def check_versus_numpy(self, x_, axis, biased, keepdims):
x_ = np.asarray(x_)
x = tf1.placeholder_with_default(
x_, shape=x_.shape if self.use_static_shape else None)
var = _reduce_variance(x, axis=axis, biased=biased, keepdims=keepdims)
np_var = np.var(x_,
axis=axis,
ddof=0 if biased else 1,
keepdims=keepdims)
if self.use_static_shape:
self.assertAllEqual(np_var.shape, var.shape)
var_ = self.evaluate(var)
# We will mask below, which changes shape, so check shape explicitly here.
self.assertAllEqual(np_var.shape, var_.shape)
# We get NaN when we divide by zero due to the size being the same as ddof
nan_mask = np.isnan(np_var)
if nan_mask.any():
self.assertTrue(np.isnan(var_[nan_mask]).all())
self.assertAllClose(np_var[~nan_mask],
var_[~nan_mask],
atol=0,
rtol=0.02)
def _finalize_for_one_state(chain_ndims, chain_variances):
"""Calculates R-hat for one group of Markov chains."""
# using notation from Brooks and Gelman (1998),
# n := num samples / chain; m := number of chains
n = chain_variances.num_samples
shape = chain_variances.mean.shape
m = tf.cast(
functools.reduce((lambda x, y: x * y), (shape[:chain_ndims])),
n.dtype)
# b/n is the between-chain variance (the variance of the chain means)
b_div_n = diagnostic._reduce_variance( # pylint:disable=protected-access
tf.convert_to_tensor(chain_variances.mean),
axis=tf.range(chain_ndims),
biased=False)
# W is the within sequence variance (the mean of the chain variances)
sum_of_chain_squared_residuals = tf.reduce_sum(
chain_variances.sum_squared_residuals,
axis=tf.range(chain_ndims))
w = sum_of_chain_squared_residuals / (m * (n - 1))
# the `true_variance_estimate` is denoted as sigma^2_+ in the 1998 paper
true_variance_estimate = ((n - 1) / n) * w + b_div_n
return (
(m + 1.) / m) * true_variance_estimate / w - (n - 1.) / (m * n)
def check_versus_numpy(self, x_, axis, biased, keepdims):
with self.cached_session():
x_ = np.asarray(x_)
x = tf.placeholder_with_default(
input=x_, shape=x_.shape if self.use_static_shape else None)
var = _reduce_variance(
x, axis=axis, biased=biased, keepdims=keepdims)
np_var = np.var(x_, axis=axis, ddof=0 if biased else 1, keepdims=keepdims)
if self.use_static_shape:
self.assertAllEqual(np_var.shape, var.shape)
var_ = self.evaluate(var)
# We will mask below, which changes shape, so check shape explicitly here.
self.assertAllEqual(np_var.shape, var_.shape)
# We get NaN when we divide by zero due to the size being the same as ddof
nan_mask = np.isnan(np_var)
if nan_mask.any():
self.assertTrue(np.isnan(var_[nan_mask]).all())
self.assertAllClose(np_var[~nan_mask], var_[~nan_mask], atol=0, rtol=0.02)
