# Dr Jonathan Gillard

Reader in Statistics

Director of Admissions

*Email:*- gillardjw@cardiff.ac.uk
*Telephone:*- +44 (0)29 2087 0619
*Location:*- Room M/1.26, Maths and Education Building , Senghennydd Road, Cardiff, CF24 4AG

- Available for postgraduate supervision

I am a Reader in Statistics but I also work at the interface of optimization, linear algebra and operational research. I pursue a number of research interests. My main current research topic is in matrix optimization problems and their statistical application but maintain active in interdisciplinary and collaborative work. I am a member of the Statistics research group at the School of Mathematics and of the Data Innovation Research Institute.

I am always interested to hear from interested PhD candidates. I currently have students working in topics such as machine learning for optimal decisions in healthcare (joint with the NHS), and anomaly detection (joint with the Office for National Statistics where I am currently seconded part-time). I am interested in supervising students in any of my research areas.

I am Director of Admissions at the School of Mathematics. For information on our diverse portfolio of courses, please see here.

### 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

### 2018

- 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)
- 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. W. 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)
- Dewart, N. and Gillard, J. W. 2018. Using Bradley-Terry models to analyse test match cricket. IMA Journal of Management Mathematics (10.1093/imaman/dpx013)
- Hurt, L.et al. 2018. Understanding and improving the care pathway for children with autism. International Journal of Health Care Quality Assurance

### 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)
- Butcher, H. L. and Gillard, J. W. 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)

### 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 Kvasov, D. 2016. 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)
- Gillard, J. and Zhigljavsky, 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. 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)
- 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)
- 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)
- 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)

### 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. 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

- 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.
- 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)
- 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. 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.

I am delighted to be a Senior Fellow of the Higher Education Academy. I am presently a module leader for two modules:

### Postgraduate

- MAT002 Statistical Methods

### Undergraduate

- MA1501 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

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

### Current supervision

### Past projects

- 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.