## Research Interests

### Directional statistics

The topic of directional statistics is concerned typically with
observations which are *directions* (unit vectors in *R*^{p}),
*axes* (lines through the origin of *R*^{p}),
or *rotations* of *R*^{p}. 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: http:dx.doi.org/10.2110/jsr.2015.16. 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.215-224. Wiley, Chichester.

### 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. 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.

### Other

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: 16 May 2016