Even after reading the FAQ, still having trouble with a "Bad initial energy" error

Questions
1

Hi there,

I know this is a question on the FAQ, so please point me back there if there is something obvious that I missed.

I have a model that is generating a ParallelSamplingError: Bad initial energy error. Here it is:

notifications_sent = 2250380
r_o = 687795
v_o_and_r_o = 26198
v_o = 248
with pm.Model() as reception_model:
    alpha = pm.Beta('alpha', alpha=1, beta=1)
    beta  = pm.Beta('beta', alpha=1, beta=1)
    gamma = pm.Beta('gamma', alpha=1, beta=1)

    r = pm.Binomial('received', n=notifications_sent, p=alpha)
    r_r = pm.Binomial('received_recorded', n=r, p=gamma, observed=r_o+v_o_and_r_o)
    
    v = pm.Binomial('viewed', n=r, p=beta)
    v_r = pm.Binomial('viewed_recorded', n=v, p=gamma, observed=v_o+v_o_and_r_o)
    
    trace = pm.sample(1000, tune=500, chains=2)

The reception_model.check_test_point() has -inf on a few RVs as expected:

alpha_logodds__     -1.39
beta_logodds__      -1.39
gamma_logodds__     -1.39
received            -5.23
viewed              -4.88
received_recorded    -inf
viewed_recorded      -inf

Checking reception_model.test_point reveals this:

{'alpha_logodds__': array(0., dtype=float32),
 'beta_logodds__': array(0., dtype=float32),
 'gamma_logodds__': array(0., dtype=float32),
 'received': array(11078, dtype=int16),
 'viewed': array(5539, dtype=int16)}

So the logodds for received_recorded and viewed_recorded result in -inf because n for each Binomial is fewer than the observed values. Following a recommendation from a FAQ answer, one approach is to set the testval for received and viewed so that they are at least as large as the observed values. So I updated the model like so:

notifications_sent = 2250380
r_o = 687795
v_o_and_r_o = 26198
v_o = 248
with pm.Model() as reception_model:
    alpha = pm.Beta('alpha', alpha=1, beta=1)
    beta  = pm.Beta('beta', alpha=1, beta=1)
    gamma = pm.Beta('gamma', alpha=1, beta=1)

    r = pm.Binomial('received', n=notifications_sent, p=alpha, testval=r_o+v_o_and_r_o+1000, dtype='int64')
    r_r = pm.Binomial('received_recorded', n=r, p=gamma, observed=r_o+v_o_and_r_o, dtype='int64')
    
    v = pm.Binomial('viewed', n=r, p=beta, testval=v_o+v_o_and_r_o+1000, dtype='int64')
    v_r = pm.Binomial('viewed_recorded', n=v, p=gamma, observed=v_o+v_o_and_r_o, dtype='int64')

This makes things worse :slight_smile:. reception_model.check_test_point() returns

alpha_logodds__         -1.39
beta_logodds__          -1.39
gamma_logodds__         -1.39
received                 -inf
viewed                   -inf
received_recorded        -inf
viewed_recorded     -14734.69

the test points are:

{'alpha_logodds__': array(0., dtype=float32),
 'beta_logodds__': array(0., dtype=float32),
 'gamma_logodds__': array(0., dtype=float32),
 'received': array(714993),
 'viewed': array(27446)}

So I guess at this point my next step should be to re-think my priors or my model structure. But I’m not sure how to think through what’s going wrong with my current model. I’d appreciate any guidance on nexts steps. Hopefully it’s just something I missed in the FAQ!

Cheers,
Jesse

2

An update:

Upon closer inspection of model.test_point in the initial model, it looks like the received test point is roughly notifications_sent * .5 / 100 and the viewed test point is roughly notifications_sent * .5 * .5 / 100. So it seems there is some kind of scaling happening in the binomial RV.

When I scale my data by 100 the model runs without the “Bad initial energy” error. Here’s the update:

notifications_sent = 2250380 / 100
r_o = 687795 / 100
v_o_and_r_o = 26198 / 100
v_o = 248 / 100
with pm.Model() as reception_model:
    alpha = pm.Beta('alpha', alpha=1, beta=1)
    beta  = pm.Beta('beta', alpha=1, beta=1)
    gamma = pm.Beta('gamma', alpha=1, beta=1)


    r = pm.Binomial('received', n=notifications_sent, p=alpha, dtype='int64')
    r_r = pm.Binomial('received_recorded', n=r, p=gamma, observed=r_o+v_o_and_r_o, dtype='int64')
    
    v = pm.Binomial('viewed', n=r, p=beta, dtype='int64')
    v_r = pm.Binomial('viewed_recorded', n=v, p=gamma, observed=v_o+v_o_and_r_o, dtype='int64')
    
    trace = pm.sample(1000, tune=1000, chains=2)
    pm.traceplot(trace, var_names=['alpha', 'beta', 'gamma'])

This doesn’t converge so it looks like I still have more work to do. I’m curious why what I did seems to get around the “Bad initial energy” issue. Is my guess at internal scaling correct?

3

This thread may be relevant: Negative binomial returning -inf logp

4

Yep. This did the trick. Setting theano.config.floatX to “float64” allowed the sampler to run with out the “Bad initial energy” error and without having to scale. Thanks for pointing me to this!