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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_hmm(observations, estimated_hmm, nsample=100, reversible=True, stationary=False, p0_prior='mixed', transition_matrix_prior='mixed', store_hidden=False, call_back=None):
 r""" Bayesian HMM based on sampling the posterior Generic maximum-likelihood estimation of HMMs Parameters observations : list of numpy arrays representing temporal data `observations[i]` is a 1d numpy array corresponding to the observed trajectory index `i` estimated_hmm : HMM HMM estimated from estimate_hmm or initialize_hmm reversible : bool, optional, default=True If True, a prior that enforces reversible transition matrices (detailed balance) is used; otherwise, a standard non-reversible prior is used. stationary : bool, optional, default=False If True, the stationary distribution of the transition matrix will be used as initial distribution. Only use True if you are confident that the observation trajectories are started from a global equilibrium. If False, the initial distribution will be estimated as usual from the first step of the hidden trajectories. nsample : int, optional, default=100 number of Gibbs sampling steps p0_prior : None, str, float or ndarray(n) Prior for the initial distribution of the HMM. Will only be active if stationary=False (stationary=True means that p0 is identical to the stationary distribution of the transition matrix). Currently implements different versions of the Dirichlet prior that is conjugate to the Dirichlet distribution of p0. p0 is sampled from: .. math: p0 \sim \prod_i (p0)_i^{a_i + n_i - 1} where :math:`n_i` are the number of times a hidden trajectory was in state :math:`i` at time step 0 and :math:`a_i` is the prior count. Following options are available: | 'mixed' (default), :math:`a_i = p_{0,init}`, where :math:`p_{0,init}` is the initial distribution of initial_model. | 'uniform', :math:`a_i = 1` | ndarray(n) or float, the given array will be used as A. | None, :math:`a_i = 0`. This option ensures coincidence between sample mean an MLE. Will sooner or later lead to sampling problems, because as soon as zero trajectories are drawn from a given state, the sampler cannot recover and that state will never serve as a starting state subsequently. Only recommended in the large data regime and when the probability to sample zero trajectories from any state is negligible. transition_matrix_prior : str or ndarray(n, n) Prior for the HMM transition matrix. Currently implements Dirichlet priors if reversible=False and reversible transition matrix priors as described in [1]_ if reversible=True. For the nonreversible case the posterior of transition matrix :math:`P` is: .. math: P \sim \prod_{i,j} p_{ij}^{b_{ij} + c_{ij} - 1} where :math:`c_{ij}` are the number of transitions found for hidden trajectories and :math:`b_{ij}` are prior counts. | 'mixed' (default), :math:`b_{ij} = p_{ij,init}`, where :math:`p_{ij,init}` is the transition matrix of initial_model. That means one prior count will be used per row. | 'uniform', :math:`b_{ij} = 1` | ndarray(n, n) or broadcastable, the given array will be used as B. | None, :math:`b_ij = 0`. This option ensures coincidence between sample mean an MLE. Will sooner or later lead to sampling problems, because as soon as a transition :math:`ij` will not occur in a sample, the sampler cannot recover and that transition will never be sampled again. This option is not recommended unless you have a small HMM and a lot of data. store_hidden : bool, optional, default=False store hidden trajectories in sampled HMMs call_back : function, optional, default=None a call back function with no arguments, which if given is being called after each computed sample. This is useful for implementing progress bars. Return ------ hmm : :class:`SampledHMM <bhmm.hmm.generic_sampled_hmm.SampledHMM>` References .. [1] Trendelkamp-Schroer, B., H. Wu, F. Paul and F. Noe: Estimation and uncertainty of reversible Markov models. J. Chem. Phys. 143, 174101 (2015). """

    # construct estimator
    from bhmm.estimators.bayesian_sampling import BayesianHMMSampler as _BHMM
    sampler = _BHMM(observations, estimated_hmm.nstates, initial_model=estimated_hmm,
                    reversible=reversible, stationary=stationary, transition_matrix_sampling_steps=1000,
                    p0_prior=p0_prior, transition_matrix_prior=transition_matrix_prior,
                    output=estimated_hmm.output_model.model_type)

    # Sample models.
    sampled_hmms = sampler.sample(nsamples=nsample, save_hidden_state_trajectory=store_hidden,
                                  call_back=call_back)
    # return model
    from bhmm.hmm.generic_sampled_hmm import SampledHMM
    return SampledHMM(estimated_hmm, sampled_hmms)