# msmtools.estimation.tmatrix_cov¶

msmtools.estimation.tmatrix_cov(C, k=None)

Covariance tensor for non-reversible transition matrix posterior.

Parameters: C ((M, M) ndarray or scipy.sparse matrix) – Count matrix k (int (optional)) – Return only covariance matrix for entires in the k-th row of the transition matrix cov – Covariance tensor for transition matrix posterior (M, M, M) ndarray

Notes

The posterior of non-reversible transition matrices is

$\mathbb{P}(T|C) \propto \prod_{i=1}^{M} \left( \prod_{j=1}^{M} p_{ij}^{c_{ij}} \right)$

Each row in the transition matrix is distributed according to a Dirichlet distribution with parameters given by the observed transition counts $$c_{ij}$$.

The covariance tensor $$\text{cov}[p_{ij},p_{kl}]=\Sigma_{i,j,k,l}$$ is zero whenever $$i \neq k$$ so that only $$\Sigma_{i,j,i,l}$$ is returned.