revise docs

docs/tex/bib.bib

@@ -652,3 +652,12 @@ @article{marin2012approximate
 number = {6},
 pages = {1167--1180}
 }
+
+@article{fisher1925theory,
+author = {Fisher, R A},
+title = {{Theory of statistical estimation}},
+journal = {Mathematical Proceedings of the Cambridge Philosophical Society},
+year = {1925},
+volume = {22},
+number = {5}
+}

docs/tex/tutorials/map-laplace.tex

@@ -22,8 +22,10 @@ \subsection{Laplace approximation}
 \end{align*}
 This requires computing a precision matrix $\Lambda$. Derived from a
 Taylor expansion, the Laplace approximation uses the Hessian of the
-negative log joint density at the MAP estimate.  It is defined
-component-wise as
+negative log joint density at the MAP estimate. For flat priors
+(equivalent to maximum likelihood), the precision matrix is known
+as the observed Fisher information \citep{fisher1925theory}.
+It is defined component-wise as
 \begin{align*}
   \Lambda_{ij}
   &=
@@ -38,4 +40,3 @@ \subsection{Laplace approximation}
 implementation in Edward's code base.
 
 \subsubsection{References}\label{references}
-

edward/inferences/laplace.py

@@ -44,6 +44,17 @@ def __init__(self, latent_vars, data=None, model_wrapper=None):
     the diagonal. This does not capture correlation among the
     variables but it does not require a potentially expensive matrix
     inversion.
+
+    Examples
+    --------
+    >>> X = tf.placeholder(tf.float32, [N, D])
+    >>> w = Normal(mu=tf.zeros(D), sigma=tf.ones(D))
+    >>> y = Normal(mu=ed.dot(X, w), sigma=tf.ones(N))
+    >>>
+    >>> qw = MultivariateNormalFull(mu=tf.Variable(tf.random_normal([D])),
+    >>>                             sigma=tf.Variable(tf.random_normal([D, D])))
+    >>>
+    >>> inference = ed.Laplace({w: qw}, data={X: X_train, y: y_train})
     """
     if isinstance(latent_vars, list):
       with tf.variable_scope("posterior"):