Uncertainty of a spatial model

Hi there,

I have encountered difficulties in determining the uncertainty of a 
spatial model. I hope you would like to share your knowledge and help 
me. Thanks in advance!

Here we assume that we have three input layers, A, B, and C, and one 
output layer R with R = A + B + C. I hope to estimate how the 
uncertainty of input layers propagates to the model output.

I learned that the input layer could be treated as a spatial random 
field, and the uncertainty could be estimated with MCMC algorithm[1]. 
However, I don't know how to include the spatial component of the model 
into the MCMC.

Any hint will be really appreciated.

Best wishes,
Jinsong

[1] Supplementary Note 4 (page 8 and 9) in 
https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-017-02142-7/MediaObjects/41467_2017_2142_MOESM1_ESM.pdf