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: "Analysis of the Gibbs sampler for a model related to James-Stein estimators"
  Abstract: Summary. We analyze a hierarchical Bayes model which is related to the usual empirical Bayes formulation of James-Stein estimators. We consider running a Gibbs sampler on this model. Using previous results about convergence rates of Markov chains, we provide rigorous, numerical, reasonable bounds on the running time of the Gibbs sampler, for a suitable range of prior distributions. We apply these results to baseball data from Efron and Morris (1975). For a different range of prior distributions, we prove that the Gibbs sampler will fail to converge, and use this information to prove that in this case the associated posterior distribution is non-normalizable. Acknowledgements. I am very grateful to Jun Liu for suggesting this project, and to Neal Madras for suggesting the use of the Submartingale Convergence Theorem herein. I thank Kate Cowles and Richard Tweedie for helpful conversations, and thank the referees for useful comments.

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"
    - "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"
    - "Adaptive Markov Chain Monte Carlo through Regeneration  Summary"

Connected through hyperedge HE-2 (induced by source paper "Convergence properties of perturbed Markov chains"):
  with members:
    - "A simulation approach to convergence rates for Markov chain Monte Carlo algorithms"
    - "Rate of Convergence of the Gibbs Sampler by Gaussian Approximation  SUMMARY"
    - "Auxiliary Variable Methods for Markov Chain Monte Carlo with Applications"
    - "Markov Chain Monte Carlo Methods Based on `Slicing' the Density Function"
    - "A note on convergence rates of Gibbs sampling for nonparametric mixtures"

Connected through hyperedge HE-3 (induced by source paper "Rates of convergence of the Hastings and Metropolis algorithms"):
  with members:
    - "Bounding Convergence Time of the Gibbs Sampler in Bayesian Image Restoration"
    - "Theoretical rates of convergence for Markov chain Monte Carlo"
    - "A simulation approach to convergence rates for Markov chain Monte Carlo algorithms"
    - "Rate of Convergence of the Gibbs Sampler by Gaussian Approximation  SUMMARY"
    - "EXACT TRANSITION PROBABILITIES FOR THE INDEPENDENCE METROPOLIS SAMPLER"
    - "Estimating L 1 Error of Kernel Estimator: Monitoring Convergence of Markov Samplers"
    - "A note on acceptance rate criteria for CLTs for Hastings-Metropolis algorithms"
    - "Exponential Convergence of Langevin Diffusions and Their Discrete Approximations"

Connected through hyperedge HE-4 (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"
    - "Geometric Ergodicity and Hybrid Markov Chains"

Connected through hyperedge HE-5 (induced by source paper "Theoretical rates of convergence for Markov chain Monte Carlo"):
  with members:
    - "Markov Chain Monte Carlo Convergence Diagnostics: A Comparative Review"
    - "A simulation approach to convergence rates for Markov chain Monte Carlo algorithms"
    - "Rates of convergence of the Hastings and Metropolis algorithms"

Connected through hyperedge HE-6 (induced by source paper "Markov Chain Monte Carlo Convergence Diagnostics: A Comparative Review"):
  with members:
    - "Applications and extensions of MCMC in IRT: Multiple item types, missing data, and rated responses"
    - "Decision Analysis by Augmented Probability Simulation"
    - "Bounding Convergence Time of the Gibbs Sampler in Bayesian Image Restoration"
    - "Perfect Simulation in Stochastic Geometry"
    - "Theoretical rates of convergence for Markov chain Monte Carlo"
    - "Maximum Working Likelihood Inference with Markov Chain Monte Carlo"
    - "Estimating Ratios of Normalizing Constants for Densities with Different Dimensions"
    - "Markov Chain Monte Carlo in Practice: A Roundtable Discussion"

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