Added SBW docstring

Author: larryshamalama

pymc/distributions/multivariate.py

@@ -2188,10 +2188,8 @@ def make_node(self, rng, size, dtype, alpha, K):
         alpha = at.as_tensor_variable(alpha)
         K = at.as_tensor_variable(intX(K))
 
-        # if at.lt(K, 0):
-        #     print(at.lt(K, 0).eval())
-        #     print(K.eval() < 0)
-        #     raise ValueError("K needs to be positive.")
+        if K.eval() < 0:
+            raise ValueError("K needs to be positive.")
 
         if alpha.ndim > 0:
             raise ValueError("The concentration parameter needs to be a scalar.")
@@ -2238,34 +2236,37 @@ def rng_fn(cls, rng, alpha, K, size):
 
 class StickBreakingWeights(Continuous):
     r"""
-    Likelihood of truncated stick-breaking weights. The weights are generated
+    Likelihood of truncated stick-breaking weights. The weights are generated from a
+    stick-breaking proceduce where :math:`x_k = v_k \prod_{\ell < k} (1 - v_\ell)` for
+    :math:`k \in \{1, \ldots, K\}` and :math
 
     .. math:
 
-
-        f(\mathbf{x}|\alpha, K) = 
+        f(\mathbf{x}|\alpha, K) =
+            B(1, \alpha)^{-K}x_{K+1}^\alpha \prod_{k=1}^{K+1}\left\{\sum_{j=k}^{K+1} x_j\right\}^{-1}
 
     ========  ===============================================
-    Support   :math:`x_i \in (0, 1)` for :math:`i \in \{1, \ldots, K+1\}`
-              such that :math:`\sum x_i = 1`
-    Mean      :math:`\dfrac{a_i}{\sum a_i}`
-    Variance  :math:`\dfrac{a_i - \sum a_0}{a_0^2 (a_0 + 1)}`
-              where :math:`a_0 = \sum a_i`
+    Support   :math:`x_k \in (0, 1)` for :math:`k \in \{1, \ldots, K+1\}`
+              such that :math:`\sum x_k = 1`
+    Mean      :math:`\mathbb{E}[x_k] = \dfrac{1}{1 + \alpha}\left(\dfrac{\alpha}{1 + \alpha}\right)^{k - 1}`
+              for :math:`k \in \{1, \ldots, K\}` and `\mathbb{E}[x_{K+1}] = \left(\dfrac{\alpha}{1 + \alpha}\right)^{K}`
     ========  ===============================================
 
     Parameters
     ----------
     alpha: float
-        Concentration parameters (alpha > 0).
+        Concentration parameter (alpha > 0).
     K: int
         The number of "sticks" to break off from an initial one-unit stick. The length
         of categories is K + 1, where the last weight is one minus the sum of all the first sticks.
 
     References
     ----------
-    .. [1] Ishwaran James
+    .. [1] Ishwaran, H., & James, L. F. (2001). Gibbs sampling methods for stick-breaking priors.
+           Journal of the American Statistical Association, 96(453), 161-173.
 
-    .. [2] Peter Mueller
+    .. [2] Müller, P., Quintana, F. A., Jara, A., & Hanson, T. (2015). Bayesian nonparametric data
+           analysis. New York: Springer.
     """
     rv_op = stickbreakingweights
 
@@ -2329,7 +2330,7 @@ def logp(value, alpha, K):
             ),
             axis=-1,
         )
-        logp += -(K - 1) * betaln(1, alpha)
+        logp += -K * betaln(1, alpha)
         logp += alpha * at.log(value[..., -1])
 
         logp = at.switch(

pymc/tests/test_distributions.py

@@ -2138,7 +2138,7 @@ def test_stickbreakingweights(self, value, alpha, K, logp):
             StickBreakingWeights("sbw", alpha=alpha, K=K, transform=None)
         pt = {"sbw": value}
         assert_almost_equal(
-            model.fastlogp(pt),
+            model.compile_logp()(pt),
             logp,
             decimal=select_by_precision(float64=6, float32=2),
             err_msg=str(pt),