Bayesian calibration with exterior model

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Hi k.f

When it comes to fitting non-standard models like this piecewise function, things get a bit tricker. To make computation efficient, pymc depends on being able to represent your model symbolically (like as an algebra problem) and the extract derivates. It does all this with a library called pytensor. So your choices are broadly to rewrite your exterior_model in pytensor code or to wrap your exterior_model in a pytensor operation. Here is the guide that walks you through the wrapping process:

and here is an example of how you might rewrite your exterior_model as a pytensor function:

with pm.Model() as model:
    # Prior parameter
    teta = pm.Normal('teta', mu=prior_param, sigma=1)
  
    exterior_model = pt.switch(pt.gt(teta,2),teta * 3 + 2,teta * 1 + 2)

    model_mean = pm.Deterministic('mu', exterior_model)
    #Likelihood
    likelihood = pm.Normal("y", mu = model_mean, sigma=1, observed=observation)

    #posterior
    trace = pm.sample(1000, cores=1)
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