BioMaths Colloquium Series - 2017/18
08 December 2017 - 3pm Maths Seminar Room
(room 224 Talbot Building 2nd floor)
Information sensitivity functions to assess parameter information gain and identifiability of dynamical systems
Dr Sanjay Pant
(College of Engineering, Swansea University, UK)
We conclude the BioMaths Colloquium Series for this Autumn term with a seminar by Dr Sanjay Pant, from the College of Engineering at Swansea University (UK). Sanjay's research ranges from cardiovascular modelling and medical device design and optimisation, to reduced order and probabilistic modelling, forward and inverse uncertainty propagation, surrogate modelling, information theory, and inverse problems.
Abstract
Abstract
A new class of functions, called the 'Information sensitivity functions' (ISFs), which quantify the information gain about the parameters through the measurements/observables of a dynamical system are presented. These functions can be easily computed through classical sensitivity functions alone and are based on Bayesian and information-theoretic approaches. While marginal information gain is quantified by decrease in differential entropy, correlations between arbitrary sets of parameters are assessed through mutual information. For individual parameters these information gains are also presented as marginal posterior variances, and, to assess the effect of correlations, as conditional variances when other parameters are given.
The easy to interpret ISFs can be used to a) identify time-intervals or regions in dynamical system behaviour where information about the parameters is concentrated; b) assess the effect of measurement noise on the information gain for the parameters; c) assess whether sufficient information in an experimental protocol (input, measurements, and their frequency) is available to identify the parameters; d) assess correlation in the posterior distribution of the parameters to identify the sets of parameters that are likely to be indistinguishable; and e) assess identifiability problems for particular sets of parameters.
The application of ISFs is presented in three areas of mathematical biosciences: i) a Windkessel model, which is widely used a boundary condition in computational fluid dynamics simulations of haemodynamics; ii) the Hodgkin-Huxley model for a biological neuron, which has formed the basis for a variety of ionic models describing excitable tissues; and iii) a kinetics model for the Influenza A virus.
The easy to interpret ISFs can be used to a) identify time-intervals or regions in dynamical system behaviour where information about the parameters is concentrated; b) assess the effect of measurement noise on the information gain for the parameters; c) assess whether sufficient information in an experimental protocol (input, measurements, and their frequency) is available to identify the parameters; d) assess correlation in the posterior distribution of the parameters to identify the sets of parameters that are likely to be indistinguishable; and e) assess identifiability problems for particular sets of parameters.
The application of ISFs is presented in three areas of mathematical biosciences: i) a Windkessel model, which is widely used a boundary condition in computational fluid dynamics simulations of haemodynamics; ii) the Hodgkin-Huxley model for a biological neuron, which has formed the basis for a variety of ionic models describing excitable tissues; and iii) a kinetics model for the Influenza A virus.
The discussions will continue over biscuits and tea/coffee after the seminar.
Hope to see many of you!
