# Creating a Dirichlet distribution from a random variable

**URL:** <https://discourse.pymc.io/t/creating-a-dirichlet-distribution-from-a-random-variable/555>\
**Category:** Questions\
**Created:** [November 14, 2017, 4:18pm UTC](https://discourse.pymc.io/t/creating-a-dirichlet-distribution-from-a-random-variable/555 "2017-11-14T16:18:09Z")\
**Posts on this page:** 4\
**Page:** 1

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**Author:** ![bicycle1885](https://avatars.discourse-cdn.com/v4/letter/b/ba9def/32.png) [@bicycle1885](https://discourse.pymc.io/u/bicycle1885)\
**Post date:** [November 14, 2017, 4:18pm UTC](https://discourse.pymc.io/t/creating-a-dirichlet-distribution-from-a-random-variable/555/1 "2017-11-14T16:18:09Z")

</div>

Hi,

I’d like to compile a model that uses a Dirichlet distribution that takes a random variable as a parameter. I tried:

```auto
import pymc3 as pm
import numpy as np

def sigmoid(x):
    return 1 / (1 + np.exp(-x))

with pm.Model() as model:
    x = pm.Normal("x")
    s = sigmoid(x)
    w = pm.Dirichlet.dist(np.array([1 - s, s]))
    pm.Mixture("y", w, [pm.Normal(mu=0), pm.Normal(mu=3)], observed=[0.1, 2.9])

```

But it failed to compile with a long exception message (pasted at the end). How can I create a random simplex that can be passed to a Dirichlet distribution as a parameter?

```auto
---------------------------------------------------------------------------
KeyError Traceback (most recent call last)
~/miniconda3/lib/python3.6/site-packages/theano/tensor/type.py in dtype_specs(self)
    269 'complex64': (complex, 'theano_complex64', 'NPY_COMPLEX64')
--> 270 }[self.dtype]
    271 except KeyError:

KeyError: 'object'

During handling of the above exception, another exception occurred:

TypeError Traceback (most recent call last)
~/miniconda3/lib/python3.6/site-packages/theano/tensor/basic.py in constant_or_value(x, rtype, name, ndim, dtype)
    249 rval = rtype(
--> 250 TensorType(dtype=x_.dtype, broadcastable=bcastable),
    251 x_.copy(),

~/miniconda3/lib/python3.6/site-packages/theano/tensor/type.py in __init__ (self, dtype, broadcastable, name, sparse_grad)
     50 self.broadcastable = tuple(bool(b) for b in broadcastable)
---> 51 self.dtype_specs() # error checking is done there
     52 self.name = name

~/miniconda3/lib/python3.6/site-packages/theano/tensor/type.py in dtype_specs(self)
    272 raise TypeError("Unsupported dtype for %s: %s"
--> 273 % (self. __class__. __name__ , self.dtype))
    274 

TypeError: Unsupported dtype for TensorType: object

During handling of the above exception, another exception occurred:

TypeError Traceback (most recent call last)
~/miniconda3/lib/python3.6/site-packages/theano/tensor/basic.py in as_tensor_variable(x, name, ndim)
    205 try:
--> 206 return constant(x, name=name, ndim=ndim)
    207 except TypeError:

~/miniconda3/lib/python3.6/site-packages/theano/tensor/basic.py in constant(x, name, ndim, dtype)
    263 ret = constant_or_value(x, rtype=TensorConstant, name=name, ndim=ndim,
--> 264 dtype=dtype)
    265 

~/miniconda3/lib/python3.6/site-packages/theano/tensor/basic.py in constant_or_value(x, rtype, name, ndim, dtype)
    258 except Exception:
--> 259 raise TypeError("Could not convert %s to TensorType" % x, type(x))
    260 

TypeError: ('Could not convert [Elemwise{sub,no_inplace}.0 Elemwise{true_div,no_inplace}.0] to TensorType', <class 'numpy.ndarray'>)

During handling of the above exception, another exception occurred:

AsTensorError Traceback (most recent call last)
<ipython-input-172-a6b8b36b0427> in <module>()
      5 x = pm.Normal("x")
      6 s = sigmoid(x)
----> 7 w = pm.Dirichlet.dist(np.array([1 - s, s]))
      8 pm.Mixture("y", w, [pm.Normal(mu=0), pm.Normal(mu=3)], observed=[0.1, 2.9])

~/miniconda3/lib/python3.6/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 

~/miniconda3/lib/python3.6/site-packages/pymc3/distributions/multivariate.py in __init__ (self, a, transform, *args, **kwargs)
    412 
    413 self.k = tt.as_tensor_variable(shape)
--> 414 self.a = a = tt.as_tensor_variable(a)
    415 self.mean = a / tt.sum(a)
    416 

~/miniconda3/lib/python3.6/site-packages/theano/tensor/basic.py in as_tensor_variable(x, name, ndim)
    210 except Exception:
    211 str_x = repr(x)
--> 212 raise AsTensorError("Cannot convert %s to TensorType" % str_x, type(x))
    213 
    214 # this has a different name, because _as_tensor_variable is the

AsTensorError: ('Cannot convert [Elemwise{sub,no_inplace}.0 Elemwise{true_div,no_inplace}.0] to TensorType', <class 'numpy.ndarray'>)

```

---

<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:** [November 14, 2017, 4:28pm UTC](https://discourse.pymc.io/t/creating-a-dirichlet-distribution-from-a-random-variable/555/2 "2017-11-14T16:28:09Z")

</div>

The correct syntax goes like this:

```python
import pymc3 as pm
import theano.tensor as tt
def sigmoid(x):
    return 1 / (1 + tt.exp(-x))

with pm.Model() as model:
    x = pm.Normal("x")
    s = sigmoid(x)
    w = pm.Dirichlet('w', a=tt.stack([1. - s, s]), shape=2)
    pm.Mixture("y", w, [pm.Normal.dist(mu=0), pm.Normal.dist(mu=3)], observed=[0.1, 2.9])

```

If you are using Normal mixture there is also a `pm.NormalMixture`: `pm.NormalMixture("y", w, mu=np.array([0.,1.]), sd=1., observed=[0.1, 2.9])`.

More information could be found in [http://docs.pymc.io/notebooks/dependent\_density\_regression.html](http://docs.pymc.io/notebooks/dependent_density_regression.html)

---

<div class="post-metadata">

**Author:** ![bicycle1885](https://avatars.discourse-cdn.com/v4/letter/b/ba9def/32.png) [@bicycle1885](https://discourse.pymc.io/u/bicycle1885)\
**Post date:** [November 14, 2017, 5:03pm UTC](https://discourse.pymc.io/t/creating-a-dirichlet-distribution-from-a-random-variable/555/3 "2017-11-14T17:03:49Z")

</div>

Thank you! It works perfectly.

I’m not actually using normal distributions but the link is helpful.

---

<div class="post-metadata">

**Author:** ![kpei](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/kpei/32/318_2.png) [@kpei](https://discourse.pymc.io/u/kpei)\
**Post date:** [November 16, 2017, 7:56pm UTC](https://discourse.pymc.io/t/creating-a-dirichlet-distribution-from-a-random-variable/555/4 "2017-11-16T19:56:54Z")

</div>

You can further condense the code through using `pm.math.sigmoid` rather than defining it manually