K Ergueler et al.
Imperial College London
When talking about Bayesian inference, you need to think about a number of things: prior distribution, likelihood, and posterior distribution. Posterior dist is proportional to the likelihood. Then there was a fantastic animated graph showing how these two are related. He's interested in the variability in the posterior distribution. When looking into sensitivity and fisher information, the Hessian is calculated using the sensitivity coefficients. Specifically, he looks at sensitivity coefficients for temporal analysis. Not all parameters behave the same way – some don't get as "excited" about the bifurcations. You can look into the sensitivity by looking at sensitivity profiles. Most parameters in a system are sloppy (showing a graph of log-eigenvalues, and to the left and top are sloppy variables, and to the right and bottom are stiff ones). He then overlaid the eigenvectors on top of this profile, and colored the eigenvectors based on the sensitivity. Red = stiff, green = sloppy. Red are more pronounced and green is less pronounced in the higher eigenvectors.
Then he uses the example of the circadian clock reaction network (Leloup and Goldbeter 1999). The reactions in the middle seem to be more important to the dynamics of the system, and the TIM branch seems more important than the PER branch (according to their analysis). In conclusion, they analysed parameter sensitivities wrt observed time points, the global qualitative behaviour of the system, and the observed system components. Parameter sensitivities define relative importance of different areas of reactions.
Personal Comments: Ah-ha! Another ICL speaker, another Latex presentation. Nice! I'm afraid I'm not completely up on the intricacies of Bayesian stats, so I may have gotten some things mixed up. Please let me know any errors I might have introduced! His graphs were very impressive, and very much contributed to the understanding of the topic.
Tuesday Session 1
Please note that this post is merely my notes on the presentation. They are not guaranteed to be correct, and unless explicitly stated are not my opinions. They do not reflect the opinions of my employers. Any errors you can happily assume to be mine and no-one else's. I'm happy to correct any errors you may spot – just let me know!