|---| | [ View source on GitHub](https://github.com/tensorflow/probability/blob/v0.25.0/tensorflow_probability/python/stats/sample_stats.py#L709-L823) | Windowed estimates of variance. tfp.stats.windowed_variance( x, low_indices=None, high_indices=None, axis=0, name=None ) Computes variances among data in the Tensor `x` along the given windows: result\[i\] = variance(x\[low_indices\[i\]:high_indices\[i\]+1\]) accurately and efficiently. To wit, if K is the size of `low_indices` and `high_indices`, and `N` is the size of `x` along the given `axis`, the computation takes O(K + N) work, O(log(N)) depth (the length of the longest series of operations that are performed sequentially), and only uses O(1) TensorFlow kernel invocations. The underlying algorithm is an adaptation of the streaming reduction for accurate variance computations given in \[1\]. This function can be useful for assessing the behavior over time of trailing-window estimators from some iterative process, such as the last half of an MCMC chain. Suppose `x` has shape `Bx + [N] + E`, where the `Bx` component has rank `axis`, and `low_indices` and `high_indices` broadcast to shape `[M]`. Then each element of `low_indices` and `high_indices` must be between 0 and N+1, and the shape of the output will be `Bx + [M] + E`. Batch shape in the indices is not currently supported. The default windows are `[0, 1), [1, 2), [1, 3), [2, 4), [2, 5), ...` This corresponds to analyzing `x` as though it were streaming, for example successive states of an MCMC sampler, and we were interested in the variance of the last half of the data at each point.


| ## Args || |---|---| | `x` | A numeric `Tensor` holding `N` samples along the given `axis`, whose windowed variances are desired. | | `low_indices` | An integer `Tensor` defining the lower boundary (inclusive) of each window. Default: elementwise half of `high_indices`. | | `high_indices` | An integer `Tensor` defining the upper boundary (exclusive) of each window. Must be broadcast-compatible with `low_indices`. Default: `tf.range(1, N+1)`, i.e., N windows that each end in the corresponding datum from `x` (inclusive)`. `axis` Scalar`Tensor`designating the axis holding samples. This is the axis of`x`along which we take windows, and therefore the axis that`low_indices`and`high_indices`index into. 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.,`'windowed_variance'\`). |



| ## Returns || |---|---| | `variances` | A numeric `Tensor` holding the windowed variances of `x` along the `axis` dimension. |
#### References \[1\]: Philippe Pebay. Formulas for Robust, One-Pass Parallel Computation of Covariances and Arbitrary-Order Statistical Moments. *Technical Report SAND2008-6212* , 2008.