1.- How to input priors?
I just don't see where I can specify the distribution of my priors. I am supposing that, by using the search limits in the optimization options window, I can at least specify the extremes of my prior (is that right?) But, that is assuming a uniform distribution of my prior. So, how can I declare a more informed prior?
2.- Log-Likelihood function
So far, I am using as payoff objective the maximization of a total log-likelihood function between my Observed and Simulated data. That total log-likelihood is calculated by calculating the LL at every timestep with LL= exp(-(LN(Observed)-LN(Simulated))^2/(2*sigma^2)) and then multiplying all of those LL together. I am not sure if this is necessary or if, just by specifying in the Payoff definition to calibrate between my observed and simulated data, VENSIM will calculate the LL automatically.
3.-Diagnostics
The "MCMC Output" page from the VENSIM documentation shows a graph with convergence diagnostics (see below). How can I obtain that graph? I understand that I have to import the .dat file as .vdfx into the model, but then what? I can't find a way to generate those diagnostics
4.- log window while running.
The log output while the MCMC is running shows some diagnostics and, while I do understand most of them in theory, I am not sure the nomenclature that VENSIM is using. For example, the MAX PSRF shows 0.4525, 11/11, <1.2 ; I am not sure what the 11/11<1.2 represents. do you have some literature recommendations to understand all of this?
5.- MCMC algorithm.
I have a person that is a bit more knowledgeable about MCMC that is helping me out, and they are asking me about the specific MCMC algorithm that VENSIM uses. I am pasting their specific questions:
Sorry for such a long message but I really hope you can help me out with this.--> Find out exactly what algorithm Vensim is using for MCMC. Especially, what it assumes about the objective function. Eg, the one in R assumes you give it the numerator of Bayes formula: P(q | data) ~ P(q)*P(data | q)
-->It would be helpful to know whether the MCMC function expects a posterior or log-posterior as well.
Thanks