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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_msm(dtrajs, lags=None, nits=None, reversible=True, connected=True, weights='empirical', errors=None, nsamples=50, n_jobs=None, show_progress=True, mincount_connectivity='1/n', only_timescales=False):
 # format data r""" Implied timescales from Markov state models estimated at a series of lag times. Parameters dtrajs : array-like or list of array-likes discrete trajectories 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. If None, the number of timescales will be automatically determined. reversible : boolean, optional Estimate transition matrix reversibly (True) or nonreversibly (False) connected : boolean, optional If true compute the connected set before transition matrix estimation at each lag separately weights : str, optional can be used to re-weight non-equilibrium data to equilibrium. Must be one of the following: * 'empirical': Each trajectory frame counts as one. (default) * 'oom': Each transition is re-weighted using OOM theory, see [5]_. errors : None | 'bayes', optional Specifies whether to compute statistical uncertainties (by default not), an which algorithm to use if yes. Currently the only option is: * 'bayes' for Bayesian sampling of the posterior Attention: * The Bayes mode will use an estimate for the effective count matrix that may produce somewhat different estimates than the 'sliding window' estimate used with ``errors=None`` by default. * Computing errors can be// slow if the MSM has many states. * There are still unsolved theoretical problems in the computation of effective count matrices, and therefore the uncertainty interval and the maximum likelihood estimator can be inconsistent. Use this as a rough guess for statistical uncertainties. nsamples : int, optional The number of approximately independent transition matrix samples generated for each lag time for uncertainty quantification. Only used if errors is not None. n_jobs : int, optional how many subprocesses to start to estimate the models for each lag time. show_progress : bool, default=True whether to show progress of estimation. 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. only_timescales: bool, default=False If you are only interested in the timescales and its samples, you can consider turning this on in order to save memory. This can be useful to avoid blowing up memory with BayesianMSM and lots of samples. Returns ------- itsobj : :class:`ImpliedTimescales <pyemma.msm.estimators.implied_timescales.ImpliedTimescales>` object Example ------- See also -------- ImpliedTimescales The object returned by this function. pyemma.plots.plot_implied_timescales Implied timescales plotting function. Just call it with the :class:`ImpliedTimescales <pyemma.msm.estimators.ImpliedTimescales>` object produced by this function as an argument. .. 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]_. Error estimation is done either using moving block bootstrapping [2]_ or a Bayesian analysis using Metropolis-Hastings Monte Carlo sampling of the posterior. Nonreversible Bayesian sampling is done by independently sampling Dirichtlet distributions of the transition matrix rows. A Monte Carlo method for sampling reversible MSMs was introduced in [3]_. Here we employ a much more efficient algorithm introduced in [4]_. .. [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] Kuensch, H. R.: The jackknife and the bootstrap for general stationary observations. Ann. Stat. 17, 1217-1241 (1989) .. [3] Noe, F.: Probability Distributions of Molecular Observables computed from Markov Models. J. Chem. Phys. 128, 244103 (2008) .. [4] Trendelkamp-Schroer, B, H. Wu, F. Paul and F. Noe: Estimation and uncertainty of reversible Markov models. http://arxiv.org/abs/1507.05990 .. [5] Nueske, F., Wu, H., Prinz, J.-H., Wehmeyer, C., Clementi, C. and Noe, F.: Markov State Models from short non-Equilibrium Simulations - Analysis and Correction of Estimation Bias J. Chem. Phys. (submitted) (2017) """

    # Catch invalid inputs for weights:
    if isinstance(weights, str):
        if weights not in ['empirical', 'oom']:
            raise ValueError("Weights must be either \'empirical\' or \'oom\'")
    else:
        raise ValueError("Weights must be either \'empirical\' or \'oom\'")
    # Set errors to None if weights==oom:
    if weights == 'oom' and (errors is not None):
        errors = None

    # format data
    dtrajs = _types.ensure_dtraj_list(dtrajs)

    if connected:
        connectivity = 'largest'
    else:
        connectivity = 'none'

    # Choose estimator:
    if errors is None:
        if weights == 'empirical':
            estimator = _ML_MSM(reversible=reversible, connectivity=connectivity)
        else:
            estimator = _OOM_MSM(reversible=reversible, connectivity=connectivity)
    elif errors == 'bayes':
        estimator = _Bayes_MSM(reversible=reversible, connectivity=connectivity,
                               nsamples=nsamples, show_progress=show_progress)
    else:
        raise NotImplementedError('Error estimation method {errors} currently not implemented'.format(errors=errors))

    if hasattr(estimator, 'mincount_connectivity'):
        estimator.mincount_connectivity = mincount_connectivity
    # go
    itsobj = _ImpliedTimescales(estimator, lags=lags, nits=nits, n_jobs=n_jobs,
                                show_progress=show_progress, only_timescales=only_timescales)
    itsobj.estimate(dtrajs)
    return itsobj