doubly-bounded data, e.g. percentage data or probabilities. A new generalization of the beta distribution is proposed, which uses a cubic transformation of the beta random variable. The new distribution is label-invariant like the beta distribution and has rational expressions for the moments. This facilitates its use in mean regression. The properties are discussed, and two examples of fitting to data are given. A modification is also explored in which the Jacobian of the transformation is omitted. This gives rise to messier expressions for the moments but better modal behaviour. In addition, the Jacobian alone gives rise to a general quadratic distribution that is of interest. The new distributions allow good fitting of unimodal data that fit poorly to the beta distribution, and could also be useful as prior distributions.

Discrete distributions from a Markov chain

arXiv (Cornell University), Jun 24, 2020

A discrete-time stochastic process derived from a model of basketball is used to generalize any d... more A discrete-time stochastic process derived from a model of basketball is used to generalize any discrete distribution. The generalized distributions can have one or two more parameters than the parent distribution. Those derived from binomial, Poisson and negative binomial distributions can be underdispersed or overdispersed. The mean can be simply expressed in terms of model parameters, thus making inference for the mean straightforward. Probabilities can be quickly computed, enabling likelihood-based inference. Random number generation is also straightforward. The properties of some of the new distributions are described and their use is illustrated with examples.

A new distribution for robust least squares

arXiv (Cornell University), Aug 14, 2014

A new distribution is introduced, which we call the twin-t distribution. This distribution is hea... more A new distribution is introduced, which we call the twin-t distribution. This distribution is heavy-tailed like the t distribution, but closer to normality in the central part of the curve. Its properties are described, e.g. the pdf, the distribution function, moments, and random number generation. This distribution could have many applications, but here we focus on its use as an aid to robustness. We give examples of its application in robust regression and in curve fitting. Extensions such as skew and multivariate twin-t distributions, and a twin of the McDonald-Newey generalised t distribution are also discussed.

Properties and Applications of some Distributions derived from Frullani's integral

arXiv (Cornell University), Aug 15, 2014

Frullani's integral dates from 1821, but a probabilistic interpretation of it has never been made... more Frullani's integral dates from 1821, but a probabilistic interpretation of it has never been made. In this paper, Frullani's integral formula is shown to result from mixing a lifetime distribution by allowing the logarithm of the scale factor to be uniformly distributed over a finite range. This gives a class of long-tailed distributions related to slash distributions, where the pdf is simply expressed in terms of the survival function of the 'parent' distribution. The resulting survival distributions have all moments finite, and can exhibit the bimodal hazard functions sometimes seen in practice. A distribution of this type analogous to the t-distribution is derived, the corresponding multivariate distributions are given, and two skewed versions of this distribution are derived. The use of the mixed distributions for inference is exemplified by fitting them to several datasets. It is expected that there will be many applications, in health, reliability, telecommunications, finance, etc.

Minimally invasive ablative techniques in the treatment of breast cancer: a systematic review and meta-analysis

International Journal of Hyperthermia, Oct 2, 2016

Purpose: Breast-conserving surgery is effective for breast cancer treatment but is associated wit... more Purpose: Breast-conserving surgery is effective for breast cancer treatment but is associated with morbidity in particular high re-excision rates. We performed a systematic review and meta-analysis to assess the current evidence for clinical outcomes with minimally invasive ablative techniques in the non-surgical treatment of breast cancer. Methods: A systematic search of the literature was performed using PubMed and Medline library databases to identify all studies published between 1994 and May 2016. Studies were considered eligible for inclusion if they evaluated the role of ablative techniques in the treatment of breast cancer and included ten patients or more. Studies that failed to fulfil the inclusion criteria were excluded. Results: We identified 63 studies including 1608 patients whose breast tumours were treated with radiofrequency (RFA), high intensity focussed ultrasound (HIFU), cryo-, laser or microwave ablation. Fifty studies reported on the number of patients with complete ablation as found on histopathology and the highest rate of complete ablation was achieved with RFA (87.1%, 491/564) and microwave ablation (83.2%, 89/107). Short-term complications were most often reported with microwave ablation (14.6%, 21/144). Recurrence was reported in 24 patients (4.2%, 24/570) and most often with laser ablation (10.7%, 11/103). The shortest treatment times were observed with RFA (15.6 ± 5.6 min) and the longest with HIFU (101.5 ± 46.6 min). Conclusion: Minimally invasive ablative techniques are able to successfully induce coagulative necrosis in breast cancer with a low side effect profile. Adequately powered and prospectively conducted cohort trials are required to confirm complete pathological ablation in all patients.

A new asymmetric generalisation of the t-distribution

arXiv (Cornell University), Jun 16, 2016

A 6-parameter fat-tailed distribution is proposed that generalises the t-distribution and allows ... more A 6-parameter fat-tailed distribution is proposed that generalises the t-distribution and allows asymmetry of scale and also of tail power, whilst avoiding the discontinuity of the second derivative of the splitt (AST) distribution. With the sixth parameter set to unity and no asymmetry, the distribution reduces to a t-distribution, but with the sixth parameter reduced, fatter tails than those of the t-distribution are allowed (the tails start earlier) and the distribution generalises Johnson's S U distribution. Data fitting is illustrated with examples.

Outliers in meta-analysis: an asymmetric trimmed-mean approach

arXiv (Cornell University), Jul 16, 2019

The adaptive asymmetric trimmed mean is a known way of estimating central location, usually in co... more The adaptive asymmetric trimmed mean is a known way of estimating central location, usually in conjunction with the bootstrap. It is here modified and applied to meta-analysis, as a way of dealing with outlying results by down-weighting the corresponding studies. This requires a modified bootstrap and a method of down-weighting studies, as opposed to removing single observations. This methodology is shown in analysis of some well-travelled datasets to down-weight outliers in agreement with other methods, and Monte-Carlo studies show that it does does not appreciably down-weight studies when outliers are absent. Conceptually simple, it does not make parametric assumptions about the outliers.

Estimating accurate covariance matrices on fitted model parameters

arXiv (Cornell University), May 11, 2021

The accurate computation of the covariance matrix of fitted model parameters is a somewhat neglec... more The accurate computation of the covariance matrix of fitted model parameters is a somewhat neglected task in Statistics. Algorithms are given for computing accurate covariance matrices derived from computing the Hessian matrix by numerical differentiation, and also for the covariance matrix of the posterior distribution of model parameters. Evaluations on two datasets where the Hessian could be computed analytically show that the numerical differentiation algorithm is very accurate.

Statistical application of barycentric rational interpolants: an alternative to splines

Computational Statistics, Feb 4, 2014

Spline curves, originally developed by numerical analysts for interpolation, are widely used in s... more Spline curves, originally developed by numerical analysts for interpolation, are widely used in statistical work, mainly as regression splines and smoothing splines. Barycentric rational interpolants have recently been developed by numerical analysts, but have yet seen very few statistical applications. We give the necesssary information to enable the reader to use barycentric rational interpolants, including a suggestion for a Bayesian prior distribution, and explore the possible statistical use of barycentric interpolants as an alternative to splines. We give the all the necessary formulae, compare the numerical accuracy to splines for some Monte-Carlo datasets, and apply both regression splines and barycentric interpolants to two real datasets. We also discuss the application of these interpolants to data smoothing, where smoothing splines would normally be used, and exemplify the use of smoothing interpolants with another real dataset. Our conclusion is that barycentric interpolants are as accurate as splines, and no more difficult to understand and program. They offer a viable alternative methodology.

High-intensity focused ultrasound in the treatment of breast fibroadenomata (HIFU-F trial)

International Journal of Hyperthermia, Oct 2, 2017

Background: High-intensity focussed ultrasound (HIFU) is a non-invasive ablative technique utilis... more Background: High-intensity focussed ultrasound (HIFU) is a non-invasive ablative technique utilising the application of high frequency ultrasound (US) pressure waves to cause tissue necrosis. This emerging technology is currently limited by prolonged treatment times. The aim of the HIFU-F trial was to perform circumferential HIFU treatment as a means of shortening treatment times. Methods: A prospective trial was set up to treat 50 consecutive patients !18 years of age. Eligible patients possessed symptomatic fibroadenomata, visible on US. Patients !25 years of age required histological confirmation of the diagnosis. Primary outcome measures were reduction in treatment time, reduction in volume on US after 12 months and complication rates. Results: HIFU treatment was performed in 51 patients (53 treatments) with a mean age of 29.8 years (SD 7.2 years) and a diameter of 2.6 cm (SD 1.4 cm). Circumferential ablation reduced treatment times by an estimated 19.9 min (SD 25.1 min), which is a 29.4% (SD 15.2%) reduction compared with whole lesion ablation. Volume reduction of 43.2% (SD 35.4%; p < 0.005, paired t-test) was observed on US at 12 months post-treatment. Local complications completely resolved at 1 month apart from skin hyperpigmentation, which persisted in nine cases at three months, six cases at 6 months and six at 12 months. Conclusion: Circumferential HIFU treatment for breast fibroadenomata is feasible to reduce both lesion size and treatment time. HIFU is a non-invasive alternative technique for the treatment of breast fibroadenomata.

Are older people putting themselves at risk when using their walking frames?

BMC Geriatrics, Mar 4, 2020

Background: Walking aids are issued to older adults to prevent falls, however, paradoxically thei... more Background: Walking aids are issued to older adults to prevent falls, however, paradoxically their use has been identified as a risk factor for falling. To prevent falls, walking aids must be used in a stable manner, but it remains unknown to what extent associated clinical guidance is adhered to at home, and whether following guidance facilitates a stable walking pattern. It was the aim of this study to investigate adherence to guidance on walking frame use, and to quantify user stability whilst using walking frames. Additionally, we explored the views of users and healthcare professionals on walking aid use, and regarding the instrumented walking frames ('Smart Walkers') utilized in this study. Methods: This observational study used Smart Walkers and pressure-sensing insoles to investigate usage patterns of 17 older people in their home environment; corresponding video captured contextual information. Additionally, stability when following, or not, clinical guidance was quantified for a subset of users during walking in an Activities of Daily Living Flat and in a gait laboratory. Two focus groups (users, healthcare professionals) shared their experiences with walking aids and provided feedback on the Smart Walkers. Results: Incorrect use was observed for 16% of single support periods and for 29% of dual support periods, and was associated with environmental constraints and a specific frame design feature. Incorrect use was associated with reduced stability. Participants and healthcare professionals perceived the Smart Walker technology positively. Conclusions: Clinical guidance cannot easily be adhered to and self-selected strategies reduce stability, hence are placing the user at risk. Current guidance needs to be improved to address environmental constraints whilst facilitating stable walking. The research is highly relevant considering the rising number of walking aid users, their increased falls-risk, and the costs of falls.

ARMA Model Identification

The Statistician, 1994

Library of Congress Cataloging-in-Publication Data Choi, ByoungSeon ARMA model identification p. ... more

New survival distributions that quantify the gain from eliminating flawed components

Reliability Engineering & System Safety, May 1, 2019

fr e ely a v ail a bl e o nli n e a n d c a n b e r e a d , d o w nlo a d e d a n d c o pi e d fo... more fr e ely a v ail a bl e o nli n e a n d c a n b e r e a d , d o w nlo a d e d a n d c o pi e d fo r n o nc o m m e r ci al p riv a t e s t u dy o r r e s e a r c h p u r p o s e s . Pl e a s e c h e c k t h e m a n u s c ri p t fo r a n y fu r t h e r c o py ri g h t r e s t ri c tio n s. Fo r m o r e info r m a tio n, in cl u di n g o u r p olicy a n d s u b mi s sio n p r o c e d u r e , pl e a s e c o n t a c t t h e R e p o si to ry Te a m a t: u si r@ s alfo r d. a c. u k .

Copulas from Order Statistics

arXiv (Cornell University), Dec 2, 2014

A new class of copulas based on order statistics was introduced by Baker ( ). Here, further prope... more A new class of copulas based on order statistics was introduced by Baker ( ). Here, further properties of the bivariate and multivariate copulas are described, such as that of likelihood ratio dominance (LRD), and further bivariate copulas are introduced that generalize the earlier work. One of the new copulas is an integral of a product of Bessel functions of imaginary argument, and can attain the Fréchet bound. The use of these copulas for fitting data is described, and illustrated with examples. It was found empirically that the multivariate copulas previously proposed are not flexible enough to be generally useful in data fitting, and further development is needed in this area.

A useful family of fat-tailed distributions

arXiv (Cornell University), Feb 4, 2022

It is argued that there is a need for fat-tailed distributions that become thin in the extreme ta... more It is argued that there is a need for fat-tailed distributions that become thin in the extreme tail. A 3-parameter distribution is introduced that visually resembles the t-distribution and interpolates between the normal distribution and the Cauchy distribution. It is fat-tailed, but has all moments finite, and the moment-generating function exists. It would be useful as an alternative to the t-distribution for a sensitivity analysis to check the robustness of results or for computations where finite moments are needed, such as in option-pricing. It can be motivated probabilistically in at least two ways, either as the random thinning of a long-tailed distribution, or as random variation of the variance of a normal distribution. Its properties are described, algorithms for random-number generation are provided, and examples of its use in data-fitting given. Some related distributions are also discussed, including asymmetric and multivariate distributions.

Blue dye for identification of sentinel nodes in breast cancer and malignant melanoma: a systematic review and meta-analysis

Future Oncology, Feb 1, 2017

The combined technique (radioisotope and blue dye) is the gold standard for sentinel lymph node b... more The combined technique (radioisotope and blue dye) is the gold standard for sentinel lymph node biopsy (SLNB) and there is wide variation in techniques and blue dyes used. We performed a systematic review to assess the need for radioisotope and the optimal blue dye for SLNB. A total of 21 studies were included. The SLNB identification rates are high with all the commonly used blue dyes. Furthermore, methylene blue is superior to iso-sulphan blue and Patent Blue V with respect to false negative rates. The combined technique remains the most accurate and effective technique for SLNB. In order to standardise the SLNB technique, comparative trials to determine the most effective blue dye and national guidelines are required.

Creating new distributions by blunting cusps

Statistics & Probability Letters, May 1, 2017

A simple method is proposed for 'blunting' cusped distributions, i.e. removing the cusp. No addit... more A simple method is proposed for 'blunting' cusped distributions, i.e. removing the cusp. No additional parameters are required. The method is applied to the asymmetric Laplace distribution, to the van Dorp and Kotz double-sided power distribution, and to the double-sided asymmetric Pareto distribution, and some properties of the blunted distributions are derived. An example of fitting the blunted asymmetric Pareto distribution to data is given.

Axillary dissection versus axillary observation for low risk, clinically node-negative invasive breast cancer: a systematic review and meta-analysis

Breast Cancer, Jul 9, 2021

Purpose 1. To systematically analyse studies comparing survival outcomes between axillary lymph-n... more Purpose 1. To systematically analyse studies comparing survival outcomes between axillary lymph-node dissection (ALND) and axilla observation (Obs), in women with low-risk, clinically node-negative breast cancer. 2. To consider results in the context of current axillary surgery de-escalation trials and studies. Methods 9 eligible studies were identified, 6 RCTs and 3 non-randomized studies (4236 women in total). Outcomes assessed: overall survival (OS) and disease-free survival (DFS). The logged (ln) hazard ratio (HR) was calculated and used as the statistic of interest. Data was grouped by follow-up. Results Meta-analyses found no significant difference in OS at 5, 10 and 25-years follow-up (5-year ln HR = 0.08, 95% CI -0.09, 0.25, 10-year ln HR = 0.33, 95% CI -0.07, 0.72, 25-year ln HR = 0.00, 95% CI -0.18, 0.19). ALND caused improvement in DFS at 5-years follow-up (ln HR = 0.16, 95% CI 0.03, 0.29), this was not demonstrated at 10 and 25-years follow-up (10-year ln HR = 0.07, 95% CI -0.09, 0.23, 25-year ln HR = -0.03, 95% CI -0.21, 0.16). Studies supporting ALND for DFS at 5-years follow-up had greater relative chemotherapy use in the ALND cohort. Conclusion ALND does not cause a significant improvement in OS in women with clinically node-negative breast cancer. ALND may improve DFS in the short term by tailoring a proportion of patients towards chemotherapy. Our evidence suggests that when the administration of systemic therapy is balanced between the two arms, axillary de-escalation studies will likely find no difference in OS or DFS.

New order-statistics-based ranking models and faster computation of outcome probabilities

Ima Journal of Management Mathematics, Feb 8, 2019

In sport, order-statistics-based models such as Henery's gamma model and the Thurstone-Mosteller ... more In sport, order-statistics-based models such as Henery's gamma model and the Thurstone-Mosteller type V model are useful in estimating competitor strengths from observed performance of players in competitions between 2 or more players. They can also be applied in many other areas, such as analysis of consumer preference data, which would be useful to marketing management. Two new families of such models derived from the exponentiated exponential and Pareto distributions are introduced. Use of order statistics-based models when there are more than 2 competitors has been hampered by lack of an efficient method of computation of outcome probabilities as a function of competitor strengths, and a fast method of computation of outcome probabilities is presented, that exploits the fact that the integral to be evaluated is an iterated integral.

Mathematical models of confirmation bias

arXiv (Cornell University), Feb 7, 2022

Confirmation bias is a cognitive bias that adversely affects management decisions, and mathematic... more Confirmation bias is a cognitive bias that adversely affects management decisions, and mathematical modelling is an aid to its detailed understanding. Bias in opinion update about the value of a parameter is modelled here assuming that observations are discounted depending on their distance from prior opinion. The models allow belief persistence, attitude polarization, and the irrational primacy effect to be explored. A general framework for exploring large-sample properties of these models is given, and an attempt made to classify the models. An interesting result is that in some models the influence of an observation always increases with distance from the prior opinion, whereas in others observations greatly at odds with prior opinion are given very little weight. The models could be useful to those exploring these phenomena in detail.

A new generalization of the beta distribution

arXiv (Cornell University), Dec 16, 2016

The beta distribution is the best-known distribution for modelling doubly-bounded data, e.g. perc... more The beta distribution is the best-known distribution for modelling doubly-bounded data, e.g. percentage data or probabilities. A new generalization of the beta distribution is proposed, which uses a cubic transformation of the beta random variable. The new distribution is label-invariant like the beta distribution and has rational expressions for the moments. This facilitates its use in mean regression. The properties are discussed, and two examples of fitting to data are given. A modification is also explored in which the Jacobian of the transformation is omitted. This gives rise to messier expressions for the moments but better modal behaviour. In addition, the Jacobian alone gives rise to a general quadratic distribution that is of interest. The new distributions allow good fitting of unimodal data that fit poorly to the beta distribution, and could also be useful as prior distributions.

Discrete distributions from a Markov chain

arXiv (Cornell University), Jun 24, 2020

A discrete-time stochastic process derived from a model of basketball is used to generalize any d... more A discrete-time stochastic process derived from a model of basketball is used to generalize any discrete distribution. The generalized distributions can have one or two more parameters than the parent distribution. Those derived from binomial, Poisson and negative binomial distributions can be underdispersed or overdispersed. The mean can be simply expressed in terms of model parameters, thus making inference for the mean straightforward. Probabilities can be quickly computed, enabling likelihood-based inference. Random number generation is also straightforward. The properties of some of the new distributions are described and their use is illustrated with examples.

A new distribution for robust least squares

arXiv (Cornell University), Aug 14, 2014

A new distribution is introduced, which we call the twin-t distribution. This distribution is hea... more A new distribution is introduced, which we call the twin-t distribution. This distribution is heavy-tailed like the t distribution, but closer to normality in the central part of the curve. Its properties are described, e.g. the pdf, the distribution function, moments, and random number generation. This distribution could have many applications, but here we focus on its use as an aid to robustness. We give examples of its application in robust regression and in curve fitting. Extensions such as skew and multivariate twin-t distributions, and a twin of the McDonald-Newey generalised t distribution are also discussed.

Properties and Applications of some Distributions derived from Frullani's integral

arXiv (Cornell University), Aug 15, 2014

Frullani's integral dates from 1821, but a probabilistic interpretation of it has never been made... more Frullani's integral dates from 1821, but a probabilistic interpretation of it has never been made. In this paper, Frullani's integral formula is shown to result from mixing a lifetime distribution by allowing the logarithm of the scale factor to be uniformly distributed over a finite range. This gives a class of long-tailed distributions related to slash distributions, where the pdf is simply expressed in terms of the survival function of the 'parent' distribution. The resulting survival distributions have all moments finite, and can exhibit the bimodal hazard functions sometimes seen in practice. A distribution of this type analogous to the t-distribution is derived, the corresponding multivariate distributions are given, and two skewed versions of this distribution are derived. The use of the mixed distributions for inference is exemplified by fitting them to several datasets. It is expected that there will be many applications, in health, reliability, telecommunications, finance, etc.

Minimally invasive ablative techniques in the treatment of breast cancer: a systematic review and meta-analysis

International Journal of Hyperthermia, Oct 2, 2016

Purpose: Breast-conserving surgery is effective for breast cancer treatment but is associated wit... more Purpose: Breast-conserving surgery is effective for breast cancer treatment but is associated with morbidity in particular high re-excision rates. We performed a systematic review and meta-analysis to assess the current evidence for clinical outcomes with minimally invasive ablative techniques in the non-surgical treatment of breast cancer. Methods: A systematic search of the literature was performed using PubMed and Medline library databases to identify all studies published between 1994 and May 2016. Studies were considered eligible for inclusion if they evaluated the role of ablative techniques in the treatment of breast cancer and included ten patients or more. Studies that failed to fulfil the inclusion criteria were excluded. Results: We identified 63 studies including 1608 patients whose breast tumours were treated with radiofrequency (RFA), high intensity focussed ultrasound (HIFU), cryo-, laser or microwave ablation. Fifty studies reported on the number of patients with complete ablation as found on histopathology and the highest rate of complete ablation was achieved with RFA (87.1%, 491/564) and microwave ablation (83.2%, 89/107). Short-term complications were most often reported with microwave ablation (14.6%, 21/144). Recurrence was reported in 24 patients (4.2%, 24/570) and most often with laser ablation (10.7%, 11/103). The shortest treatment times were observed with RFA (15.6 ± 5.6 min) and the longest with HIFU (101.5 ± 46.6 min). Conclusion: Minimally invasive ablative techniques are able to successfully induce coagulative necrosis in breast cancer with a low side effect profile. Adequately powered and prospectively conducted cohort trials are required to confirm complete pathological ablation in all patients.

A new asymmetric generalisation of the t-distribution

arXiv (Cornell University), Jun 16, 2016

A 6-parameter fat-tailed distribution is proposed that generalises the t-distribution and allows ... more A 6-parameter fat-tailed distribution is proposed that generalises the t-distribution and allows asymmetry of scale and also of tail power, whilst avoiding the discontinuity of the second derivative of the splitt (AST) distribution. With the sixth parameter set to unity and no asymmetry, the distribution reduces to a t-distribution, but with the sixth parameter reduced, fatter tails than those of the t-distribution are allowed (the tails start earlier) and the distribution generalises Johnson's S U distribution. Data fitting is illustrated with examples.

Outliers in meta-analysis: an asymmetric trimmed-mean approach

arXiv (Cornell University), Jul 16, 2019

The adaptive asymmetric trimmed mean is a known way of estimating central location, usually in co... more The adaptive asymmetric trimmed mean is a known way of estimating central location, usually in conjunction with the bootstrap. It is here modified and applied to meta-analysis, as a way of dealing with outlying results by down-weighting the corresponding studies. This requires a modified bootstrap and a method of down-weighting studies, as opposed to removing single observations. This methodology is shown in analysis of some well-travelled datasets to down-weight outliers in agreement with other methods, and Monte-Carlo studies show that it does does not appreciably down-weight studies when outliers are absent. Conceptually simple, it does not make parametric assumptions about the outliers.

Estimating accurate covariance matrices on fitted model parameters

arXiv (Cornell University), May 11, 2021

The accurate computation of the covariance matrix of fitted model parameters is a somewhat neglec... more The accurate computation of the covariance matrix of fitted model parameters is a somewhat neglected task in Statistics. Algorithms are given for computing accurate covariance matrices derived from computing the Hessian matrix by numerical differentiation, and also for the covariance matrix of the posterior distribution of model parameters. Evaluations on two datasets where the Hessian could be computed analytically show that the numerical differentiation algorithm is very accurate.

Statistical application of barycentric rational interpolants: an alternative to splines

Computational Statistics, Feb 4, 2014

Spline curves, originally developed by numerical analysts for interpolation, are widely used in s... more Spline curves, originally developed by numerical analysts for interpolation, are widely used in statistical work, mainly as regression splines and smoothing splines. Barycentric rational interpolants have recently been developed by numerical analysts, but have yet seen very few statistical applications. We give the necesssary information to enable the reader to use barycentric rational interpolants, including a suggestion for a Bayesian prior distribution, and explore the possible statistical use of barycentric interpolants as an alternative to splines. We give the all the necessary formulae, compare the numerical accuracy to splines for some Monte-Carlo datasets, and apply both regression splines and barycentric interpolants to two real datasets. We also discuss the application of these interpolants to data smoothing, where smoothing splines would normally be used, and exemplify the use of smoothing interpolants with another real dataset. Our conclusion is that barycentric interpolants are as accurate as splines, and no more difficult to understand and program. They offer a viable alternative methodology.

High-intensity focused ultrasound in the treatment of breast fibroadenomata (HIFU-F trial)

International Journal of Hyperthermia, Oct 2, 2017

Background: High-intensity focussed ultrasound (HIFU) is a non-invasive ablative technique utilis... more Background: High-intensity focussed ultrasound (HIFU) is a non-invasive ablative technique utilising the application of high frequency ultrasound (US) pressure waves to cause tissue necrosis. This emerging technology is currently limited by prolonged treatment times. The aim of the HIFU-F trial was to perform circumferential HIFU treatment as a means of shortening treatment times. Methods: A prospective trial was set up to treat 50 consecutive patients !18 years of age. Eligible patients possessed symptomatic fibroadenomata, visible on US. Patients !25 years of age required histological confirmation of the diagnosis. Primary outcome measures were reduction in treatment time, reduction in volume on US after 12 months and complication rates. Results: HIFU treatment was performed in 51 patients (53 treatments) with a mean age of 29.8 years (SD 7.2 years) and a diameter of 2.6 cm (SD 1.4 cm). Circumferential ablation reduced treatment times by an estimated 19.9 min (SD 25.1 min), which is a 29.4% (SD 15.2%) reduction compared with whole lesion ablation. Volume reduction of 43.2% (SD 35.4%; p < 0.005, paired t-test) was observed on US at 12 months post-treatment. Local complications completely resolved at 1 month apart from skin hyperpigmentation, which persisted in nine cases at three months, six cases at 6 months and six at 12 months. Conclusion: Circumferential HIFU treatment for breast fibroadenomata is feasible to reduce both lesion size and treatment time. HIFU is a non-invasive alternative technique for the treatment of breast fibroadenomata.

Are older people putting themselves at risk when using their walking frames?

BMC Geriatrics, Mar 4, 2020

Background: Walking aids are issued to older adults to prevent falls, however, paradoxically thei... more Background: Walking aids are issued to older adults to prevent falls, however, paradoxically their use has been identified as a risk factor for falling. To prevent falls, walking aids must be used in a stable manner, but it remains unknown to what extent associated clinical guidance is adhered to at home, and whether following guidance facilitates a stable walking pattern. It was the aim of this study to investigate adherence to guidance on walking frame use, and to quantify user stability whilst using walking frames. Additionally, we explored the views of users and healthcare professionals on walking aid use, and regarding the instrumented walking frames ('Smart Walkers') utilized in this study. Methods: This observational study used Smart Walkers and pressure-sensing insoles to investigate usage patterns of 17 older people in their home environment; corresponding video captured contextual information. Additionally, stability when following, or not, clinical guidance was quantified for a subset of users during walking in an Activities of Daily Living Flat and in a gait laboratory. Two focus groups (users, healthcare professionals) shared their experiences with walking aids and provided feedback on the Smart Walkers. Results: Incorrect use was observed for 16% of single support periods and for 29% of dual support periods, and was associated with environmental constraints and a specific frame design feature. Incorrect use was associated with reduced stability. Participants and healthcare professionals perceived the Smart Walker technology positively. Conclusions: Clinical guidance cannot easily be adhered to and self-selected strategies reduce stability, hence are placing the user at risk. Current guidance needs to be improved to address environmental constraints whilst facilitating stable walking. The research is highly relevant considering the rising number of walking aid users, their increased falls-risk, and the costs of falls.