I would like to fit some data with measurement X_obs, Y_obs, and known measurement error of Y_err,
and I tried to use ppc to check the my fitting results.
Here is my model
X_shared=shared(X_obs) Y_err_shared=shared(Y_err) with model: a = pm.HalfNormal('a', 6) b = pm.HalfNormal('b', 30) Y_max = pm.Uniform('Y_max', upper = X_shared * a + b, lower=0,shape=len(X_obs)) model_y = pm.Normal('Model_Y', mu=real_Y, sd=Y_err_shared, observed=Y_obs)
The measurement error follows the Gaussian distribution, and the real Y follows the uniform distribution.
If I directly replace the shared variable X_shared and Y_err_shared and run sample_ppc,
it will show “incompatible shape” error.
As I found in pymc3 documents, this is probably because the shape of shared variable cannot be updated when the shared variable involves the shape of another variable (Y_max).
My first question is if there is an alternative way to run ppc on this model ?
I currently use a dumb solution that I add e.g. 1000 fake data points, with X and Y not likely to affect the posterior, to run the pm.sample. So I can have sufficient shape to put my predicted X, and I can just updated the shared variable with the same shape. But this solution would be useless for non-Uniform likelihood.
The other possible way is to use the Uniform convolve with Normal directly as likelihood, so I don’t need the Y_max variable. I am wondering if pymc3 provides some easier way to convolve two distribution? or we could only use a custom likelihood?
My third question is: The default sample_ppc only calculate the observed variable (model_y), but what I interested is Ymax. I tried to set vars=model.free_RVs in sample_ppc, but it only return something called “‘a_log__’”, “‘b_log__’”, and ‘Y_max_interval__’. I am wondering what is the correct way to ask sample_ppc to sample all variable?
Any suggestions would be appreciated.