msmbuilder.tpt.mfpts

msmbuilder.tpt.mfpts(msm, sinks=None, lag_time=1.0, errors=False, n_samples=100)

Gets the Mean First Passage Time (MFPT) for all states to a set of sinks.

Parameters:

msm : msmbuilder.MarkovStateModel

MSM fit to the data.

sinks : array_like, int, optional

Indices of the sink states. There are two use-cases:

• None [default] : All MFPTs will be calculated, and the

  result is a matrix of the MFPT from state i to state j. This uses the fundamental matrix formalism.

• list of ints or int : Only the MFPTs into these sink

  states will be computed. The result is a vector, with entry i corresponding to the average time it takes to first get to any sink state from state i

lag_time : float, optional

Lag time for the model. The MFPT will be reported in whatever units are given here. Default is (1) which is in units of the lag time of the MSM.

errors : bool, optional

Pass “True” if you want to calculate a distribution of MFPTs accounting for MSM model error due to finite sampling

n_samples : int, optional

If “errors” is True, this is the number of MFPTs you want to compute (default = 100). For each computation, all nonzero transition probabilities (i,j) will be treated as Gaussian random variables, with mean equal to the transition probability and standard deviation equal to the standard errot of the mean of the binomial distribution with n observations, where n is the row-summed counts of row i.

NOTE: This implicitly assumes the Central Limit Theorem is a good approximation for the error, so this method works best with well-sampled data.

Returns:

mfpts : np.ndarray, float

MFPT in time units of lag_time, which depends on the input value of sinks:

• If sinks is None, then mfpts’s shape is (n_states, n_states).

  Where mfpts[i, j] is the mean first passage time to state j from state i.

• If sinks contains one or more states, then mfpts’s shape

  is (n_states,). Where mfpts[i] is the mean first passage time from state i to any state in sinks.

References

[R68]

Grinstead, C. M. and Snell, J. L. Introduction to Probability. American Mathematical Soc., 1998.

As of November 2014, this chapter was available for free online:

http://www.dartmouth.edu/~chance/teaching_aids/books_articles/probability_book/Chapter11.pdf