I am having some problems related to Partial Abductive Inference in Gaussian Bayesian Networks (Bayesian Networks which accommodates the continuous nature of the random variables and follow jointly a Gaussian distribution).

My questions are:

Can the algorithms like junction tree propagation be applicable as it is for the discrete variable Bayesian Networks, in the case of the Gaussian Bayesian Networks?

If no, which algorithms are applicable in the case of the Gaussian Bayesian Networks?

Is there any complexity proof for the Partial Abductive Inference in case of Gaussian Bayesian Networks (As it is known that the task is NP-hard in case of discrete variable Bayesian Networks)?

Can the Evolutionary algorithms or MCMC sampling criteria be applied for approximate Partial Abductive Inference in Gaussian Bayesian Networks?

I will be highly grateful to you all for any help. Thanks in advance...