Assume I have a regression model with a couple of parameters that I estimate from observed data: obs = f(data; parameters), where f is a deterministic function.
I am successfully using Pyro to estimate the posterior distribution of the parameters, which allows me to draw samples and get a posterior distribution for the observations, given input data values.
Now, I would like to invert the model, that is, getting samples of data, given observations. Of course, f is complex and I don’t know how to implement its inverse.
Also, I would like to do some sensitivity analysis, that is, get a posterior distribution for the observations as a function of one of the parameters and averaging over all values of the other parameters and the input data.
For example, if there are 2 parameters a and b, obs = f(data, a, b). If I had the joint distribution P(obs, data, a, b), model inversion would be getting \int P(data|obs) dP(a) dP(b) (marginal over the parameters) and sensitivity analysis for parameter a would be getting P(obs,a) by doing the marginalization over data and b.
Is there any documetation or tutorial on how to do this kind of analysis?