DOC: correct typos in docstrings (#3350)

* Update math.py

* Update sampling.py

* Update stats.py

* Update updates.py

* Update opvi.py

* Update updates.py

* Spelling fix

Author: rsdel2007

pymc3/math.py

@@ -134,15 +134,15 @@ def logit(p):
 def log1pexp(x):
     """Return log(1 + exp(x)), also called softplus.
 
-    This function is numerically more stable than the naive approch.
+    This function is numerically more stable than the naive approach.
     """
     return tt.nnet.softplus(x)
 
 
 def log1mexp(x):
     """Return log(1 - exp(-x)).
 
-    This function is numerically more stable than the naive approch.
+    This function is numerically more stable than the naive approach.
 
     For details, see
     https://cran.r-project.org/web/packages/Rmpfr/vignettes/log1mexp-note.pdf

pymc3/sampling.py

@@ -230,7 +230,7 @@ def sample(draws=500, step=None, init='auto', n_init=200000, start=None, trace=N
         Starting point in parameter space (or partial point)
         Defaults to trace.point(-1)) if there is a trace provided and model.test_point if not
         (defaults to empty dict). Initialization methods for NUTS (see `init` keyword) can
-        overwrite the default. For 'SMC' if should be a list of dict with length `chains`.
+        overwrite the default. For 'SMC' it should be a list of dict with length `chains`.
     trace : backend, list, or MultiTrace
         This should be a backend instance, a list of variables to track, or a MultiTrace object
         with past values. If a MultiTrace object is given, it must contain samples for the chain
@@ -869,7 +869,7 @@ def _prepare_iter_population(draws, chains, step, start, parallelize, tune=None,
     # 5. configure the PopulationStepper (expensive call)
     popstep = PopulationStepper(steppers, parallelize)
 
-    # Because the preperations above are expensive, the actual iterator is
+    # Because the preparations above are expensive, the actual iterator is
     # in another method. This way the progbar will not be disturbed.
     return _iter_population(draws, tune, popstep, steppers, traces, population)
 

pymc3/stats.py

@@ -199,7 +199,7 @@ def waic(trace, model=None, pointwise=False, progressbar=False):
     p_waic: effective number parameters
     var_warn: 1 if posterior variance of the log predictive
          densities exceeds 0.4
-    waic_i: and array of the pointwise predictive accuracy, only if pointwise True
+    waic_i: an array of the pointwise predictive accuracy, only if pointwise True
     """
     model = modelcontext(model)
 

pymc3/variational/opvi.py

@@ -6,10 +6,10 @@
 yield unreliable decisions.
 
 Recently on NIPS 2017 `OPVI  <https://arxiv.org/abs/1610.09033/>`_ framework
-was presented. It generalizes variational inverence so that the problem is
+was presented. It generalizes variational inference so that the problem is
 build with blocks. The first and essential block is Model itself. Second is
 Approximation, in some cases :math:`log Q(D)` is not really needed. Necessity
-depends on the third and forth part of that black box, Operator and
+depends on the third and fourth part of that black box, Operator and
 Test Function respectively.
 
 Operator is like an approach we use, it constructs loss from given Model,

pymc3/variational/updates.py

@@ -865,7 +865,7 @@ def adamax(loss_or_grads=None, params=None, learning_rate=0.002, beta1=0.9,
            beta2=0.999, epsilon=1e-8):
     """Adamax updates
 
-    Adamax updates implemented as in [1]_. This is a variant of of the Adam
+    Adamax updates implemented as in [1]_. This is a variant of the Adam
     algorithm based on the infinity norm.
 
     Parameters