Given a list of estimated component covariance matrices, a list of true
component covariance matrices, an estimate of the total variation, and the
true total variation, `multi_stein_loss_cov`

will calculate multiway
Stein's loss between the estimates and the truth.

1 | ```
multi_stein_loss_cov(B, Sigma, b, sigma)
``` |

`B` |
A list of positive definite matrices. These are the 'estimates' of the component covariance matrices. |

`Sigma` |
A list of positive definite matrices. These are the 'true' component covariance matrices. |

`b` |
A numeric. This is an 'estimate' of the total variation parameter, the 'standard devation' version of it. |

`sigma` |
A numeric. This is the 'true' total variation parameter, the 'standard devation' version of it. |

Multiway Stein's loss is a generalization of Stein's loss. More details on multiway Stein's loss and the Bayes rules under it can be found in Gerard and Hoff (2015).

The function `multi_stien_loss`

also calculates multiway Stein's loss,
but uses the lower-triangular Cholesky square roots of the component
covariance matrices as input.

A numeric, the multiway Stein's loss between the 'truth' and the 'estimates'.

David Gerard.

Gerard, D., & Hoff, P. (2015).
Equivariant
minimax dominators of the MLE in the array normal model. *Journal of
Multivariate Analysis*, 137, 32-49.

`multi_stein_loss`

, `get_equi_bayes`

.

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