msmbuilder.msm._ratematrix.hessian¶

msmbuilder.msm._ratematrix.hessian(theta, counts, t=1)¶

Estimate of the hessian of the log-likelihood with respect to theta.

Parameters:

theta : array of shape = (n*(n-1)/2 + n) for dense or shorter The free parameters of the model. These values are the (possibly sparse) linearized elements of the log of the upper triangular portion of the symmetric rate matrix, S, followed by the log of the equilibrium distribution. counts : array of shape = (n, n) The matrix of observed transition counts. inds : array of ints or None If supplied, only compute a block of the Hessian at the specified indices. t : double The lag time.

Returns:

m : array, shape=(len(theta), len(theta)) An estimate of the hessian of the log-likelihood

Notes

This computation follows equation 3.6 of [1].

References

[R42]

Kalbfleisch, J. D., and Jerald F. Lawless. “The analysis of panel data under a Markov assumption.” J. Am. Stat. Assoc. 80.392 (1985): 863-871.