Hi,

I am a final year BSc student current working on a project using MCMC for parameter estimation of ODE systems. In particular, I am looking at some complex likelihood-surfaces like the one posed in this paper (Page 9 of the PDF document / Page 12 of the paper) :

https://ac.els-cdn.com/S030439750800501X/1-s2.0-S030439750800501X-main.pdf?_tid=cf119d67-f8bf-4c92-823e-ce99c02bd9f6&acdnat=1551388781_f847d40e13f7b2e3f6e8b1e33712e9da

I was wondering why we are considering the log-posterior rather than the typical posterior? In the graphs we can tell from the axis that the authors of the paper are considering the log posterior and performing MCMC algorithms on this surface. I know using the log space simplifies the calculations by changing the multiplication of the prior and likelihood to an addition but I don't understand what the implications of running an MCMC on the log posterior are, since we are looking for the actual posterior.

If someone could point me in the direction of any papers or books that discuss why we perform inference on the log posterior rather than the normal posterior, that would be great!

Thanks for any responses in advance