# Using a bounded variable within a Mixture

**URL:** <https://discourse.pymc.io/t/using-a-bounded-variable-within-a-mixture/766>\
**Category:** Questions\
**Created:** [January 20, 2018, 5:06am UTC](https://discourse.pymc.io/t/using-a-bounded-variable-within-a-mixture/766 "2018-01-20T05:06:52Z")\
**Posts on this page:** 9\
**Page:** 1

<div class="post-metadata">

**Author:** ![mullachv](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/mullachv/32/400_2.png) [@mullachv](https://discourse.pymc.io/u/mullachv)\
**Post date:** [January 20, 2018, 5:06am UTC](https://discourse.pymc.io/t/using-a-bounded-variable-within-a-mixture/766/1 "2018-01-20T05:06:53Z")

</div>

I am trying to use a Bounded variable within a Mixture model. I have the following so far:

```auto

with pm.Model() as model:
    alpha = pm.Gamma('alpha', 1,1)
    beta = pm.Beta('beta', 1, alpha, shape=K)
    w = pm.Deterministic('w', stick_breaking(beta))
    #a = pm.Uniform('a', 0, 50, shape=K)
    #b = pm.Uniform('b', 0, 50, shape=K)
    mu = pm.Uniform('mu', 0, 50, shape=K)
    bp = pm.Bound(pm.Poisson, lower=1)('bp', mu=mu)
    x = pm.Mixture('obs', w, bp.dist(), observed=df['x1'].values)

```

It throws the following error:

```auto
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
<ipython-input-121-ee34f0f15713> in <module>()
      8 mu = pm.Uniform('mu', 0, 50, shape=K)
      9 bp = pm.Bound(pm.Poisson, lower=1)('bp', mu=mu)
---> 10 x = pm.Mixture('obs', w, bp.dist(), observed=df['x1'].values)

AttributeError: 'FreeRV' object has no attribute 'dist'

```

How do I correct this?

---

<div class="post-metadata">

**Author:** ![aloctavodia](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/aloctavodia/32/8642_2.png) [@aloctavodia](https://discourse.pymc.io/u/aloctavodia)\
**Post date:** [January 24, 2018, 2:26pm UTC](https://discourse.pymc.io/t/using-a-bounded-variable-within-a-mixture/766/2 "2018-01-24T14:26:02Z")

</div>

I think you should write `bp` as `bp = pm.Bound(pm.Poisson, lower=1).dist(mu=mu)`

---

<div class="post-metadata">

**Author:** ![mullachv](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/mullachv/32/400_2.png) [@mullachv](https://discourse.pymc.io/u/mullachv)\
**Post date:** [January 24, 2018, 3:38pm UTC](https://discourse.pymc.io/t/using-a-bounded-variable-within-a-mixture/766/3 "2018-01-24T15:38:44Z")

</div>

@aloctavodia  
You mean like this?

```auto

with pm.Model() as model:
    alpha = pm.Gamma('alpha', 1,1)
    beta = pm.Beta('beta', 1, alpha, shape=K)
    w = pm.Deterministic('w', stick_breaking(beta))
    #a = pm.Uniform('a', 0, 50, shape=K)
    #b = pm.Uniform('b', 0, 50, shape=K)
    mu = pm.Uniform('mu', 0, 50, shape=K)
    bp = pm.Bound(pm.Poisson, lower=1).dist( mu=mu)
    #x = pm.Mixture('obs', w, pm.Poisson.dist(mu), observed=df['x1'].values)
    x = pm.Mixture('obs', w, bp, observed=df['x1'].values)

```

I get the following error:

```auto
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
C:\Anaconda3\envs\stpy35\lib\site-packages\pymc3\distributions\mixture.py in _comp_modes(self)
     95 try:
---> 96 return tt.as_tensor_variable(self.comp_dists.mode)
     97 except AttributeError:

AttributeError: '_DiscreteBounded' object has no attribute 'mode'

During handling of the above exception, another exception occurred:

TypeError Traceback (most recent call last)
<ipython-input-15-811a1e7927a9> in <module>()
      9 bp = pm.Bound(pm.Poisson, lower=1).dist( mu=mu)
     10 #x = pm.Mixture('obs', w, pm.Poisson.dist(mu), observed=df['x1'].values)
---> 11 x = pm.Mixture('obs', w, bp, observed=df['x1'].values)

C:\Anaconda3\envs\stpy35\lib\site-packages\pymc3\distributions\distribution.py in __new__ (cls, name, *args, **kwargs)
     34 raise TypeError("observed needs to be data but got: {}".format(type(data)))
     35 total_size = kwargs.pop('total_size', None)
---> 36 dist = cls.dist(*args, **kwargs)
     37 return model.Var(name, dist, data, total_size)
     38 else:

C:\Anaconda3\envs\stpy35\lib\site-packages\pymc3\distributions\distribution.py in dist(cls, *args, **kwargs)
     45 def dist(cls, *args, **kwargs):
     46 dist = object. __new__ (cls)
---> 47 dist. __init__ (*args, **kwargs)
     48 return dist
     49 

C:\Anaconda3\envs\stpy35\lib\site-packages\pymc3\distributions\mixture.py in __init__ (self, w, comp_dists, *args, **kwargs)
     62 
     63 try:
---> 64 comp_modes = self._comp_modes()
     65 comp_mode_logps = self.logp(comp_modes)
     66 self.mode = comp_modes[tt.argmax(w * comp_mode_logps, axis=-1)]

C:\Anaconda3\envs\stpy35\lib\site-packages\pymc3\distributions\mixture.py in _comp_modes(self)
     96 return tt.as_tensor_variable(self.comp_dists.mode)
     97 except AttributeError:
---> 98 return tt.stack([comp_dist.mode for comp_dist in self.comp_dists],
     99 axis=1)
    100 

TypeError: '_DiscreteBounded' object is not iterable

```

---

<div class="post-metadata">

**Author:** ![aloctavodia](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/aloctavodia/32/8642_2.png) [@aloctavodia](https://discourse.pymc.io/u/aloctavodia)\
**Post date:** [January 24, 2018, 4:08pm UTC](https://discourse.pymc.io/t/using-a-bounded-variable-within-a-mixture/766/4 "2018-01-24T16:08:06Z")

</div>

ups!

I guess this will also fail, right?

```python
bp = pm.Bound(pm.Poisson, lower=1).dist(mu=mu, shape=K)

```

so, try this

```python
bp = [pm.Bound(pm.Poisson, lower=1).dist(mu=mu[i]) for i in range(K)]

```

---

<div class="post-metadata">

**Author:** ![mullachv](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/mullachv/32/400_2.png) [@mullachv](https://discourse.pymc.io/u/mullachv)\
**Post date:** [January 24, 2018, 6:45pm UTC](https://discourse.pymc.io/t/using-a-bounded-variable-within-a-mixture/766/5 "2018-01-24T18:45:24Z")

</div>

@aloctavodia  
Yes, that second one works. Thank you very much.

However, how do I refer to the variable by name? So I can grab it from trace, like so trace[‘myvar’]. Here is the code in case someone else needs to use similar tricks:

```auto
with pm.Model() as model:
    alpha = pm.Gamma('alpha', 1,1)
    beta = pm.Beta('beta', 1, alpha, shape=K)
    w = pm.Deterministic('w', stick_breaking(beta))
    #a = pm.Uniform('a', 0, 50, shape=K)
    #b = pm.Uniform('b', 0, 50, shape=K)
    mu = pm.Uniform('mu', 0, 50, shape=K)
    bp = [pm.Bound(pm.Poisson, lower=1).dist( mu=mu[i]) for i in range(K)] 
    #x = pm.Mixture('obs', w, pm.Poisson.dist(mu), observed=df['x1'].values)
    x = pm.Mixture('obs', w, bp, observed=df['x1'].values)

```

---

<div class="post-metadata">

**Author:** ![aloctavodia](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/aloctavodia/32/8642_2.png) [@aloctavodia](https://discourse.pymc.io/u/aloctavodia)\
**Post date:** [January 24, 2018, 6:50pm UTC](https://discourse.pymc.io/t/using-a-bounded-variable-within-a-mixture/766/6 "2018-01-24T18:50:52Z")

</div>

Not sure if that’s possible with the current implementation of `Mixture`. Maybe @AustinRochford has a solution.

---

<div class="post-metadata">

**Author:** ![mullachv](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/mullachv/32/400_2.png) [@mullachv](https://discourse.pymc.io/u/mullachv)\
**Post date:** [January 24, 2018, 6:52pm UTC](https://discourse.pymc.io/t/using-a-bounded-variable-within-a-mixture/766/7 "2018-01-24T18:52:53Z")

</div>

ok, thank you @aloctavodia. Is it possible for me to message you in private, so perhaps you could show me around the codebase and that way help myself quicker and perhaps other folks as well?

---

<div class="post-metadata">

**Author:** ![aloctavodia](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/aloctavodia/32/8642_2.png) [@aloctavodia](https://discourse.pymc.io/u/aloctavodia)\
**Post date:** [January 24, 2018, 7:08pm UTC](https://discourse.pymc.io/t/using-a-bounded-variable-within-a-mixture/766/8 "2018-01-24T19:08:04Z")

</div>

You can contact me in private, no problem. But if you have a question that may also help others, is better to ask it publicly so other can benefit from it and also you may get a better/faster answer from others than from me.

---

<div class="post-metadata">

**Author:** ![AustinRochford](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/austinrochford/32/92_2.png) [@AustinRochford](https://discourse.pymc.io/u/AustinRochford)\
**Post date:** [January 24, 2018, 7:18pm UTC](https://discourse.pymc.io/t/using-a-bounded-variable-within-a-mixture/766/9 "2018-01-24T19:18:27Z")

</div>

I think `bp` needs to have `shape` \> 1 in order for a mixture to make sense.