human: Given a node-centered hypergraph: <hypergraph>, where nodes represent papers and hyperedges represent groups of papers sharing a common citing paper.

Details of the hypergraph:
Center node: "Geometric Ergodicity and Hybrid Markov Chains"
  Abstract: Various notions of geometric ergodicity for Markov chains on general state spaces exist. In this paper, we review certain relations and implications among them. We then apply these results to a collection of chains commonly used in Markov chain Monte Carlo simulation algorithms, the so-called hybrid chains. We prove that under certain conditions, a hybrid chain will "inherit" the geometric ergodicity of its constituent parts. Acknowledgements. We thank Charlie Geyer for a number of very useful comments regarding spectral theory and central limit theorems. We thank Alison Gibbs, Phil Reiss, Peter Rosenthal, and Richard Tweedie for very helpful discussions. We thank the referee and the editor for many excellent suggestions.

Connected through hyperedge HE-1 (induced by source paper "A simulation approach to convergence rates for Markov chain Monte Carlo algorithms"):
  with members:
    - "Markov Chain Monte Carlo Convergence Diagnostics: A Comparative Review"
    - "Bounding Convergence Time of the Gibbs Sampler in Bayesian Image Restoration"
    - "Theoretical rates of convergence for Markov chain Monte Carlo"
    - "Rate of Convergence of the Gibbs Sampler by Gaussian Approximation  SUMMARY"
    - "Analysis of the Gibbs sampler for a model related to James-Stein estimators"
    - "Convergence properties of perturbed Markov chains"
    - "Rates of convergence of the Hastings and Metropolis algorithms"
    - "A note on convergence rates of Gibbs sampling for nonparametric mixtures"

Connected through hyperedge HE-2 (induced by source paper "A note on convergence rates of Gibbs sampling for nonparametric mixtures"):
  with members:
    - "A simulation approach to convergence rates for Markov chain Monte Carlo algorithms"
    - "Convergence properties of perturbed Markov chains"
    - "Auxiliary Variable Methods for Markov Chain Monte Carlo with Applications"
    - "A Note on the Dirichlet Process Prior in Bayesian Nonparametric Inference with Partial Exchangeability 1"

Connected through hyperedge HE-3 (induced by source paper "APPLICATIONS OF CHEEGER'S CONSTANT TO THE CONVERGENCE RATE OF MARKOV CHAINS ON R n"):
  with members:
    - "A simulation approach to convergence rates for Markov chain Monte Carlo algorithms"
    - "Analysis of the Gibbs sampler for a model related to James-Stein estimators"

Connected through hyperedge HE-4 (induced by source paper "Outperforming the Gibbs sampler empirical estimator for nearest neighbor random fields"):
  with members:
    - "Von Mises type statistics for single site updated local interaction random fields"

Connected through hyperedge HE-5 (induced by source paper "A note on acceptance rate criteria for CLTs for Hastings-Metropolis algorithms"):
  with members:
    - "Rates of convergence of the Hastings and Metropolis algorithms"
    - "EXACT TRANSITION PROBABILITIES FOR THE INDEPENDENCE METROPOLIS SAMPLER"
    - "Exponential Convergence of Langevin Diffusions and Their Discrete Approximations"

Question: Please tell me which class the center node belongs to. The 7 classes are: Neural_Networks, Reinforcement_Learning, Probabilistic_Methods, Theory, Genetic_Algorithms, Case_Based, Rule_Learning. Directly output the class name.

gpt: Probabilistic_Methods