# Dr Jonathan Gillard

Reader in Statistics

Director of Admissions

- gillardjw@cardiff.ac.uk
- +44 (0)29 2087 0619
- 2.03, Abacws, Senghennydd Road, Cathays, Cardiff, CF24 4AG

- Available for postgraduate supervision

## Overview

I am a Reader in Statistics but I also work at the interface of optimization, linear algebra and operational research. My research is intradisciplinary, straddling several separate disciplines within mathematics. I work on large-scale data-driven and computationally-intensive topics, and on industrial problems with societal impact, having current or past collaborations with the NHS, Welsh Ambulance Service Trust, Airbus and the Office for National Statistics, for example. My main current research topic is in matrix optimization problems and their statistical application.

I am Deputy Head of the School of Mathematics and I lead its Statistics Research Group. I am management board member of the Data Innovation Research Institute and am delighted to be Deputy Chair of Cardiff University's strategic partnership with the Office for National Statistics.

I am always interested to hear from interested PhD candidates. I currently have students working in big data, global optimization and learner analytics. I am interested in supervising students in any of my research areas.

## Biography

### Professional memberships

- Member of the European Network for Business and Industrial Statistics
- Member of the International Society for Global Optimization
- Senior Fellow of the Higher Education Academy

## Publications

### 2021

- Gillard, J., O'Riordan, E. and Zhigljavsky, A. 2021. Simplicial and minimal-variance distances in multivariate data analysis. Journal of Statistical Theory and Practice
- Zilinskas, A.et al. 2021. Multistart with early termination of descents. Journal of Global Optimization 79, pp. 447-462. (10.1007/s10898-019-00814-w)

### 2020

- Wilde, H., Knight, V. and Gillard, J. 2020. Evolutionary dataset optimisation: learning algorithm quality through evolution. Applied Intelligence 50, pp. 1172-1191. (10.1007/s10489-019-01592-4)
- Wilde, H., Knight, V. and Gillard, J. 2020. Matching: a Python library for solving matching games. Journal of Open Source Software 5(48), article number: 2169. (10.21105/joss.02169)

### 2019

- Ford, S., Gillard, J. and Pugh, M. 2019. Creating a taxonomy of mathematical errors for undergraduate mathematics. MSOR Connections 18(1), pp. 37-45. (10.21100/msor.v18i1)
- Dewart, N. and Gillard, J. W. 2019. Using Bradley-Terry models to analyse test match cricket. IMA Journal of Management Mathematics 30(2), pp. 187-207. (10.1093/imaman/dpx013)

### 2018

- Gillard, J. and Usevich, K. 2018. Structured low-rank matrix completion for forecasting in time series analysis. International Journal of Forecasting 34(4), pp. 582-597. (10.1016/j.ijforecast.2018.03.008)
- Gillard, J. and Zhigljavsky, A. 2018. Optimal directional statistic for general regression. Statistics and Probability Letters 143, pp. 74. (10.1016/j.spl.2018.07.025)
- Hurt, L.et al. 2018. Understanding and improving the care pathway for children with autism. International Journal of Health Care Quality Assurance 32(1), pp. 208-223. (10.1108/IJHCQA-08-2017-0153)
- Gillard, J. and Zhigljavsky, A. 2018. Optimal estimation of direction in regression models with large number of parameters. Applied Mathematics and Computation 318, pp. 281-289. (10.1016/j.amc.2017.05.050)

### 2017

- Gillard, J. W. 2017. An initial analysis and reflection of the metrics used in the Teaching Excellence Framework in the UK. Perspectives: Policy and Practice in Higher Education 22(2), pp. 49-57. (10.1080/13603108.2017.1409669)
- Vile, J. L.et al. 2017. A queueing theoretic approach to set staffing levels in time-dependent dual-class service systems. Decision Sciences 48(4), pp. 766-794. (10.1111/deci.12236)
- Butcher, H. and Gillard, J. 2017. Simple nuclear norm based algorithms for imputing missing data and forecasting in time series. Statistics and Its Interface 10(1), pp. 19-25. (10.4310/SII.2017.v10.n1.a2)
- Gillard, J. W. and Kvasov, D. E. 2017. Lipschitz optimization methods for fitting a sum of damped sinusoids to a series of observations. Statistics and Its Interface 10(1), pp. 59-70. (10.4310/SII.2017.v10.n1.a6)

### 2016

- Davies, G., Gillard, J. and Zhigljavsky, A. 2016. Comparative study of different penalty functions and algorithms in survey calibration. In: Comparative Study of Different Penalty Functions and Algorithms in Survey Calibration., Vol. 107., pp. 87-127., (10.1007/978-3-319-29975-4_6)
- Gillard, J. W. and Zhigljavsky, A. A. 2016. Weighted norms in subspace-based methods for time series analysis. Numerical Linear Algebra with Applications 23(5), pp. 947-967. (10.1002/nla.2062)
- Vile, J. L.et al. 2016. Time-dependent stochastic methods for managing and scheduling Emergency Medical Services. Operations Research for Health Care 8, pp. 42-52. (10.1016/j.orhc.2015.07.002)
- Evans, D. and Gillard, J. W. 2016. Difference-based methods for truncating the singular value decomposition. Communications in Statistics - Simulation and Computation 45(3), pp. 863-879. (10.1080/03610918.2013.875572)
- Gillard, J. W.et al. 2016. Rostering staff at a mathematics support service using a finite-source queueing model. IMA Journal of Management Mathematics 27(2), pp. 201-209. (10.1093/imaman/dpu017)
- Gillard, J. W. and Zhigljavsky, A. 2016. Global optimization for structured low rank approximation. Presented at: International Conference of Numerical Analysis and Applied Mathematics 2015, Rhodes, Greece, 22-28 September 2015AIP Conference Proceedings, Vol. 1738. American Institute of Physics pp. 400003., (10.1063/1.4952191)

### 2015

- Gillard, J. W. 2015. Linear time-dependent reference intervals where there is measurement error in the time variable - a parametric approach. Statistical Methods in Medical Research 24(6), pp. 788-802. (10.1177/0962280211426617)
- Gillard, J. W. and Zhigljavsky, A. A. 2015. Stochastic algorithms for solving structured low-rank approximation problems. Communications in Nonlinear Science and Numerical Simulation 21(1-3), pp. 70-88. (10.1016/j.cnsns.2014.08.023)
- Davies, G. P., Gillard, J. W. and Zhigljavsky, A. A. 2015. Calibration in survey sampling as an optimization problem. In: Migdalas, A. and Karakitsiou, A. eds. Optimization, Control, and Applications in the Information Age., Vol. 130. Springer Proceedings in Mathematics & Statistics Vol. 130. Springer, pp. 67-89., (10.1007/978-3-319-18567-5_4)

### 2014

- Gillard, J. W. and Knight, V. A. 2014. Using singular spectrum analysis to obtain staffing level requirements in emergency units. Journal of the Operational Research Society 65(5), pp. 735-746. (10.1057/jors.2013.41)
- Gillard, J. W. 2014. Method of moments estimation in linear regression with errors in both variables. Communications in Statistics: Theory and Methods 43(15), pp. 3208-3222. (10.1080/03610926.2012.698785)

### 2013

- Pickles, T.et al. 2013. Rasch analysis of the PedsQL 3.0 diabetes module. [Abstract]. Trials 14(S1), article number: 40. (10.1186/1745-6215-14-S1-O40)
- Quinn, L.et al. 2013. Reliability and minimal detectable change of physical performance measures in individuals with pre-manifest and manifest Huntington disease. Physical Therapy 93(7), pp. 942-956. (10.2522/ptj.20130032)
- Vile, J.et al. 2013. Integrating demand forecasting and workforce planning strategies for emergency medical services. Presented at: Operational Research Applied to Health Services (ORAHS), Istanbul, Turkey, July 2013.
- Gillard, J. W. and Zhigljavsky, A. A. 2013. Optimization challlenges in the structured low rank approximation problem. Journal of Global Optimization 57(3), pp. 733-751. (10.1007/s10898-012-9962-8)

### 2012

- Lewis, R.et al. 2012. A wide-ranging computational comparison of high-performance graph colouring algorithms. Computers & Operations Research 39(9), pp. 1933-1950. (10.1016/j.cor.2011.08.010)
- Gillard, J. W., Robathan, K. J. and Wilson, R. 2012. Student perception of the effectiveness of mathematics support at Cardiff University. Teaching Mathematics and its Applications 31(2), pp. 84-94. (10.1093/teamat/hrs006)
- Vile, J. L.et al. 2012. Predicting ambulance demand using singular spectrum analysis. Journal of the Operational Research Society 63, pp. 1556-1565. (10.1057/jors.2011.160)
- Gillard, J. W. 2012. A generalised Box-Cox transformation for the parametric estimation of clinical reference intervals. Journal of Applied Statistics 39(10), pp. 2231-2245. (10.1080/02664763.2012.706266)

### 2011

- Gillard, J. W. 2011. Asymptotic variance–covariance matrices for the linear structural model. Statistical Methodology 8(3), pp. 291-303. (10.1016/j.stamet.2010.12.002)
- Gillard, J. W., Robathan, K. J. and Wilson, R. 2011. Measuring the effectiveness of a mathematics support service: an email survey. Teaching Mathematics and its Applications 30(1), pp. 43-52. (10.1093/teamat/hrq017)
- Gillard, J. W. and Zhigljavsky, A. A. 2011. Analysis of structured low rank approximation as an optimization problem. Informatica 22(4), pp. 489-505.

### 2010

- Gillard, J. W. 2010. An overview of linear structural models. Revstat 8(1), pp. 57-80.
- Vile, J. L.et al. 2010. Forecasting Welsh ambulance demand using singular spectrum analysis. Presented at: 36th International ORAHS conference, Genova, Italy, 18-23 July 2010 Presented at Testi, A. ed.Operations Research for Patient-Centered Health Care Delivery: Proceedings of the XXXVI International ORAHS Conference. Economia Vol. 5. Milan: Franco Angeli pp. 196-208.
- Gillard, J. W., Levi, M. L. and Wilson, R. 2010. Diagnostic testing at UK universities: an e-mail survey. Teaching Mathematics and its Applications 29(2), pp. 69-75. (10.1093/teamat/hrq004)
- Gillard, J. W. 2010. Cadzow's basic algorithm, alternating projections and singular spectrum analysis. Statistics and Its Interface 3(3), pp. 333-343. (10.4310/SII.2010.v3.n3.a7)

### 2009

- Gillard, J. W. and Iles, T. C. 2009. Methods of fitting straight lines where both variables are subject to measurement error. Current Clinical Pharmacology 4(3), pp. 164-171. (10.2174/157488409789375302)
- Phillips, J., Smith, M. and Gillard, J. W. 2009. Do competitive swimmers have altered scapular upward rotation angles compared to non-swimmers?. Presented at: 6th All – Wales Conference on Sport and Exercise Medicine and Science, Aberystwyth, UK, 3 July 2009.
- Holmes, A., Smith, M. and Gillard, J. 2009. Does scapula position change in the dominant arm of competitive swimmers after a swimming training session?. Presented at: 6th All – Wales Conference on Sport and Exercise Medicine and Science, Aberystwyth, UK, 3 July 2009.
- Holmes, A., Smith, M. and Gillard, J. 2009. Does scapula position change in the dominant arm of competitive swimmers after a swimming training session?. Presented at: The Association of Chartered Physiotherapists in Sports Medicine Annual Conference, Leeds, UK, 4 September 2009.

### 2008

- Wilson, R. and Gillard, J. W. 2008. Some problems associated with running a Maths Support Service. Presented at: CETL-MSOR Conference 2008, Lancaster University, Lancaster, UK, 8-9 September 2008 Presented at Green, D. ed.CETL-MSOR Conference 2008 Conference Proceedings. Birmingham: The Maths, Stats & OR Network pp. 94-99.

### 2007

- Gillard, J. W. 2007. Errors in variables regression: What is the appropriate model?. PhD Thesis, Cardiff University.

## Teaching

I am delighted to be a Senior Fellow of the Higher Education Academy.

I am presently a module leader for MA1501 Statistical Inference, and have published a textbook with Springer entitled "A First Course in Statistical Inference".

### Research interests

- Matrix low-rank approximation and its interface in statistical methodologies such as time series analysis
- Development of novel statistical techniques for applied and interdisciplinary research
- Innovative teaching methods and the analysis of survey data generated from student evaluations

### Research group

## Supervision

I am interested in supervising PhD students in the areas of:

- low-rank matrix optimization problems and their applications
- time series analysis
- statistical methodology for industrial application
- learner analytics

### Current supervision

### Past projects

Some examples of previous projects include:

- Julie Vile (2013): Time-Dependent Stochastic Modelling for Predicting Demand and Scheduling of Emergency Medical Services.
- Gareth Davies (2018): Examination of Approaches to Calibration in Survey Sampling.
- Henry Wilde (2021): New Methods for Algorithm Evaluation and Cluster Initialisation with applications to Healthcare