Professor Jon Gillard

(he/him)

BSc (Hons), PhD, PGCert, SFHEA.

2026

• Gillard, J. 2026. Galton's bend revisited: Conditions for linearity of E[Y|x]. Sankhya B (10.1007/s13571-026-00415-0)

2025

• Usevich, K. et al., 2025. Structured nuclear norm matrix completion: Guaranteeing exact recovery via block-column scaling. Numerical Linear Algebra with Applications 32 (4) e70031. (10.1002/nla.70031)
• Gillard, J. and Usevich, K. 2025. Low-rank approximations in statistics. In: Lovric, M. ed. International Encyclopedia of Statistical Science. Springer. , pp.1398-1400. (10.1007/978-3-662-69359-9_338)
• Gillard, J. et al. 2025. Optimising healthcare queues: a case study on chronic respiratory illness. IMA Journal of Management Mathematics 36 (2), pp.255-274. (10.1093/imaman/dpaf002)

2024

• Knight, V. et al. 2024. Recognising and evaluating the effectiveness of extortion in the Iterated Prisoner’s Dilemma. PLoS ONE 19 (7) e0304641. (10.1371/journal.pone.0304641)

2023

• Gillard, J. , O'Riordan, E. and Zhigljavsky, A. 2023. Polynomial whitening for high-dimensional data. Computational Statistics 38 , pp.1427-1461. (10.1007/s00180-022-01277-6)
• Gillard, J. , Knight, V. and Wilde, H. 2023. A novel initialisation based on hospital-resident assignment for the k-modes algorithm. Soft Computing 27 , pp.9441-9457. (10.1007/s00500-023-08407-2)
• Gillard, J. and Usevich, K. 2023. Hankel low-rank approximation and completion in time series analysis and forecasting: a brief review. Statistics and Its Interface 16 (2), pp.287-303. (10.4310/22-SII735)

2022

• Gillard, J. W. and Usevich, K. 2022. Matrix optimization problems in statistics. In: Pardalos, P. M. and Prokopyev, O. A. eds. Encyclopedia of Optimization. Springer. , pp.[n/a]. (10.1007/978-3-030-54621-2_771-1)
• Gillard, J. , O'Riordan, E. and Zhigljavsky, A. 2022. Simplicial and minimal-variance distances in multivariate data analysis. Journal of Statistical Theory and Practice 16 9. (10.1007/s42519-021-00227-7)

2021

• 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) 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)
• 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)
• 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)

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 2015. AIP Conference Proceedings. Vol. 1738.American Institute of Physics. , pp.400003. (10.1063/1.4952191)

2015

• 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)
• 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)

2014

• 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)
• 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)

2013

• Pickles, T. et al. 2013. Rasch analysis of the PedsQL 3.0 diabetes module. [Abstract]. Trials 14 (S1) 040. (10.1186/1745-6215-14-S1-O40)
• 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)
• 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.

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. 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)
• 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)

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. 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)
• 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. Published in: 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.

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)
• 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.
• 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.
• 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.

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. Published in: 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.