|---| | [ View source on GitHub](https://github.com/tensorflow/probability/blob/v0.25.0/tensorflow_probability/python/stats/sample_stats.py#L644-L706) | Cumulative estimates of variance. tfp.stats.cumulative_variance( x, sample_axis=0, name=None ) Given `N` samples of a scalar-valued random variable `X`, we can compute cumulative variance estimates result\[i\] = variance(x\[0:i+1\]) in O(N) work and O(log(N)) depth (the length of the longest series of operations that are performed sequentially), with O(1) TF kernel invocations. This implementation also arranges to do so in a numerically accurate manner, i.e., without incurring a subtraction of floating-point numbers of size quadratic in the data `x`. The underlying algorithm is from \[1\].


| ## Args || |---|---| | `x` | A numeric `Tensor` holding samples. | | `sample_axis` | Scalar `Tensor` designating the axis holding samples. Other axes are treated in batch. Default value: `0` (leftmost dimension). | | `name` | Python `str` name prefixed to Ops created by this function. Default value: `None` (i.e., `'cumulative_variance'`). |



| ## Returns || |---|---| | `cum_var` | A `Tensor` of same shape and dtype as `x` giving cumulative variance estimates. The zeroth element is the variance of a size-1 set of samples, so 0. |
#### References \[1\]: Philippe Pebay. Formulas for Robust, One-Pass Parallel Computation of Covariances and Arbitrary-Order Statistical Moments. *Technical Report SAND2008-6212* , 2008.