Hi everyone,
I’m having some trouble specifying this potential in PyMC3. Could one of you give me some advice on how to implement it?
To give a brief explanation:
alpha - is a constant that is specified by the user and does not need to be inferred by the model
T - the parameter that I’m interested in inferring based from this exponential potential
Nt - the length of the vector T
The caveat is that the parameter T needs to be positive and bound by some upper and lower limits (specified by user).
Currently, I’ve tried to implement this using DensityDist but I get a “nan energy” error.
Thanks for you help!
How is your current implementation looks like?
In general, the logp function (that you would wrap in a DensityDist) is alpha * fn_s(T), bounded by the constrain.
Hi @junpenglao! Thanks for answering.
See my code below:
var_alpha = theano.shared(value = 1., borrow = False)
phi_e = pm.Uniform(‘phi_e’, lower = lb_phi_e, upper = ub_phi_e, shape = (ub_phi_e.size))
S1_phi_e = (phi_e/phi_e.sum()*np.log(phi_e/phi_e.sum())).sum()
pm.DensityDist(‘phi_e_potential’, logp = -var_alpha*S1_phi_e)
The error I receive with this approach is “TypeError: ‘TensorVariable’ object is not callable”
To followup, I’ve had a bit of success when I implement the potential as follows:
pm.Potential(‘phi_e_potential’, np.exp(-var_alpha*S1_phi_e))
However, I get “ValueError: Bad initial energy: nan. The model might be misspecified.” when the initial value is not properly specified
If you are normalizing the uniform like this: phi_e/phi_e.sum(), you should use a Dirichlet distribution as prior instead.
