def moving_mean_variance(value, decay, name=None):
  """Compute exponentially weighted moving {mean,variance} of a streaming value.

  The exponentially-weighting moving `mean_var` and `variance_var` are updated
  by `value` according to the following recurrence:

  ```python
  variance_var = decay * (variance_var + (1-decay) * (value - mean_var)**2)
  mean_var     = decay * mean_var + (1 - decay) * value
  ```

  Note: `mean_var` is updated *after* `variance_var`, i.e., `variance_var` uses
  the lag-`1` mean.

  For derivation justification, see [Finch (2009; Eq. 143)][1].

  Unlike `assign_moving_mean_variance`, this function handles
  variable creation.

  Args:
    value: `float`-like `Tensor`. Same shape as `mean_var` and `variance_var`.
    decay: A `float`-like `Tensor`. The moving mean decay. Typically close to
      `1.`, e.g., `0.999`.
    name: Optional name of the returned operation.

  Returns:
    mean_var: `Variable` representing the `value`-updated exponentially weighted
      moving mean.
    variance_var: `Variable` representing the `value`-updated
      exponentially weighted moving variance.

  Raises:
    TypeError: if `value_var` does not have float type `dtype`.
    TypeError: if `value`, `decay` have different `base_dtype`.

  #### References

  [1]: Tony Finch. Incremental calculation of weighted mean and variance.
       _Technical Report_, 2009.
       http://people.ds.cam.ac.uk/fanf2/hermes/doc/antiforgery/stats.pdf
  """
  with tf.compat.v1.variable_scope(name, "moving_mean_variance",
                                   [value, decay]):
    value = tf.convert_to_tensor(value=value, name="value")
    base_dtype = value.dtype.base_dtype
    if not base_dtype.is_floating:
      raise TypeError(
          "value.base_dtype({}) does not have float type `dtype`.".format(
              base_dtype.name))
    decay = tf.convert_to_tensor(value=decay, dtype=base_dtype, name="decay")
    variance_var = tf.compat.v2.Variable(
        name="moving_variance",
        initial_value=tf.zeros(shape=value.shape, dtype=value.dtype),
        trainable=False)
    mean_var = tf.compat.v2.Variable(
        name="moving_mean",
        initial_value=tf.zeros(shape=value.shape, dtype=value.dtype),
        trainable=False)
    return assign_moving_mean_variance(
        mean_var, variance_var, value, decay)
Compute exponentially weighted moving {mean,variance} of a streaming value.

  The exponentially-weighting moving `mean_var` and `variance_var` are updated
  by `value` according to the following recurrence:

  ```python
  variance_var = decay * (variance_var + (1-decay) * (value - mean_var)**2)
  mean_var     = decay * mean_var + (1 - decay) * value
  ```

  Note: `mean_var` is updated *after* `variance_var`, i.e., `variance_var` uses
  the lag-`1` mean.

  For derivation justification, see [Finch (2009; Eq. 143)][1].

  Unlike `assign_moving_mean_variance`, this function handles
  variable creation.

  Args:
    value: `float`-like `Tensor`. Same shape as `mean_var` and `variance_var`.
    decay: A `float`-like `Tensor`. The moving mean decay. Typically close to
      `1.`, e.g., `0.999`.
    name: Optional name of the returned operation.

  Returns:
    mean_var: `Variable` representing the `value`-updated exponentially weighted
      moving mean.
    variance_var: `Variable` representing the `value`-updated
      exponentially weighted moving variance.

  Raises:
    TypeError: if `value_var` does not have float type `dtype`.
    TypeError: if `value`, `decay` have different `base_dtype`.

  #### References

  [1]: Tony Finch. Incremental calculation of weighted mean and variance.
       _Technical Report_, 2009.
       http://people.ds.cam.ac.uk/fanf2/hermes/doc/antiforgery/stats.pdf