deeptime.markov.tools.estimation.prior_rev¶
- deeptime.markov.tools.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
\[b_{ij} = \left \{ \begin{array}{rl} \alpha & i \leq j \\ 0 & \text{elsewhere} \end{array} \right . \]Examples
>>> import numpy as np >>> from deeptime.markov.tools.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.]])