Oneday conference in Geometry and StatisticsJune 23, 2014Department of Mathematical Sciences,University of Bath 
We would like to bring this oneday conference not only to the attention of the Statistics community but also to the Geometers of all kinds!
The aim of this oneday conference is to attract pure mathematicians and in particular, Geometers, to work together with Statisticians in this area by highlighting interesting and powerful applications of Geometry to Statistics.
The conference takes a very broad view of the interplay between Geometry (Differential, Algebraic, Convex, etc) and Statistics which includes:
 the model functional space approach called Information Geometry which endows the space of probability densities with appropriate differential geometric structures and from there develops method to analyse data
 the data geometry approach which gives geometries to the space of the data and for which prominent examples are the computational geometry based algorithms used in Robust Statistics
 the geometric approach to enhance/understand modern Monte Carlo sampling techniques such as Hamiltonian Monte Carlo
 to extend the scope of the applications of Geometry research and hence to increase its impact
 to develop new projects (research and student) jointly with Statisticians
Geometry and Statistics
There is a long history of using geometrical ideas in Statistics. Whereas global Euclidean geometry matches many contexts very well, increasingly, advances and challenges in science and elsewhere are throwing up important problems which demand that alternatives be used. A variety of geometries  affine, convex, differential, algebraic  have been emerging to meet these challenges, the premise being that, given a statistical problem, an appropriate geometry can inform a novel, enhanced methodology for it.
Invited Speakers
 Eva Riccomagno (Genoa)
 Peter
Jupp (St Andrews)
 CTJ Dodson (Manchester)
 Johannes Rauh (Max Planck Institute, Leipzig)
 Paul Marriott (Waterloo)
 Frank Critchley (Open University)
 Michael Betancourt (Warwick)
 Paul Vos (East Carolina)
Final Program
09:30  10:30  Registration & Coffee in the Atrium on Level 1 of 4 West 
10:30  11:10  Karim AnayaIzquierdo
(Bath) / Paul Vos
(East Carolina) A brief introduction to the interplay between Geometry and Statistics 
11:10  11:50  Kit Dodson (Manchester) Information geometric illustrations of some simple statistical models This
talk outlines information geometric methods to provide natural
neighbourhoods that respect the
intrinsic
geometry of the space of states, for visualization and monitoring of
some simple cases of statistically influenced systems. Typical
recurring practical situations involve the modelling of real processes
that are 'nearly' Poisson or 'nearly' uniform, and we see a
complimentarity in the geometry available to represent these two.
Similarly we encounter 'nearly' independent Poisson, and 'nearly'
independent Gaussian processes. We look also at first order
inhomogeneous dynamics of stochastic behaviour trajectories with
applications to evolutionary processes and an epidemic model.

11:50  12:30  Peter
Jupp (St Andrews) Geometry of Yokes In the
differentialgeometric approach to statistical asymptotics a central
concept is that of a yoke (alias contrast function, alias divergence
function). A yoke on a manifold M is a realvalued function on
the `square' M x M of M which satisfies
some mild conditions. Each yoke on Θ gives rise to
(i) natural coordinate systems taking values in (co)tangent spaces to M, (ii) a family of tensors (including a Riemannian metric) on M, (iii) a symplectic structure on a neighbourhood of the diagonal of M x M. The aim of this talk is to give an overview of these geometrical objects and to indicate some applications to statistical inference. 
12:30  13:40  Lunch in the Atrium on Level 1 of 4 West 
13:40  14:20  Eva
Riccomagno (Genoa) Algebraic Representation of Gaussian Markov Combinations Markov
combinations for structural metaanalysis problems provide a way of
constructing a statistical model that takes into account two or more
marginal distributions by imposing conditional independence
constraints. Here we consider Gaussian distributions and discuss how
the covariance and concentration matrices of the different combinations
can be found via matrix operations. Further we investigate the
properties of the combinations via algebraic statistics tools.

14:20  15:00  Paul
Marriott (Waterloo) / Frank
Critchley (Open University)
When are first order asymptotics adequate? ... a diagnostic This talk looks at boundary effects on inference in an important class of models including, notably, logistic regression. Asymptotic results are not uniform across such models. Accordingly, whatever their order, methods asymptotic in sample size will ultimately “break down” as the boundary is approached, in the sense that effects such as infinite skewness, discreteness and collinearity will dominate. In this paper, a highly interpretable diagnostic tool is proposed, allowing the analyst to check if the boundary is going to have an appreciable effect on standard inferential techniques. 
15:00  15:40  Coffee / Tea in the Atrium on Level 1 of 4 West 
15:40  16:20  Michael
Betancourt (Warwick) Geometric Bayesian Inference Bayesian inference
requires the practical manipulation
of probability distributions, which itself depends critically on
efficient exploration, especially in high
dimensions. In this talk I’ll discuss how tools from differential
geometry yield systematic
exploration of complicated probability distributions and admit powerful
strategies for scalable
inference.

16:20  17:00  Johannes
Rauh (Max Planck Institute, Leipzig) The geometry of exponential random graph models ERGMs
are natural statistical models that are used in network analysis.
However, in some applications it has been observed that they behave
very
similarly to an ErdosRenyi random graph and therefore often do not
describe real data. We tried to understand this phenomenon by studying
the convex support polytope of the model. I will also talk about
another
point of view in terms of large deviations and graph limits, due to
Chatterjee and Diaconis.

Registration & Payment
Registration fee: £20  to help cover the costs of the meeting.
To register and pay using a credit/debit card, please complete the Registration form
(The link will transfer you to the University online store, then you will be asked to create a customer account, using your email address, billing address, and a password you create)To register for the conference and pay in cash on the day, please complete the alternative Registration form
The registration fee
includes
lunch and coffee breaks
Posters
Postgraduate students and postdoctoral researchers are particularly encouraged to submit a poster. If you would like to present your poster please indicate so in the registration form.
Venue and Travel information
The talks will take place in the Wolfson Lecture Room,Room 1.7 (campus map), breaks and the poster session will be held in the Atrium outside the Wolfson Room. Click for information about travelling to the University and nearby hotels.
Main contact: Karim AnayaIzquierdo
Some books and papers on Geometry and Statistics
 Amari, S. (1985). DifferentialGeometrical methods in Statistics. Lecture Notes in Statistics. Springer
 Amari, S. and Nagaoka, H. (2000). Methods of Information Geometry. volume 191 of Translations of Mathematical Monographs. Oxford University Press and American Mathematical Society.
 Arwini, K and Dodson. C.T.J. (2008). Information Geometry. Lecture Notes in Mathematics. Springer.
 Gibilisco, P. et al (eds). (2010). Algebraic
and Geometric Methods in Statistics. Cambridge
University Press.
 Kass, R. E. and Vos, P. W. (1997). Geometrical Foundations of Asymptotic Inference. Wiley.
 Murray, M.K and Rice, J.W. (1993). Differential Geometry and Statistics. Chapman and Hall.
 Pistone, G., Riccomagno, E. and Wynn, H. (2000).
Algebraic
Statistics. CRC Press.
 Saville, D.J and Wood, G.R. (1991). Statistical Methods: The Geometric Approach. Springer.
 Marriott, P. and Salmon, M. (eds). Applications
of Differential Geometry to Econometrics. CUP.
 Marriott, P. and Vos, P.W. (2010). Geometry in Statistics. Wiley Interdisciplinary reviews: Computational Statistics.
 Nielsen, F. and Barbaresco, F. (2013). Geometric
Science of Information. Lecture Notes in Computer Science.
Springer.
 Geometric Science of Information
 WoGAS workshops: I, II & III
 IGAIA: I,II & III
 Algebraic
Statistics