How to define likelihood?

Questions
1

I have read the paper they was wrote the likelihood function with same as distributed Gaussian. But they are don’t need to the relative function between parameter and observation data (at the section 2.2)
with this case How to define the likelihood function to apply bayesian to?
following this is the paper which I remind to.

the papaer
please help me how to inform in the pymc3?

2

If you look at formula (8), the data likelihood is coded in \delta where \delta = d - \text{M}(x, z) (the line below).
For coding this in PyMC3, you can either rewrite formula (8) as a pm.Potential, or more intuitively, using formula (6) and (7):

def M_func(x, z):
    # define the M (x, z) - the output of QoIs from simulation
    ...

with pm.Model() as m:
    ...
    mu = M_func(x, z)
    pm.MvNormal('d', mu, cov=pm.math.dot(pm.math.dot(mu.T, sigma_square), mu)+identity_sigma, observed=d)

You will need to get the right shape for sigma_square and identity_sigma