Correct. That gives a prior on x, which is then subject to inference based upon observed data.
I do have an n-length array of params, x, with a shared variance, var_of_x. However, I’d like that variance to remain fixed, as opposed to being an inferred value. Something like:
# priors
theta = pm.Normal("theta", mu=0, sigma=100, shape=(data_array.shape))
model_error = pm.ChiSquared("model_error", nu=5)
# likelihood
y_mu = pm.math.dot(theta, data_array) + x
y = pm.Normal("y", mu=y_mu, sig=model_error)
except with some more complicated transformations going on in the likelihood function.
I’d like for x in this situation to be a random variable. By using x as a point estimate right now, my model_error term is accounting for all of the variance, when in reality I know that x should have var_of_x, which would reduce the model_error.