# Why does my model show logp of zero?

**URL:** <https://discourse.pymc.io/t/why-does-my-model-show-logp-of-zero/5258>\
**Category:** Questions\
**Created:** [June 11, 2020, 11:14am UTC](https://discourse.pymc.io/t/why-does-my-model-show-logp-of-zero/5258 "2020-06-11T11:14:41Z")\
**Posts on this page:** 4\
**Page:** 1

<div class="post-metadata">

**Author:** ![bridgeland](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/bridgeland/32/2773_2.png) [@bridgeland](https://discourse.pymc.io/u/bridgeland)\
**Post date:** [June 11, 2020, 11:14am UTC](https://discourse.pymc.io/t/why-does-my-model-show-logp-of-zero/5258/1 "2020-06-11T11:14:41Z")

</div>

My simple model is exhibiting a logp of zero. It seems impossible that there is zero likelihood of the observed data.

The model has two observed variables — one a normal and the other a binomial. There are five other random variables.

```
naive_perceived = 0.4
opportunities = 61
true_pursued = 45
true_won = 7

with pm.Model() as model:
    winnable_p = pm.Uniform('winnable_p', 0, 1) 
    skill = pm.Beta('skill', 2.0, 5.0)
    winnable = pm.Binomial('winnable', opportunities, winnable_p) 
    winnable_pursuit_p = pm.Deterministic(
        'winnable_pursuit_p', 
        naive_perceived * (1 - skill) + skill)
    unwinnable_pursuit_p = pm.Deterministic(
        'unwinnable_pursuit_p',
        naive_perceived * (1 - skill))
    winnable_pursued = pm.Binomial('winnable_pursued', winnable, winnable_pursuit_p)
    unwinnable_pursued = pm.Binomial('unwinnable_pursued', opportunities - winnable, unwinnable_pursuit_p)
    pursued = pm.Normal('pursued', winnable_pursued + unwinnable_pursued, sd=1, observed=true_pursued) 
    won = pm.Binomial('won', winnable_pursued, skill, observed=true_won) 
    trace = pm.sample(25000, step=pm.NUTS())

```

Diagram, with double-line border used to tag the two deterministic variables.

 ![simple_zero_logp](https://canada1.discourse-cdn.com/flex036/uploads/pymc3/original/2X/8/81ffc3ebae48694dc97fb636b9c21dbd249db090.png)

The model logp is zero throughout:

 ![image](https://canada1.discourse-cdn.com/flex036/uploads/pymc3/original/2X/e/e673874cc4167446fa44c1de86fd18c098434fb8.png)

What am I doing wrong?

(Yes, this is the same question as [this one](https://discourse.pymc.io/t/what-does-zero-logp-mean/5235), a question that attracted no responses — although @junpenglao kindly corrected its category. This version shows a far simpler model that exhibits the same problem, and a diagram. Arguably my earlier question was too taxing, asking the wise pymc3 community to first understand what I was trying to do before advising me on what I was doing wrong. Sadly once I realized my mistake, the duration for editing the original question had expired.)

---

<div class="post-metadata">

**Author:** ![junpenglao](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/junpenglao/32/8_2.png) [@junpenglao](https://discourse.pymc.io/u/junpenglao)\
**Post date:** [June 11, 2020, 12:31pm UTC](https://discourse.pymc.io/t/why-does-my-model-show-logp-of-zero/5258/2 "2020-06-11T12:31:31Z")

</div>

Seems the sampler is stuck at the initial position and does not move, usually, model with discrete free parameter is pretty difficult to inference (in this case, `Binomial` nodes with no observed).  
There is no obvious solution I can see right away - maybe approximate it with a Beta distribution?

---

<div class="post-metadata">

**Author:** ![junpenglao](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/junpenglao/32/8_2.png) [@junpenglao](https://discourse.pymc.io/u/junpenglao)\
**Post date:** [June 11, 2020, 12:40pm UTC](https://discourse.pymc.io/t/why-does-my-model-show-logp-of-zero/5258/3 "2020-06-11T12:40:27Z")

</div>

Actually, running the model the trace look ok - the problem here that `trace['model_logp']` is all zeros is a bug ([https://github.com/pymc-devs/pymc3/issues/3188](https://github.com/pymc-devs/pymc3/issues/3188)) that have not been fixed yet.

For now you can do:

```auto
logp_fn = model.logp

model_logp = np.zeros((25000, trace.nchains))
for i in trace.chains:
  for s in range(25000):
    model_logp[s, i] = logp_fn(trace.point(s, i))

plt.plot(model_logp, alpha=.2);

```

---

<div class="post-metadata">

**Author:** ![bridgeland](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/bridgeland/32/2773_2.png) [@bridgeland](https://discourse.pymc.io/u/bridgeland)\
**Post date:** [June 12, 2020, 9:09am UTC](https://discourse.pymc.io/t/why-does-my-model-show-logp-of-zero/5258/4 "2020-06-12T09:09:52Z")

</div>

That explains it. From the referenced issue, it looks like model\_logp is only implemented in two samplers (NUTS and HMC) so far. Maybe not even a bug, just a feature that has not yet been fully implemented.