Description
Hi,
I have a model with a set of latent variables, which I am trying to evaluate. So far I have worked in a custom MCMC world and want to switch to HMC/NUTS. However, I was unable to have it as a drop in replacement, as the model variables in PyMC3 are Subtensor{}.0, whereas the 'simulation' of the world I am using expects to have actual values to perform the arithmetics.
The latent space can be viewed as a 6 independent variables. Those are evaluated by a 'black-box' external function and return a vector of values that need to match a predefined distribution (1D gaussian).
Something along the lines of:
basic_model = Model()
with basic_model:
x = Normal('x', mu=0, sd=1, shape=6)
# Expected value of outcome
_, _, q2d, _ = evalWorld(x)
y = np.linalg.norm(q2d, axis = 1)
# Likelihood (sampling distribution) of observations
Y_obs = Normal('Y_obs', mu=target_mu, sd=target_sigma, observed=y)
# I want y to match N(target_mu, target_sigma)
step = NUTS()
# draw n posterior samples
trace = sample(n, step=step, start=start)
What do I have to do to x in order to pass possible values/samples of x, rather than the distribution variable itself?
I am aware that HMC requires a gradient of Y_obsm which may be a problem, as some aspects of evalWorld may not be differentiable.