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# tfp.stats.variance

Estimate variance using samples.

``````tfp.stats.variance(
x,
sample_axis=0,
keepdims=False,
name=None
)
``````

Given `N` samples of scalar valued random variable `X`, variance may be estimated as

``````Var[X] := N^{-1} sum_{n=1}^N (X_n - Xbar) Conj{(X_n - Xbar)}
Xbar := N^{-1} sum_{n=1}^N X_n
``````
``````x = tf.random_normal(shape=(100, 2, 3))

# var[i, j] is the sample variance of the (i, j) batch member of x.
var = tfp.stats.variance(x, sample_axis=0)
``````

Notice we divide by `N` (the numpy default), which does not create `NaN` when `N = 1`, but is slightly biased.

#### Args:

• `x`: A numeric `Tensor` holding samples.
• `sample_axis`: Scalar or vector `Tensor` designating axis holding samples, or `None` (meaning all axis hold samples). Default value: `0` (leftmost dimension).
• `keepdims`: Boolean. Whether to keep the sample axis as singletons.
• `name`: Python `str` name prefixed to Ops created by this function. Default value: `None` (i.e., `'variance'`).

#### Returns:

• `var`: A `Tensor` of same `dtype` as the `x`, and rank equal to `rank(x) - len(sample_axis)`