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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:
 def timescales_hmsm(dtrajs, nstates, lags=None, nits=None, reversible=True, stationary=False, connectivity=None, mincount_connectivity='1/n', separate=None, errors=None, nsamples=100, stride=None, n_jobs=None, show_progress=True):
 r""" Calculate implied timescales from Hidden Markov state models estimated at a series of lag times. Warning: this can be slow! Parameters dtrajs : array-like or list of array-likes discrete trajectories nstates : int number of hidden states lags : int, array-like with integers or None, optional integer lag times at which the implied timescales will be calculated. If set to None (default) as list of lag times will be automatically generated. For a single int, generate a set of lag times starting from 1 to lags, using a multiplier of 1.5 between successive lags. nits : int (optional) number of implied timescales to be computed. Will compute less if the number of states are smaller. None means the number of timescales will be determined automatically. connectivity : str, optional, default = None Defines if the resulting HMM will be defined on all hidden states or on a connected subset. Connectivity is defined by counting only transitions with at least mincount_connectivity counts. If a subset of states is used, all estimated quantities (transition matrix, stationary distribution, etc) are only defined on this subset and are correspondingly smaller than nstates. Following modes are available: * None or 'all' : The active set is the full set of states. Estimation is done on all weakly connected subsets separately. The resulting transition matrix may be disconnected. * 'largest' : The active set is the largest reversibly connected set. * 'populous' : The active set is the reversibly connected set with most counts. mincount_connectivity : float or '1/n' minimum number of counts to consider a connection between two states. Counts lower than that will count zero in the connectivity check and may thus separate the resulting transition matrix. The default evaluates to 1/nstates. separate : None or iterable of int Force the given set of observed states to stay in a separate hidden state. The remaining nstates-1 states will be assigned by a metastable decomposition. reversible : boolean (optional) Estimate transition matrix reversibly (True) or nonreversibly (False) stationary : bool, optional, default=False If True, the initial distribution of hidden states is self-consistently computed as the stationary distribution of the transition matrix. If False, it will be estimated from the starting states. Only set this to true if you're sure that the observation trajectories are initiated from a global equilibrium distribution. errors : None | 'bayes' Specifies whether to compute statistical uncertainties (by default not), an which algorithm to use if yes. The only option is currently 'bayes'. This algorithm is much faster than MSM-based error calculation because the involved matrices are much smaller. nsamples : int Number of approximately independent HMSM samples generated for each lag time for uncertainty quantification. Only used if errors is not None. n_jobs : int how many subprocesses to start to estimate the models for each lag time. show_progress : bool, default=True Show progressbars for calculation? Returns ------- itsobj : :class:`ImpliedTimescales <pyemma.msm.ImpliedTimescales>` object See also -------- ImpliedTimescales The object returned by this function. pyemma.plots.plot_implied_timescales Plotting function for the :class:`ImpliedTimescales <pyemma.msm.ImpliedTimescales>` object Example ------- [[ 5.786] [ 5.143] [ 4.44 ] [ 3.677]] .. autoclass:: pyemma.msm.estimators.implied_timescales.ImpliedTimescales :members: :undoc-members: .. rubric:: Methods .. autoautosummary:: pyemma.msm.estimators.implied_timescales.ImpliedTimescales :methods: .. rubric:: Attributes .. autoautosummary:: pyemma.msm.estimators.implied_timescales.ImpliedTimescales :attributes: References Implied timescales as a lagtime-selection and MSM-validation approach were suggested in [1]_. Hidden Markov state model estimation is done here as described in [2]_. For uncertainty quantification we employ the Bayesian sampling algorithm described in [3]_. .. [1] Swope, W. C. and J. W. Pitera and F. Suits: Describing protein folding kinetics by molecular dynamics simulations: 1. Theory. J. Phys. Chem. B 108: 6571-6581 (2004) .. [2] F. Noe, H. Wu, J.-H. Prinz and N. Plattner: Projected and hidden Markov models for calculating kinetics and metastable states of complex molecules. J. Chem. Phys. 139, 184114 (2013) .. [3] J. D. Chodera et al: Bayesian hidden Markov model analysis of single-molecule force spectroscopy: Characterizing kinetics under measurement uncertainty arXiv:1108.1430 (2011) """

    # format data
    dtrajs = _types.ensure_dtraj_list(dtrajs)

    # MLE or error estimation?
    if errors is None:
        if stride is None:
            stride = 1
        estimator = _ML_HMSM(nstates=nstates, reversible=reversible, stationary=stationary, connectivity=connectivity,
                             stride=stride, mincount_connectivity=mincount_connectivity, separate=separate)
    elif errors == 'bayes':
        if stride is None:
            stride = 'effective'
        estimator = _Bayes_HMSM(nstates=nstates, reversible=reversible, stationary=stationary,
                                connectivity=connectivity, mincount_connectivity=mincount_connectivity,
                                stride=stride, separate=separate, show_progress=show_progress, nsamples=nsamples)
    else:
        raise NotImplementedError('Error estimation method'+str(errors)+'currently not implemented')

    # go
    itsobj = _ImpliedTimescales(estimator, lags=lags, nits=nits, n_jobs=n_jobs,
                                show_progress=show_progress)
    itsobj.estimate(dtrajs)
    return itsobj