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One-day conference in Geometry and Statistics

June 23, 2014

 Department of      Mathematical Sciences,
 University of Bath
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We would like to bring this one-day conference not only to the attention of the Statistics community but also to the Geometers of all kinds!

The aim of this one-day 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
 As such, the conference intends to bring opportunities
  • 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
The format of this one-day conference consists of a series of talks by researchers who have worked on this area  that will highlight the key elements of the interplay between Geometry and Statistics  in their particular areas of expertise.


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


Final Program

09:30 - 10:30 Registration & Coffee in the Atrium on Level 1 of 4 West
10:30 - 11:10 Karim Anaya-Izquierdo (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 differential-geometric 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 real-valued 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 meta-analysis 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 Erdos-Renyi 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 Anaya-Izquierdo

Some books and papers on Geometry and Statistics

  1. Amari, S.  (1985). Differential-Geometrical methods in Statistics. Lecture Notes in Statistics. Springer
  2. Amari, S. and Nagaoka, H. (2000). Methods of Information Geometry. volume 191 of Translations of Mathematical Monographs. Oxford University Press and American Mathematical Society.
  3. Arwini, K and Dodson. C.T.J. (2008). Information Geometry. Lecture Notes in Mathematics. Springer.
  4. Gibilisco, P. et al (eds). (2010). Algebraic and Geometric Methods in Statistics.  Cambridge University Press.
  5. Kass, R. E. and Vos, P. W. (1997). Geometrical Foundations of Asymptotic Inference. Wiley.
  6. Murray,  M.K and Rice, J.W. (1993). Differential Geometry and Statistics. Chapman and Hall.
  7. Pistone, G., Riccomagno, E. and Wynn, H. (2000). Algebraic Statistics. CRC Press.
  8. Saville, D.J and Wood, G.R. (1991). Statistical Methods: The Geometric Approach. Springer.
  9. Marriott, P. and Salmon, M. (eds). Applications of Differential Geometry to Econometrics. CUP.
  10. Marriott, P. and Vos, P.W. (2010). Geometry in Statistics.  Wiley Interdisciplinary reviews: Computational Statistics. 
  11. Nielsen, F. and Barbaresco, F. (2013). Geometric Science of Information. Lecture Notes in Computer Science. Springer.
Previous conferences on Geometry and Statistics and other related links