Sampling a multivariate normal with priors on the individual components of the mean

Questions
1

I have a 3D likelihood model that is multivariate normal where I compute the mean with

mu = [1/x1, x2/x1, x3/x1]

where x1, x2, and x3 have respectively a Gamma, Beta, and Uniform prior.
I tried to implement this in PyMC3 with

with pm.Model() as myModel:

x1 = pm.Gamma('x1', alpha=2, beta=1)
x2 = pm.Beta('x2', alpha=2, beta=3)
x3 = pm.Uniform('x3', lower=0.0, upper=1)        
mu = np.array([1/x1, x2/x1, x3/x1])
cov = np.identity(3)
x = pm.MvNormal('x', mu=mu, cov=cov, observed=np.array([0.51, 1.2, 0.27]))

trace = pm.sample(5000)`

but I got the rather cryptic error message:

AsTensorError: (‘Cannot convert [Elemwise{true_div,no_inplace}.0 Elemwise{true_div,no_inplace}.0\n Elemwise{true_div,no_inplace}.0] to TensorType’, <class ‘numpy.ndarray’>)

pointing to the line with pm.MvNormal()

Is what I’m trying to do within PyMC’s current capabilities? If yes, do you have any help on what the error message means?

2

Found the cause of the error message. It should read:

mu = [1/x1, x2/x1, x3/x1]

I.e. without the np.array(). Apologies for the noise.

3

FYI, you can also stack the RVs together using mu = tt.stack([1/x1, x2/x1, x3/x1])