Statistics
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Department of Mathematics & Statistics
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Dr Tilman Davies

Office: Science III, room 222
Phone: 479-7772
Email: tdavies@maths.otago.ac.nz


Senior Lecturer of Statistics

Director of Studies (100 level statistics)

Research Interests

I'm primarily interested in the applied modelling of planar point patterns in space and space-time. Recent collaborations have also piqued an interest in identifying and fitting appropriate regression models for various biostatistical applications.

In the 2015 round, I was successful as a Principal Investigator in securing a Marsden Fast-start research grant. This provides funding to work on some of the areas mentioned below for the three years 2016-2018; alongside Associate Investigators Dr Benjamin Taylor and Prof Martin Hazelton. If you have a strong academic record and are interested in working with us as a postgraduate student, please feel free to contact me.

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

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. I've recently completed authoring an introductory book on R - The Book of R: A First Course in Programming and Statistics is available now. In 2017 I was the recipient of a University of Otago Early Career Award for Distinction in Research.

Qualifications

  • 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).

Teaching 2017

  • Sem 1: STAT110, STAT241
  • Sem 2: I will coordinate STAT352, which will be lectured by Baylee Smith and Chuen-Yen Hong.

(Past taught)

  • STAT115 (Sem 2, 2013; 2014), STAT241 (Sem 1, 2015; 2016), STAT380 (Sem 1, 2012; 2013), STAT352 (Sem 2, 2012-2016), STAT442 (Sem 2, 2012)

Graduate/Honours Students

  • 2015-present: Baylee Smith for a Masters in Archaeology. I'm the statistics co-supervisor for Baylee (with Dr Tim Thomas at the Dept. of Archaeology here at Otago as primary supervisor) as she investigates the spatial patterns of historic Māori pā sites scattered throughout New Zealand.

(Past supervised)

  • 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 at the Dept. of Archaeology here at Otago).
  • 2013: Claire Flynn for Honours in Statistics.

Publications

  • Davies TM, Baddeley A (2017) Fast computation of spatially adaptive kernel estimates, Statistics and Computing {to appear}.
  • Davies TM, Marshall JC, Hazelton ML (2017) Tutorial on kernel estimation of continuous spatial and spatiotemporal relative risk, Statistics in Medicine {to appear}.
  • 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)

  • Davies TM, Flynn CR, Hazelton ML (2017) On the utility of asymptotic bandwidth selectors for spatially adaptive kernel density estimation, Submitted for publication

Software

  • 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.
  • 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. Much of the package qualities at release are attributed to the sterling efforts of BM Taylor.