Fix support of LKJCorr

[aseyboldt]

LKJCorr did not use an interval transformation to fix the support of the entries of the corr matrix to [-1, 1]. Because of this advi did not work at all and nuts reported diverging transitions in almost every sample:

with pm.Model() as model:
    corr = pm.LKJCorr('corr', n=1, p=2)
    trace = pm.sample(2000, tune=1000, init=None)
   trace['diverging'].mean()

gives 0.998.

This should fix #1852.

[twiecki]

Great catch!

======================================================================
ERROR: test_lkj_0 (pymc3.tests.test_distributions.TestMatchesScipy)
----------------------------------------------------------------------
Traceback (most recent call last):
  File "/home/travis/miniconda2/envs/testenv/lib/python2.7/site-packages/nose_parameterized/parameterized.py", line 365, in standalone_func
    return func(*(a + p.args), **p.kwargs)
  File "/home/travis/build/pymc-devs/pymc3/pymc3/tests/test_distributions.py", line 561, in test_lkj
    assert_almost_equal(model.fastlogp(pt), lp, decimal=6, err_msg=str(pt))
  File "/home/travis/build/pymc-devs/pymc3/pymc3/model.py", line 724, in __call__
    return self.f(**state)
  File "/home/travis/miniconda2/envs/testenv/lib/python2.7/site-packages/theano/compile/function_module.py", line 822, in __call__
    self[k] = arg
  File "/home/travis/miniconda2/envs/testenv/lib/python2.7/site-packages/theano/compile/function_module.py", line 512, in __setitem__
    self.value[item] = value
  File "/home/travis/miniconda2/envs/testenv/lib/python2.7/site-packages/theano/compile/function_module.py", line 463, in __setitem__
    (str(item), msg))
TypeError: Unknown input or state: lkj. The function has 1 named input (lkj_interval_).
-------------------- >> begin captured logging << --------------------
pymc3: DEBUG: Applied interval-transform to lkj and added transformed lkj_interval_ to model.
--------------------- >> end captured logging << ---------------------

[AustinRochford]

I recently ran into this, thanks for catching it!

[fonnesbeck]

@aseyboldt Looks like the key to the dict on line 560 of test_distributions needs to be the transformed variable rather than the original.

[aseyboldt]

I fixed it by disabling the transformation. Is there a better way that does not involve adding the log det manually in the tests?

[fonnesbeck]

That's probably fine, given the intention of the test.