My Research

My research interests are in statistical models of Shape and Directions. I am also working mainly on the computational methods related to shape and directions.

Many distributional assumptions for Statistical models in Shape and Directions originate from Multi-Variate Normal distributions (MVN) in two ways. One is to project MVN's onto a lower dimensional curved space after some appropriate shape or direction preserving mapping. The other is to condition MVN's  to lay on the shape spaces or spheres.

Both of these approaches give rise to challenging issues for statistical inference. My main research is focused on these problems.

Google scholar citations

Publications

  • Le, H. and Kume, A  (2000). The Frèchet mean and the shape of the means Advances of Applied Probability, Vol.32  p101-114.
  • Kume, A and Le, H.(2000). Estimating the Frèchet mean in Bookstein shape spaces Advances of Applied Probability, Vol.32  p663-674.
  • Le, H. and Kume, A  (2000). Detection of Shape Changes in Biological Features The Journal of Microscopy, Vol.200  p140-147. Le, H., and Kume, A.
  • Kume, A. and Le, H. (2003). On Frechèt means in simplex shape spaces. Advances of Applied Probability, 35(4):885-897.
  • Kume, A. and Wood, A. T.A. (2005). Saddlepoint approximations for the Bingham and Fisher-Bingham normalising constants. Biometrika.92:465-476.
  • Kume, A. and Walker, S.G. (2006) Sampling from compositional and directional distributions. Statistics and Computing, 16(3):261 - 265.
  • Kume, A., Dryden, I.L. and Le, H. (2007). Shape space smoothing splines for planar landmark data. Biometrika, 94(3), 513-528.
  • Kume, A. and Wood, A. T.A. (2007). On the derivatives of the normalising constant of the Bingham distribution. Statistics and Probability Letters, Vol. 77, pp. 832-837.
  • Hashorva E., Kotz S. and Kume, A. (2007)  Lp-norm generalised symmetrised Dirichlet distributions, Albanian Journal of Mathematics, Vol. 1, pp. 36-52.
  • Dryden, I.L., Kume, A., Le, H. and Wood, A. T.A. (2008).The MDS model for shape: an alternative approach. Biometrika, 95 (4): 779-798.
  • Kume, A. and Walker, S.G. (2008) On the Fisher--Bingham Distribution, Statistics and Computing.19: 167–172.
  • Kume, A. and Welling, M. (2010) Maximum Likelihood Estimation for the Offset-Normal Shape Distributions Using EM, J. Computational and Graphical Statistics, 19, No. 3: 702–723.
  • Dryden, I.L., Kume, A., Le, H. and Wood, A. T.A. (2010). Statistical inference for functions of the covariance matrix of stationary Gaussian vector time series Annals of the Institute of Statistical Mathematics, 62: 967:994.
  • Breuer, L. and Kume, A. (2010) An EM algorithm for Markovian arrival processes observed at discrete times. B. Muller-Clostermann, K. Echtle, E. Rathgeb (Eds.): MMB & DFT 2010, LNCS 5987, pp. 242--258. Springer, Heidelberg.
  • Kume, A. and Hashorva, E. (2012) Calculation of Bayes Premium for Conditional Elliptical Risks. Insurance: Mathematics and Economics, 51 (3). pp. 632-635. ISSN 0167-6687
  • Kume, A and Preston S. and Wood A.T.A. (2013) Saddlepoint approximations for the normalising constant of Fisher–Bingham distributions on products of spheres and Stiefel manifolds Biometrika 100 (4): 971-984.
  • Sei, T. and Kume. A. (2014) Calculating the normalising constant of the Bingham distribution on the sphere using the holonomic gradient method. Statistics and Computing, 1-12.
  • Kume, A. and Walker, S.G. (2014) On the Bingham distribution with large dimension Journal of Multivariate Analysis 124, 345-352.
  • Sei, T. and Kume, A. (2015). Calculating the normalising constant of the Bingham distribution on the sphere using the holonomic gradient method. Statistics and Computing [Online] 25:321-332. Available at: http://doi.org/10.1007/s11222-013-9434-0.
  • Kume, A. and Sei, T. (2017). On the exact maximum likelihood inference of Fisher–Bingham distributions using an adjusted holonomic gradient method. Statistics and Computing [Online] 28. Available at: http://dx.doi.org/10.1007%2Fs11222-017-9765-3.
  • Campbell-White, J., Froebrich, D. and Kume, A. (2018). Shape Analysis of HII Regions - I. Statistical Clustering. Monthly Notices of the Royal Astronomical Society [Online] 477:5486-5500. Available at: https://doi.org/10.1093/mnras/sty954.
  • Kume, A. and Leisen, F. and Lijoi, A. (2018). Limiting behaviour of the stationary search cost distribution driven by a generalized gamma process. Electronic Communications in Probability [Online] 23:Paper no 11. Available at: http://dx.doi.org/10.1214/18-ECP111.
  • Fontanella, L. and Ippoliti, L, and Kume, A. (2018). The Offset Normal Shape Distribution for Dynamic Shape Analysis. J. Computational and Graphical Statistics, To appear.

Conference abstracts


  • Fontanella, L. and Fusilli, C and Ippoliti, L, and Kume, A, (2012) Modelling Facial Expressions through Shape Polynomial Regression, JCS - CLADAG 2012, First Edition: August 2012 - ISBN 978-88-6129-916-0.
  • Kume, A. and Dryden, I.L, Inference on the projected shape distributions of Gaussian random matrices, September 2012, Special session on Image Processing and Shape Analysis, Statistiche Woche Vienna, Austria.
  • Kume, A. and Dryden, I.L. Shape inference based on multivariate normal matrix distributions, July 2012, New Statistics and Modern Natural Sciences, 31st Leeds Annual Statistical Research (LASR) Workshop, Department of Statistics, University of Leeds, ISBN 978-0-85316-310-7
  • Luigi Ippoliti, Kume, A. and Gattone, A. Describing facial expressions through shape polynomial regression, July 2012, New Statistics and Modern Natural Sciences, 31st Leeds Annual Statistical Research (LASR) Workshop, Department of Statistics, University of Leeds, ISBN 978-0-85316-310-7
  • Kume, A. Estimating landmark correlation via maximum likelihood, January 2012, Third UK Meeting on Morphometrics and Shape Analysis, York, UK.
  • Kume, A. Consistent Estimation of the Shape of the Means with Applications in 3-D Shape Analysis, December 2011, Special session on Multivariate Distribution Theory, International Conference on Advances in Probability and Statistics, Hong Kong.
  • Kume, A. A likelihood approach to shape analysis, September 2009, Complex models and computational methods for estimation and prediction, Milano, Italy.
  • Kume, A. An introduction to shape analysis with applications in biology, May 2009, 4th Annual Symposium of CBMI 'Making Sense of Biological Data'. Canterbury, UK.
  • Kume, A. and Le, H.L. Fitting smoothing splines to data in shape spaces of planar configurations, July 2004, Statistical Analysis of Images in the 6th World Congress of the Bernoulli Society for Mathematical Statistics and Probability and 67th Annual Meeting of the Institute of Mathematical Statistics, Barcelona. Spain.
  • Kume, A., Dryden, I.L., Le, H., Wood, A. T.A. (2002) Fitting cubic splines to data in shape spaces of planar configurations In Mardia, K.V., Aykroyd, R.G., and McDonnell, P., editors, Proceedings in Statistics of Large Datasets, LASR2002, pages 119--122. University of Leeds.
  • Dryden, I.L., Kume, A., Le, H., Wood, A. T.A., and Laughton, C. (2002) Size-and-shape analysis of DNA molecular dynamics simulations In Mardia, K.V., Aykroyd, R.G., and McDonnell, P., editors, Proceedings in Statistics of Large Datasets, LASR2002, pages 23--26. University of Leeds.