msmtools.estimation.prior_rev

msmtools.estimation.prior_rev(C, alpha=-1.0)

Prior counts for sampling of reversible transition matrices.

Prior is defined as

b_ij= alpha if i<=j b_ij=0 else

Parameters:

• C ((M, M) ndarray or scipy.sparse matrix) – Count matrix
• alpha (float (optional)) – Value of prior counts

Returns:

B – Matrix of prior counts

Return type:

(M, M) ndarray

Notes

The reversible prior is a matrix with -1 on the upper triangle. Adding this prior respects the fact that for a reversible transition matrix the degrees of freedom correspond essentially to the upper triangular part of the matrix.

The prior is defined as

\[\begin{split}b_{ij} = \left \{ \begin{array}{rl} \alpha & i \leq j \\ 0 & \text{elsewhere} \end{array} \right .\end{split}\]

Examples

>>> import numpy as np
>>> from msmtools.estimation import prior_rev

>>> C = np.array([[10, 1, 0], [2, 0, 3], [0, 1, 4]])
>>> B = prior_rev(C)
>>> B
array([[-1., -1., -1.],
       [ 0., -1., -1.],
       [ 0.,  0., -1.]])