Peter Jupp's Home Page

Contact information:

Prof P E Jupp
School of Mathematics and Statistics
University of St Andrews
St Andrews
KY16 9SS

phone: 01334 46 3704
fax: 01334 46 3748

Research Interests

Directional statistics

The topic of directional statistics is concerned typically with observations which are directions (unit vectors in Rp), axes (lines through the origin of Rp), or rotations of Rp. More generally, observations can be points in a compact Riemannian manifold.

A famous data set on the rotation group SO(3) is the set of vectorcardiogram data of Downs, Liebman and Mackay (1971).

One of the main techniques in directional statistics is that of embedding the sample space in a suitable Hilbert space.

Differential geometry of parametric inference

Asymptotic expansions can be expressed efficiently in the language of differential geometry. The invariant quantities which arise have geometric interpretations and provide a way of taming complicated expansions.

Quantum stochastics

Every measurement on a quantum system gives rise to a probability distribution on the outcome space. Thus measurements transform families of quantum states into families of probability distributions.

Some publications

Directional statistics

  • Mardia, K.V. and Jupp, P.E. (2000) Directional Statistics, Wiley, Chichester. Errata.
  • Jupp, P.E. (2001) Modifications of the Rayleigh and Bingham tests for uniformity of directions. J. Mult. Anal. 77, 1-20.
  • Jupp, P.E. (2002) Spherical Statistics. In Encyclopedia of Environmetrics. (A. H. El-Shaarawi and W. W. Piegorsch, eds.),
    Wiley, Chichester, Volume 4, 2097-2099.
  • Jupp, P.E., Kim, P.T., Koo, J.-Y. and Wiegert, P. (2003) The intrinsic distribution and selection bias of long-period cometary orbits. J. Amer. Statist. Assoc. 98, 515-521. here.
  • Chikuse, Y. and Jupp, P.E. (2004) A test of uniformity on shape spaces. J. Mult. Anal. 88, 163-176.
  • Watamori, Y. and Jupp, P.E. (2005) Improved likelihood ratio and score tests on concentration parameters of von Mises-Fisher distributions.
    Statistics & Probability Letters 72, 93-102.
  • Jupp, P.E. (2005) Sobolev tests of goodness of fit of distributions on compact Riemannian manifolds. Ann. Statist. 33, 2957-2966. math.ST/0603135.
  • Stone, J.V. and Jupp, P.E. (2007) Free-Lunch Learning: Modeling spontaneous recovery of memory. Neural Computation 19, 194-217.
  • Jupp, P.E. (2008) Data-driven Sobolev tests of uniformity on compact Riemannian manifolds. Ann. Statist. 36, 1246-1260. Erratum.
  • Stone, J.V. and Jupp, P.E. (2008) Falling towards forgetfulness: synaptic decay prevents spontaneous recovery of memory. PLoS Computational Biology 4: e1000143.
  • Jupp, P.E. and Stone, J.V. (2008) Free-lunch learning and directional distributions in artificial neural networks. Acta et Commentationes Universitatis Tartuensis de Mathematica 12, 101-108.
  • Byrne, R.W., Noser, R.N., Bates, L.A. and Jupp, P.E. (2009) How did they get here from there? Detecting changes of direction in terrestrial ranging. Animal Behaviour 77, 619-631.
    A brief description of the test introduced in this paper and a link to appropriate R code are available here.
  • Jupp, P.E. (2009) Data-driven tests of uniformity on product manifolds. J. Statist. Planning & Infce. 139, 3820-3829. Erratum.
  • Bachmann, F., Hielscher, R., Jupp, P.E., Pantleon, W., Schaeben, H. and Wegert, E. (2010) Inferential statistics of electron backscatter diffraction data from within individual crystalline grains. J. Appl. Cryst.43, 1338-1355. 10.1107/S002188981003027X.
  • Arnold, R. and Jupp, P.E. (2013) Statistics of orthogonal axial frames. Biometrika 100, 571-586. doi: 10.1093/biomet/ast01.
  • Yeh, S.-Y., Harris, K.D.M. and Jupp, P.E. (2013) A drifting Markov process on the circle, with physical applications. Proc. Roy. Soc. A 469, 20130092.
  • Bachmann, F., Jupp, P.E. and Schaeben, H. (2014) Estimating the number and locations of Euler poles. Int. J. Geomath. 5, 289-301. doi:10.1007/s13137-014-0064-2.
  • Owen, A., Jupp, P.E., Nichols, G.J., Hartley, A.J., Weissmann, G.S. & Sadykova, D. (2015) Statistical estimation of the position of an apex: application to the geological record. J. Sedimentary Research. 85,142-152. doi: A link to appropriate R code is available here.
  • Jupp, P.E. (2015) Copulae on products of compact Riemannian manifolds. J. Mult. Anal. 140, 92-98. doi: 10.1016/j.jmva.2015.04.008.
  • Chikuse, Y. & Jupp, P. E. (2015) Some families of distributions on higher shape spaces. In Geometry Driven Statistics: a Festschrift for Kanti Mardia. (I.L. Dryden and J.T. Kent, eds.) pp.206-217. Wiley, Chichester. Erratum.
  • Arnold, R., Jupp, P.E. & Schaeben, H. (2018) Statistics of ambiguous rotations. J. Mult. Anal. 165, 73-85. Erratum.
        An earlier version of this paper is available at arXiv:1701.01579v1.
  • Healy, D. & Jupp, P.E. (2018) Bimodal or quadrimodal? Statistical tests for the shape of fault patterns.
    EarthArXiv:10.17605/OSF.IO/V6R28. A link to appropriate R code is available here.
  • Differential geometry of parametric inference

  • Larsen, P.V. and Jupp, P.E. (2003) Parametrization-invariant Wald tests. Bernoulli 9, 167-182.
  • Jupp, P.E. (2010) A van Trees inequality for estimators on manifolds. J. Mult. Anal. 101, 1814-1825. Online from Science Direct. doi:10.1016/j.jmva.2010.03.007.
  • Fewster, R.M. and Jupp, P. E. (2013) Information on parameters of interest decreases under transformations. Journal of Multivariate Analysis 120, 34-39.

    Quantum stochastics

  • Barndorff-Nielsen, O.E., Gill, R.D. and Jupp, P.E. (2001) Quantum information. In Mathematics Unlimited - 2001 and Beyond,
    (B. Engquist & W. Schmid, eds.), 83-107. Springer-Verlag, Heidelberg.
  • Barndorff-Nielsen, O.E., Gill, R.D. and Jupp, P.E. (2003) On quantum statistical inference. J. Roy. Statist. Soc. B 65, 775-816. quant-ph/0307191.
    The original long version of this survey paper is available here.
  • Jupp, P.E., Kim, P.T., Koo, J.Y. and Pasienka, A. (2012) Testing quantum states for purity. J. Roy. Statist. Soc. C 61, 753-763. doi: 10.1111/j.1467-9876.2012.01040.x

    Estimation of population size

  • Goudie, I.B.J., Jupp, P.E. & Ashbridge, J. (2007) Plant-capture estimation of the size of a homogeneous population. Biometrika 94, 243-248. Erratum.
  • Fewster, R.M., Buckland, S.T., Burnham, K.P., Borchers, D.L., Jupp, P.E., Laake, J.L., and Thomas, L. (2009) Estimating the encounter rate variance in distance sampling. Biometrics 65, 225-236. Online from Blackwell-Synergy.
  • Fewster, R.M. and Jupp, P.E. (2009) Inference on population size in binomial detectability models. Biometrika 96, 805-820. Abstract. Free access PDF from Oxford Journals. Erratum.
  • Borchers, D.L., Marques, T.A., Gunnlaugsson, Th. and Jupp, P.E. (2010) Estimating distance sampling detection functions when distances are measured with errors. J. Agric. Biol. Environ. Statistics 15, 346-361.


  • Parnell, C.E. and Jupp, P.E. (2000) Statistical analysis of the energy distribution of sub-microflares in the quiet sun. Astrophysical Journal 529, 554-569.
  • Jupp, P.E. Regoli, G. and Azzalini, A. (2016) A general setting for symmetric distributions and their relationship to general distributions. Journal of Multivariate Analysis 148, 107-119. DOI: 10.1016/j.jmva.2016.02.011.

    A complete list of publications may be found here

    Last updated: 6 July 2018