Including Potentials of Neighbours

Questions
3

The Autologistic is not a term I’ve heard except in terms of autoregressive neural models. The most appropriate one I think that is relevant is Markov Random Fields. The way I like to think of it is more of a binary segmentation problem where only some examples are observed. I have implemented a version using a binary glm without the condition on neighbours. Which worked fairly well as there was no real spatial information encoded. e.g.

with pm.Model() as model:
    sd = pm.Exponential('sd',lam=3.0)
    mean = pm.Normal('mu' ,mu=0., sd=10.)
    
    data={
    'x' : x.flatten(),
    'y' : observations.flatten()
    }
    prior= {
        'Intercept' : pm.Normal.dist(mu=mean, sd=sd),
        'x' : pm.Normal.dist(mu=mean, sd=sd)
    }
    pm.GLM.from_formula('y ~ x', data, family=pm.glm.families.Binomial(), priors=prior)
    trace = pm.sample(1000,init='adapt_diag')

This results in a very stark classification, spatially.
I was trying to implement something that now included spatial information, such as the neighbouring potentials so that neighbouring pixels would be a bit more likely to be uncertain as to the classification.