pyemma.msm.estimation.log_likelihood¶
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pyemma.msm.estimation.
log_likelihood
(C, T)¶ Log-likelihood of the count matrix given a transition matrix.
Parameters: - C ((M, M) ndarray or scipy.sparse matrix) – Count matrix
- T ((M, M) ndarray orscipy.sparse matrix) – Transition matrix
Returns: logL – Log-likelihood of the count matrix
Return type: float
Notes
The likelihood of a set of observed transition counts C=(cij) for a given matrix of transition counts T=(tij) is given by
L(C|P)=M∏i=1(M∏j=1pcijij)The log-likelihood is given by
l(C|P)=M∑i,j=1cijlogpij.The likelihood describes the probability of making an observation C for a given model P.
Examples
>>> from pyemma.msm.estimation import log_likelihood
>>> T = np.array([[0.9, 0.1, 0.0], [0.5, 0.0, 0.5], [0.0, 0.1, 0.9]])
>>> C = np.array([[58, 7, 0], [6, 0, 4], [0, 3, 21]]) >>> logL = log_likelihood(C, T) >>> logL -38.280803472508182
>>> C = np.array([[58, 20, 0], [6, 0, 4], [0, 3, 21]]) >>> logL = log_likelihood(C, T) >>> logL -68.214409681430766
References
[1] Prinz, J H, H Wu, M Sarich, B Keller, M Senne, M Held, J D Chodera, C Schuette and F Noe. 2011. Markov models of molecular kinetics: Generation and validation. J Chem Phys 134: 174105