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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 bayesian_hidden_markov_model(dtrajs, nstates, lag, nsamples=100, reversible=True, stationary=False, connectivity=None, mincount_connectivity='1/n', separate=None, observe_nonempty=True, stride='effective', conf=0.95, dt_traj='1 step', store_hidden=False, show_progress=True):
 r""" Bayesian Hidden Markov model estimate using Gibbs sampling of the posterior Returns a :class:`BayesianHMSM` that contains the estimated hidden Markov model [1]_ and a Bayesian estimate [2]_ that contains samples around this estimate to estimate uncertainties. Parameters dtrajs : list containing ndarrays(dtype=int) or ndarray(n, dtype=int) discrete trajectories, stored as integer ndarrays (arbitrary size) or a single ndarray for only one trajectory. lag : int lagtime for the MSM estimation in multiples of trajectory steps nstates : int the number of metastable states in the resulting HMM reversible : bool, optional, default = True If true compute reversible MSM, else non-reversible MSM 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. 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. observe_nonempty : bool If True, will restricted the observed states to the states that have at least one observation in the lagged input trajectories. nsamples : int, optional, default=100 number of transition matrix samples to compute and store stride : str or int, default='effective' stride between two lagged trajectories extracted from the input trajectories. Given trajectory s[t], stride and lag will result in trajectories Setting stride = 1 will result in using all data (useful for maximum likelihood estimator), while a Bayesian estimator requires a longer stride in order to have statistically uncorrelated trajectories. Setting stride = None 'effective' uses the largest neglected timescale as an estimate for the correlation time and sets the stride accordingly. conf : float, optional, default=0.95 size of confidence intervals dt_traj : str, optional, default='1 step' Description of the physical time corresponding to the trajectory time step. May be used by analysis algorithms such as plotting tools to pretty-print the axes. By default '1 step', i.e. there is no physical time unit. Specify by a number, whitespace and unit. Permitted units are (* is an arbitrary string):
 | 'fs', 'femtosecond*' | 'ps', 'picosecond*' | 'ns', 'nanosecond*' | 'us', 'microsecond*' | 'ms', 'millisecond*' | 's', 'second*' store_hidden : bool, optional, default=False store hidden trajectories in sampled HMMs show_progress : bool, default=True Show progressbars for calculation? Returns ------- An :class:`BayesianHMSM` object containing a transition matrix and various other HMM-related quantities and statistical uncertainties. Example ------- Note that the following example is only qualitative and not quantitatively reproducible because random numbers are involved We compute the stationary distribution (here given by the maximum likelihood estimate), and the 1-sigma uncertainty interval. You can see that the uncertainties are quite large (we have seen only very few transitions between the metastable states: 0.459176653019 - 0.268314552886 + 0.715326151685 0.540823346981 - 0.284761476984 + 0.731730375713 Let's look at the lifetimes of metastable states. Now we have really huge uncertainties. In states where one state is more probable than the other, the mean first passage time from the more probable to the less probable state is much higher than the reverse: 7.18543434854 - 6.03617757784 + 80.1298222741 8.65699332061 - 5.35089540896 + 30.1719505772 In contrast the relaxation timescale is less uncertain. This is because for a two-state system the relaxation timescale is dominated by the faster passage, which is less uncertain than the slower passage time: 3.35310468086 - 2.24574587978 + 8.34383177258 .. autoclass:: pyemma.msm.estimators.bayesian_hmsm.BayesianHMSM :members: :undoc-members: .. rubric:: Methods .. autoautosummary:: pyemma.msm.estimators.bayesian_hmsm.BayesianHMSM :methods: .. rubric:: Attributes .. autoautosummary:: pyemma.msm.estimators.bayesian_hmsm.BayesianHMSM :attributes: References .. [1] 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) .. [2] J. D. Chodera Et Al: Bayesian hidden Markov model analysis of single-molecule force spectroscopy: Characterizing kinetics under measurement uncertainty. arXiv:1108.1430 (2011) """

    bhmsm_estimator = _Bayes_HMSM(lag=lag, nstates=nstates, stride=stride, nsamples=nsamples, reversible=reversible,
                                  stationary=stationary,
                                  connectivity=connectivity, mincount_connectivity=mincount_connectivity,
                                  separate=separate, observe_nonempty=observe_nonempty,
                                  dt_traj=dt_traj, conf=conf, store_hidden=store_hidden, show_progress=show_progress)
    return bhmsm_estimator.estimate(dtrajs)