Information geometry: optimal experiment design and other applications
The concept of information is useful in physical problems which involve measurement and uncertainty or otherwise naturally contain stochasticity. For example, information quantifies how much one can
learn' from a set of noisy measurements drawn from a network of sensors. The mathematical theory of information geometry allows one to use geometric tools to study information in a general setting. The various theorems and constructions of Riemannian geometry can then be used to, for instance, theoretically extremise the information and determine an optimal experimental tuning for a sensor model. In this talk, we introduce the ideas of information geometry with particular emphasis on thetheory of experiments', and discuss some recent mathematical results in the field. We consider a concrete example problem of estimating the parameters of a `target' from noisy bearings measurements, i.e. placing sensors to best estimate the position of some object. Some applications of information geometry to general relativity, thermodynamics, and game theory are also discussed.
Mr Arthur Suvorov, The University of Melbourne