# When treating a small data, how to choose a model

**URL:** <https://discourse.pymc.io/t/when-treating-a-small-data-how-to-choose-a-model/12240>\
**Category:** General\
**Tags:** modeling\
**Created:** [June 1, 2023, 4:31am UTC](https://discourse.pymc.io/t/when-treating-a-small-data-how-to-choose-a-model/12240 "2023-06-01T04:31:06Z")\
**Posts on this page:** 4\
**Page:** 1

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**Author:** ![Toma](https://avatars.discourse-cdn.com/v4/letter/t/c6cbf5/32.png) [@Toma](https://discourse.pymc.io/u/Toma)\
**Post date:** [June 1, 2023, 4:31am UTC](https://discourse.pymc.io/t/when-treating-a-small-data-how-to-choose-a-model/12240/1 "2023-06-01T04:31:06Z")

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Hello everyone.

I’m a junior data analyst using Bayesian modeling.  
I have a question about the way choosing model and creating a more accurate model.

Now, I’m trying to use Gaussian Mixture modeling to derive the posterior distribution  
the below is the status of the problem I’m facing.

**Status**

- the amount of the data I use as explanatory variable is 365 per variable
- the distribution of the target variable has a two peak, so I made two prior distribution per variable.
- the range of one posterior distribution ‘beta’ is about -20 to less than 20, and the mean is around zero
- about the other, the range is also around zero.

For this problem, I’ve just tried a Gaussian mixture regression model with pymc3.  
the below is the code of this.

```auto
type or paste code here
with pm.Model() as model:
        weight = pm.Dirichlet('weight', a=np.array([1, 1]), shape = (1, 2))
        alpha = pm.Normal('alpha', mu = 0, sigma = 10, shape = (1, 2))
        beta = pm.Normal('beta1', mu = 0, sigma = 10, shape = (1, 2))
        sigma = pm.HalfNormal('sigma', sigma=10, shape=2)
      
        mu = alpha + beta1 * X_1['last_year_pb_mean'].values[:, None]
    
        pv_obs = pm.NormalMixture('pb_obs', w = weight, mu=mu, sigma=sigma, observed=np.log(PRTIMES['pb_rounded']))
        trace = pm.sample(2000,tune= 1000,target_accept= 0.99, cores = 1)
        pm.plot_trace(trace, compact=True)
        pm.plot_posterior(trace, var_names=['beta'], hdi_prob=0.95)

        y_1 = pm.sample_posterior_predictive(trace, samples=1000, model=model)
        y_pred_1 = y_1['pb_obs']

pm.traceplot(trace)

```

but the result of this is so bad, the posterior is far from the actual model.(figure2, the left is posterior and the right is actual.)

I keeps searching some information, I can’t have find solution.

how can the problem be solved?

here is the results, figures and the waic of this model is 2.529136938170937

| | mean | sd | hdi\_3% | hdi\_97% | mcse\_mean | mcse\_sd | ess\_bulk | ess\_tail | r\_hat |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| alpha[0, 0] | 0.262 | 9.994 | -18.358 | 18.348 | 0.174 | 0.158 | 3313.0 | 2881.0 | 1.0 |
| alpha[0, 1] | 3.329 | 0.009 | 3.312 | 3.345 | 0.000 | 0.000 | 2765.0 | 2383.0 | 1.0 |
| beta1[0, 0] | -0.139 | 9.907 | -17.974 | 18.936 | 0.190 | 0.161 | 2739.0 | 2448.0 | 1.0 |
| beta1[0, 1] | 0.058 | 0.009 | 0.040 | 0.073 | 0.000 | 0.000 | 3536.0 | 2517.0 | 1.0 |
| weight[0, 0] | 0.003 | 0.003 | 0.000 | 0.008 | 0.000 | 0.000 | 2776.0 | 1736.0 | 1.0 |
| weight[0, 1] | 0.997 | 0.003 | 0.992 | 1.000 | 0.000 | 0.000 | 2776.0 | 1736.0 | 1.0 |
| sigma[0] | 7.891 | 6.236 | 0.006 | 19.008 | 0.112 | 0.079 | 1480.0 | 654.0 | 1.0 |
| sigma[1] | 0.171 | 0.006 | 0.159 | 0.183 | 0.000 | 0.000 | 3503.0 | 2466.0 | 1.0 |

**figure0**

 ![output](https://canada1.discourse-cdn.com/flex036/uploads/pymc3/original/2X/e/e47808a0945ad80b8f31a11355c5d301f8fca268.png)

**figure1**

 ![output1](https://canada1.discourse-cdn.com/flex036/uploads/pymc3/original/2X/c/c4acef933cef764cb968c3fec3a70d15b43c8265.png)

**figure2**

 ![output2](https://canada1.discourse-cdn.com/flex036/uploads/pymc3/original/2X/7/7c56a8fa2fa9074cfd0d75ceb6f676a2c9025a78.png)

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<div class="post-metadata">

**Author:** ![cluhmann](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/cluhmann/32/3083_2.png) [@cluhmann](https://discourse.pymc.io/u/cluhmann)\
**Post date:** [June 2, 2023, 3:03am UTC](https://discourse.pymc.io/t/when-treating-a-small-data-how-to-choose-a-model/12240/2 "2023-06-02T03:03:28Z")

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Welcome!

Do you have any simulated data to work with? It is often suggested to develop models (at least initially) using data where you have full control (or knowledge) over the underlying generative process.

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<div class="post-metadata">

**Author:** ![Toma](https://avatars.discourse-cdn.com/v4/letter/t/c6cbf5/32.png) [@Toma](https://discourse.pymc.io/u/Toma)\
**Post date:** [June 2, 2023, 4:36am UTC](https://discourse.pymc.io/t/when-treating-a-small-data-how-to-choose-a-model/12240/3 "2023-06-02T04:36:13Z")

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Thank for answering!

No, I don’t have simulation data.

That looks a meaningful discovery for me.  
I thank for your advice.

I’ll try to make this.  
Then, if I’m troubled, can I ask you a question?

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<div class="post-metadata">

**Author:** ![cluhmann](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/cluhmann/32/3083_2.png) [@cluhmann](https://discourse.pymc.io/u/cluhmann)\
**Post date:** [June 2, 2023, 1:58pm UTC](https://discourse.pymc.io/t/when-treating-a-small-data-how-to-choose-a-model/12240/4 "2023-06-02T13:58:47Z")

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> [@Toma](#):
>
> the posterior is far from the actual model

If you don’t have the true, underlying model, then I’m not sure what to make of this statement.

> [@Toma](#):
>
> Then, if I’m troubled, can I ask you a question?

Of course!