MC._log_likelihood_z¶

MC._log_likelihood_z(model, temp=None)¶

This function estimate the likelihood of the current free energy or diffusion profile over the bins in a simulation box. It is used to calculated the diffusion in z-direction over z-coordinate. This likelihood is necessary to decide whether the MC step will be accepted.

\[\ln \ L = \sum_{j \rightarrow i} \ln \left ( \left[ \left( e^{\mathbf{R}\Delta_{ij}t_{\alpha}} \right)_{ij}\right]^{N_{ij}(\Delta_{ij}t_{\alpha})} \right)\]

with \(R\) as the rate matrix from _init_rate_matrix_pbc(), \(\Delta_{ij}t_{\alpha}\) as the current lag time and \(N_{ij}(\Delta_{ij}t_{\alpha})\) as the transition matrix. The transition matrix contains the numbers of all observed transition \(j \rightarrow i\) at a given lag time in a simulated trajectory. This matrix is sampled with the function poreana.sample.Sample.init_diffusion_mc() from a simulated trajectory at the beginning and depends on the lag time.

Parameters:

modelinteger: Model class set with the model function
templist: Profile which was adapted in the current MC (free energy or diffusion)

Returns:

log_likefloat: Likelihood for the current profiles in a simulation box