Performance speedup for updating posterior with new data

Questions
2

I had a look at your code. Unfortunately, I dont see much more room to improve the speed, as the Interpolation rv always need to reinitialized, and the bottom neck in the evaluation of scipy Spline smooth function is also difficult to improve without rewriting everything in theano.

Alternatively, if you are happy with using some other distribution as an approximation, it would simplify the code a lot:

new_data = pd.DataFrame(data=[generate_data() for _ in range(1)], columns=generate_data().keys())
output_shared = theano.shared(new_data['output'].values)
x1_shared = theano.shared(new_data['x1'].values)
    
mu0 = theano.shared(trace['alpha_0'].mean(), name='hyper_mu0')
sd0 = theano.shared(trace['alpha_0'].std(), name='hyper_sd0')
mu1 = theano.shared(trace['alpha_1'].mean(), name='hyper_mu1')
sd1 = theano.shared(trace['alpha_1'].std(), name='hyper_sd1')

with pm.Model() as update_model:
    alpha_0 = pm.StudentT('alpha_0', mu=mu0, sd=sd0, nu=1, testval=0.)
    alpha_1 = pm.StudentT('alpha_1', mu=mu1, sd=sd1, nu=1, testval=0.)
    theta = (alpha_0 + alpha_1 * x1_shared)

    likelihood = pm.Poisson(
        'output',
        mu=np.exp(theta),
        observed=output_shared,
    )
    trace = pm.sample(1000)
    traces.append(trace)
    
for _ in range(1, 10):
    new_data = pd.DataFrame(data=[generate_data() for _ in range(1)], columns=generate_data().keys())
    output_shared.set_value(new_data['output'].values)
    x1_shared.set_value(new_data['x1'].values)
    mu0.set_value(trace['alpha_0'].mean())
    sd0.set_value(trace['alpha_0'].std())
    mu1.set_value(trace['alpha_1'].mean())
    sd1.set_value(trace['alpha_1'].std())
    
    with update_model:
        trace = pm.sample(1000)
        traces.append(trace)
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