Given a list of estimates of the lower-triangular Cholesky square roots of
component covariance matrices, a list of true lower-triangular Cholesky
square roots of component covariance matrices, an estimate of the total
variation, and the true total variation, `multi_stein_loss`

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

1 | ```
multi_stein_loss(B, Psi, b, psi)
``` |

`B` |
A list of lower triangular matrices. These are the 'estimates' of the lower-triangular Cholesky square roots of the component covariance matrices. |

`Psi` |
A list of lower triangular matrices. These are the 'true' lower-triangular Cholesky square roots of the component covariance matrices. |

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

`psi` |
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_cov`

also calculates multiway Stein's
loss, but uses the component covariance matrices (not the Cholesky roots) 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_cov`

, `get_equi_bayes`

.

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