# Bayesian IRT Pymc3 - Parameter inference

**URL:** <https://discourse.pymc.io/t/bayesian-irt-pymc3-parameter-inference/4938>\
**Category:** Questions\
**Created:** [April 26, 2020, 5:32am UTC](https://discourse.pymc.io/t/bayesian-irt-pymc3-parameter-inference/4938 "2020-04-26T05:32:23Z")\
**Posts on this page:** 2\
**Page:** 1

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**Author:** ![pbcacao](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/pbcacao/32/2672_2.png) [@pbcacao](https://discourse.pymc.io/u/pbcacao)\
**Post date:** [April 26, 2020, 5:32am UTC](https://discourse.pymc.io/t/bayesian-irt-pymc3-parameter-inference/4938/1 "2020-04-26T05:32:23Z")

</div>

I would like to estimate IRT model using PyMC3.  
I generated data with the following distribution:

```
alpha_fix = 4
beta_fix = 100
theta= np.random.normal(100,15,1000)
prob = np.exp(alpha_fix*(theta-beta_fix))/(1+np.exp(alpha_fix*(theta-beta_fix)))
prob_tt = tt._shared(prob)

```

Then I created a model using PyMC3 to infer the parameter:

```
irt = pm.Model()
with irt:
# Priors
alpha = pm.Normal('alpha',mu = 4 , tau = 1)
beta = pm.Normal('beta',mu = 100 , tau = 15)
thau = pm.Normal('thau' ,mu = 100 , tau = 15)

# Modelling
p = pm.Deterministic('p',tt.exp(alpha*(thau-beta))/(1+tt.exp(alpha*(thau-beta))))

out = pm.Normal('o',p,observed = prob_tt)

```

Then I infer through the model:

```
with irt: 
    mean_field = pm.fit(10000,method='advi', callbacks=[pm.callbacks.CheckParametersConvergence(diff='absolute')])

```

Finally, Sample from the model to get compute posterior:

 ![image](https://canada1.discourse-cdn.com/flex036/uploads/pymc3/original/2X/4/433986044a577976b5f67e8e374209dbf70a9918.png)

```
pm.plot_posterior(mean_field.sample(1000), color='LightSeaGreen');

```

But the results of the “alpha” (mean of 2.2) is relatively far from the expected one (4) even though the prior on alpha was well-calibrated.

Would you have an idea of the origin of this gap and how to fix it?

Thanks a lot,

---

<div class="post-metadata">

**Author:** ![nkaimcaudle](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/nkaimcaudle/32/2142_2.png) [@nkaimcaudle](https://discourse.pymc.io/u/nkaimcaudle)\
**Post date:** [April 27, 2020, 12:31am UTC](https://discourse.pymc.io/t/bayesian-irt-pymc3-parameter-inference/4938/2 "2020-04-27T00:31:20Z")

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Hi

I cannot offer a full answer but I noticed that the sampling stops after 10,000 before the convergence call back kicks in. I increased the n iter to 100,000 and the convergence halts sampling after around 50k or 60k steps.

Now the alpha is closer to 3.4 with approx 25% of the mass above 4.0

 ![2020-04-27_08-22](https://canada1.discourse-cdn.com/flex036/uploads/pymc3/original/2X/2/2821eefeb9386b50f173eb0a552761e38b5ff91b.png)