# Sampling an interpolated model with MCMC

Is it safe to run a MCMC by interpolating in tabulated data of a model? For background, I have output of a model that involves a set of coupled non-linear differential equations. Calculating models on the fly is slow, so I've tried using a MCMC simulation where the function call is an interpolation in a grid of pre-calculated output, rather than the actual output for a given set of parameters.

My question is, basically, has this kind of application been studied before? I've been Googling for scholarly material for a while and looking in some textbooks for clues but I can't find anything that discusses this. My gut instinct is that the results of the MCMC calculation are as reliable as the interpolation scheme but I'm not sure if there are any formal breakdowns in the subtle details of the chains.

I have a reasonable background in maths and physics but I'm not a master statistician. I apologize if I've overlooked an obvious answer!

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What do you call "output of a model"? "calculating a model"? "grid of precalculated output"? What do you want to simulate with a MCMC? Why a MCMC and not standard simulations?.. –  Stéphane Laurent Sep 17 '12 at 17:36
Well, the model is of stellar structure. I have a code (Fortran) that, given parameters like the mass of the star and its chemical content, it solves a system of about 11 differential equations to produce a model, from which you can take observable properties like the brightness of the star. I'm starting with measurements of such things (e.g. brightness) and trying to get the best-fitting model parameters (e.g. mass). I'm using a MCMC to get the posterior distributions of the parameters, given a likelihood of the model matching the observations, within Gaussian errors. Does that help...? –  Warrick Sep 18 '12 at 7:57