pythonbayesianpymc3pymc

Incremental model update with PyMC3


Is it possible to incrementally update a model in pyMC3. I can currently find no information on this. All documentation is always working with a priori known data.

But in my understanding, a Bayesian model also means being able to update a belief. Is this possible in pyMC3? Where can I find info in this?

Thank you :)


Solution

  • Following @ChrisFonnesbeck's advice, I wrote a small tutorial notebook about incremental prior updating. It can be found here:

    https://github.com/pymc-devs/pymc-examples/blob/main/examples/howto/updating_priors.ipynb

    Basically, you need to wrap your posterior samples in a custom Continuous class that computes the KDE from them. The following code does just that:

    def from_posterior(param, samples):
    
        class FromPosterior(Continuous):
    
            def __init__(self, *args, **kwargs):
                self.logp = logp
                super(FromPosterior, self).__init__(*args, **kwargs)
    
        smin, smax = np.min(samples), np.max(samples)
        x = np.linspace(smin, smax, 100)
        y = stats.gaussian_kde(samples)(x)
        y0 = np.min(y) / 10 # what was never sampled should have a small probability but not 0
    
        @as_op(itypes=[tt.dscalar], otypes=[tt.dscalar])
        def logp(value):
            # Interpolates from observed values
            return np.array(np.log(np.interp(value, x, y, left=y0, right=y0)))
    
        return FromPosterior(param, testval=np.median(samples))
    

    Then you define the prior of your model parameter (say alpha) by calling the from_posterior function with the parameter name and the trace samples from the posterior of the previous iteration:

    alpha = from_posterior('alpha', trace['alpha'])