Thanks so much for your reply Jesse.
I am starting to think about another approach to my problem. You are spot on with the GP model. My current problem lies in the idea that the way my code currently executes is that the GP model is calculated separately and generates ‘coupling coefficients’ (cc) for each emission source in a specified location (effectively the GP equation without the Q emission rate component). C (x, y, z) is solved by summing the products of Q X cc for each emission source, then adding a background value. This is done for each time point in a time series and compared to observed values. The value of Q (an unknown) for each source is passed into the MCMC calculation as a LogNormal Distribution of possible values. The background (unknown) is also passed in as a Normal distribution.
What I am trying to do is pass in the source locations as distributions for x and y to be sampled in the MCMC run, but as the location information is required for the GP calculation of the cc’s, I would need to calculate those on the fly in the MCMC itself. I need to find a way to represent the x/y location data as one MCMC parameter, then loop through a dataframe (the time series) and somehow return the a list of cc’s which are treated as Deterministic parameters, dependent on the x/y distributions.
I know that is a bunch of text. Sorry for no code at this point (there are limits to what I can post). I plan to go off and have a good rethink, but in the event my ramblings make sense to you and you can think of a direction to send me in I would again appreciate the feedback.
Cheers.
Jason