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Dr Tilman Davies

Office: Science III, room 222
Phone: 479-7772

Senior Lecturer of Statistics

Director of Studies (100 level statistics)

Research Interests

I'm primarily interested in the smoothing and applied modelling of planar point patterns in space and space-time. Recent collaborations have also piqued an interest in developing Bayesian models for spatially varying phenomena.

In the 2019 round, I was successful as Principal Investigator in securing a Marsden Fund research grant. Together with Associate Investigators Prof Martin Hazelton and Prof Adrian Baddeley, we seek over the next few years to develop new methodology for analysing spatial point pattern data, principally to better distinguish between fixed and random components therein (see below).

My areas of research include:

  • Kernel smoothing and density-ratios (click here to interact with a 3D graphic depicting the estimated relative risk of primary biliary cirrhosis (Prince et al. 2001) in a region of the UK)
  • Computational statistics, R programming
  • Planar point patterns and spatial statistics
  • Applications in geographical epidemiology and biology

If you have a strong academic record and are interested in working with me as a postgraduate student on topics related to the above, get in touch.

Other stuff: In 2014 I received the Worsely Early Career Research Award from the New Zealand Statistical Association (NZSA), and received AStat accreditation from the Statistical Society of Australia (SSAI) in 2016. My introductory book on R - The Book of R: A First Course in Programming and Statistics was also published in 2016. In 2017 I was the recipient of a University of Otago Early Career Award for Distinction in Research. As of 2018 I hold an adjunct research fellow position at the Dept. of Mathematics and Statistics at Curtin University in Perth (Western Australia) where I collaborate with the spatial point pattern analysis group. From 2019 I am an Associate Editor of the Australian and New Zealand Journal of Statistics.


  • Bachelor of Computer and Mathematical Sciences (BCM) 2007. Double major in Applied Statistics and German, University of Western Australia (Perth).
  • Bachelor of Science Honours (BScHons) 2008. First-class Honours in Statistics. Massey University New Zealand (Palmerston North).
  • Doctor of Philosophy (Ph.D.) 2012. Spatial and Spatiotemporal Point Process Modelling in Epidemiology, Massey University New Zealand (Palmerston North).
  • Accredited Statistician (AStat) 2016. Statistical Society of Australia Inc. (SSAI Canberra).


  • 2019: Principal Investigator, Marsden Fund (Royal Society of New Zealand) Grant 19-UOO-191. "A new generation of statistical models for spatial point process data". Associate Investigators Prof Adrian Baddeley (Curtin University, Australia) and Prof Martin Hazelton (University of Otago, NZ). NZ$705,000; March 2020 - March 2023.
  • 2015: Principal Investigator, Marsden Fund (Royal Society of New Zealand) Fast-start Grant 15-UOO-092. "Smoothing and inference for point process data with applications to epidemiology". Associate Investigators Dr Ben Taylor (Lancaster University, UK) and Prof Martin Hazelton (University of Otago, NZ). NZ$300,000; March 2016 - March 2019.
  • 2012: Principal Investigator, University of Otago Research Grant-in-aid: "Statistical Methods for Spatial Intensity Estimation and their Performance in Epidemiology". NZ$5,700; Jan 2013 - Dec 2013.

Teaching 2022

(Past taught)

  • STAT110 (Sem 1, 2017-2019; SS, 2020-2021), STAT115 (Sem 2, 2013-2014; 2021), STAT241 (Sem 1, 2015-2018), STAT260 (Sem 2, 2019-2021); STAT372 (Sem 1, 2019-2021); STAT380 (Sem 1, 2012-2013), STAT352 (Sem 2, 2012-2016), STAT442 (Sem 2, 2012), HUBS191 (Sem 1, 2021)

Graduate/Honours Students

  • 2021-present: Bethany Macdonald for PhD in Statistics (co-supervised by Prof Martin Hazelton and Prof Adrian Baddeley).
  • 2020-present: Anna Redmond for PhD in Statistics (co-supervised by Dr Matthew Schofield and A/Prof Phil Sheard).

(Past supervised)

  • 2019: Anna Redmond for Honours in Statistics (co-supervised by Dr Matthew Schofield).
  • 2018-2019: Megan Drysdale for Masters in Statistics (co-supervisor; A/Prof David Fletcher as primary supervisor).
  • 2018-2019: Marilette Lötter for Honours in Statistics.
  • 2017-2018: Qing Ruan for a Postgraduate Diploma in Statistics (co-supervised by Dr Ting Wang).
  • 2015-2018: Baylee Smith for a Masters in Archaeology (co-supervisor; Dr Tim Thomas, Dept. of Anthropology and Archaeology as primary supervisor).
  • 2015: Patrick Brown for a Postgraduate Diploma in Applied Statistics (co-supervised by A/Prof. David Fletcher).
  • 2014: Baylee Smith for a joint Honours project in Statistics and Archaeology (co-supervised by Professor Charles Higham, Dept. of Anthropology and Archaeology).
  • 2013: Claire Flynn for Honours in Statistics.


  • Baddeley A, Davies TM, Rakshit S, Nair G, McSwiggan G (2022) Diffusion smoothing for spatial point patterns, Statistical Science 37 1 123-142.
  • Crump JA, Davies TM (2022) Towards equitable scheduling of global health teleconferences: a spatial exploration of the world's population and health by time zone, BMJ Open 12 e056696.
  • Davies TM, Banerjee S, Martin AP, Turnbull RE (2022) A nearest-neighbour Gaussian process spatial factor model for censored, multi-depth geochemical data, Journal of the Royal Statistical Society Series C (Applied Statistics) 71 4 1014-1043.
  • Hazelton ML, Davies TM (2022) Pointwise comparison of two multivariate density functions, Scandinavian Journal of Statistics {to appear}.
  • Baddeley A, Nair G, Rakshit S, McSwiggan G, Davies TM (2021) Analysing point patterns on networks -- a review, Spatial Statistics 42 100435.
  • Elson R, Davies TM, Lake IR, Vivancos R, Blomquist PB, Charlett A, Dabrera G (2021) The spatio-temporal distribution of COVID-19 infection in England between January and June 2020, Epidemiology and Infection 149 e73 1-6.
  • Elson R, Davies TM, Jenkins C, Vivancos R, O'Brien SJ, Lake IR (2020) Application of kernel smoothing to estimate the spatio-temporal variation in risk of STEC O157 in England, Spatial and Spatio-temporal Epidemiology 32 100305.
  • Davies TM, Lawson AB (2019) An evaluation of likelihood-based bandwidth selectors for spatial and spatiotemporal kernel estimates, Journal of Statistical Computation and Simulation 89 7 1131-1152.
  • Davies TM, Schofield MR, Cornwall J, Sheard PW (2019) Modelling multilevel spatial behaviour in binary-mark muscle fibre configurations, Annals of Applied Statistics 13 3 1329-1347.
  • Rakshit S, Davies TM, Moradi MM, McSwiggan G, Nair G, Mateu J, Baddeley A (2019) Fast kernel smoothing of point patterns on a large network using 2D convolution, International Statistical Review 87 3 531-556.
  • Davies TM, Baddeley A (2018) Fast computation of spatially adaptive kernel estimates, Statistics and Computing 28 4 937-956.
  • Davies TM, Flynn CR, Hazelton ML (2018) On the utility of asymptotic bandwidth selectors for spatially adaptive kernel density estimation, Statistics & Probability Letters 138 75-81.
  • Davies TM, Marshall JC, Hazelton ML (2018) Tutorial on kernel estimation of continuous spatial and spatiotemporal relative risk, Statistics in Medicine 37 7 1191-1221.
  • Davies TM (2016) The Book of R: A First Course in Programming and Statistics No Starch Press, San Francisco, USA; 832pp.
  • Davies TM, Jones K, Hazelton ML (2016) Symmetric adaptive smoothing regimens for estimation of the spatial relative risk function, Computational Statistics & Data Analysis 101 12-28.
  • Davies TM, Sheard PW, Cornwall J (2016) Letter to the Editor: Comment on Makino et al. and observations on spatial modeling, Anatomical Science International 91 4 423-424.
  • Farrell S, Davies TM, Cornwall J (2015) Use of clinical anatomy resources by musculoskeletal outpatient physiotherapists in Australian public hospitals: A cross-sectional study, Physiotherapy Canada 67 3 273-279.
  • Fletcher JGR, Stringer MD, Briggs CA, Davies TM, Woodley SJ (2015) Computerised tomographic morphometry of adult thoracic intervertebral discs, European Spine Journal 24 10 2321-2329.
  • Smith BA, Davies TM, Higham CFW (2015) Spatial and social variables in the Bronze Age phase 4 cemetery of Ban Non Wat, Northeast Thailand, Journal of Archaeological Science: Reports 4 34 362-370.
  • Taylor BM, Davies TM, Rowlingson BS, Diggle PJ (2015) Bayesian inference and data augmentation schemes for spatial, spatiotemporal and multivariate log-Gaussian Cox processes in R, Journal of Statistical Software 63 7 1-48.
  • Cornwall J, Davies TM, Lees D (2013) Student injuries in the dissecting room, Anatomical Sciences Education 6 6 404-409.
  • Davies TM (2013) Jointly optimal bandwidth selection for the planar kernel-smoothed density-ratio, Spatial and Spatio-temporal Epidemiology 5 1 51-65.
  • Davies TM (2013) Scaling oversmoothing factors for kernel estimation of spatial relative risk, Epidemiological Methods 2 1 67-83.
  • Davies TM, Bryant DJ (2013) On circulant embedding for Gaussian random fields in R, Journal of Statistical Software 55 9 1-21.
  • Davies TM, Cornwall J, Sheard PW (2013) Modelling dichotomously marked muscle fibre configurations, Statistics in Medicine 32 24 4240-4258.
  • Davies TM, Hazelton ML (2013) Assessing minimum contrast parameter estimation for spatial and spatiotemporal log-Gaussian Cox processes, Statistica Neerlandica 67 4 355-389.
  • Taylor BM, Davies TM, Rowlingson BS, Diggle PJ (2013) lgcp - An R package for inference with spatial and spatiotemporal log-Gaussian Cox processes, Journal of Statistical Software 52 4 1-40.
  • Zhang ZJ, Davies TM, Gao J, Wang Z, Jiang QW (2013) Identification of high-risk regions for schistosomiasis in the Guichi region of China: an adaptive kernel density estimation-based approach, Parasitology 140 7 868-875.
  • Zhang ZJ, Chen DM, Chen Y, Davies TM, Vaillancourt JP, Liu WB (2012) Risk signals of an influenza pandemic caused by highly pathogenic avian influenza subtype H5N1: Spatio-temporal perspectives, Veterinary Journal 192 3 417-421.
  • Davies TM, Hazelton ML, Marshall JC (2011) sparr: Analyzing spatial relative risk using fixed and adaptive kernel density estimation in R, Journal of Statistical Software 39 1 1-14.
  • Sanson RL, Harvey N, Garner MG, Stevenson MA, Davies TM, Hazelton ML, O'Connor J, Dubé C, Forde-Folle KN, Owen K (2011) Foot-and-mouth disease model verification and 'relative validation' through a formal model comparison, OIE Scientific and Technical Review 30 2 527-540.
  • Davies TM, Hazelton ML (2010) Adaptive kernel estimation of spatial relative risk, Statistics in Medicine 29 23 2423-2437.
  • Hazelton ML, Davies TM (2009) Inference based on kernel estimates of the relative risk function in geographical epidemiology, Biometrical Journal 51 1 98-109.

(Under review)

  • Baddeley A, Davies TM, Hazelton ML, Rakshit S, Turner R (2022) Fitting spatial cluster process models, Submitted for publication.
  • Redmond AK, Davies TM, Schofield MR, Sheard PW (2022) New tools for investigation of muscle fiber-type spatial distributions across histological sections, Submitted for publication.


  • sparr (spatial relative risk). Contributed R package; joint work with ML Hazelton and JC Marshall (Massey University, NZ). This software allows the computation of kernel-smoothed density-ratios, both fixed- and adaptive-bandwidth versions. Tools are provided for 'optimal' bandwidth and significance (tolerance) contour calculation.
  • spagmix (spatial Gaussian mixtures). Contributed R package; joint work with AK Redmond (University of Otago). This package contains a number of functions to design artificial spatial and spatiotemporal scenarios and generate associated datasets. The functionality supports research efforts into spatial and spatiotemporal probability density and relative risk surface estimation.
  • lgcp (log-Gaussian Cox processes). Contributed R package; joint work with BM Taylor, BS Rowlingson, and PJ Diggle (Lancaster University, UK). This package focuses on inference concerning the log-Gaussian Cox process, a flexible doubly stochastic mechanism for point pattern data in space and space-time. The package includes implementation of the Metropolis-adjusted Langevin algorithm (MALA), which enables conditional simulation of the latent Gaussian field.