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: "Rates of convergence of the Hastings and Metropolis algorithms"
  Abstract: We apply recent results in Markov chain theory to Hastings and Metropolis algorithms with either independent or symmetric candidate distributions, and provide necessary and sufficient conditions for the algorithms to converge at a geometric rate to a prescribed distribution . In the independence case (in IR k ) these indicate that geometric convergence essentially occurs if and only if the candidate density is bounded below by a multiple of ; in the symmetric case (in IR only) we show geometric convergence essentially occurs if and only if has geometric tails. We also evaluate recently developed computable bounds on the rates of convergence in this context: examples show that these theoretical bounds can be inherently extremely conservative, although when the chain is stochastically monotone the bounds may well be effective.

Connected through hyperedge HE-1 (induced by source paper "WEAK CONVERGENCE AND OPTIMAL SCALING OF RANDOM WALK METROPOLIS ALGORITHMS"):
  with members:
    - "Adaptive proposal distribution for random walk Metropolis algorithm"
    - "FROM METROPOLIS TO DIFFUSIONS: GIBBS STATES AND OPTIMAL SCALING"

Connected through hyperedge HE-2 (induced by source paper "EXACT TRANSITION PROBABILITIES FOR THE INDEPENDENCE METROPOLIS SAMPLER"):
  with members:
    - "Self Regenerative Markov Chain Monte Carlo  Summary"
    - "A note on acceptance rate criteria for CLTs for Hastings-Metropolis algorithms"

Connected through hyperedge HE-3 (induced by source paper "Exponential Convergence of Langevin Diffusions and Their Discrete Approximations"):
  with members:
    - "A note on acceptance rate criteria for CLTs for Hastings-Metropolis algorithms"
    - "Self-Targeting Candidates for Metropolis-Hastings Algorithms"
    - "Geometric and Subgeometric Convergence of Diffusions with Given Stationary Distributions, and Their Discretizations"

Connected through hyperedge HE-4 (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"
    - "A note on convergence rates of Gibbs sampling for nonparametric mixtures"
    - "Adaptive Markov Chain Monte Carlo through Regeneration  Summary"

Connected through hyperedge HE-5 (induced by source paper "Estimating L 1 Error of Kernel Estimator: Monitoring Convergence of Markov Samplers"):
  with members:
    - "A simulation approach to convergence rates for Markov chain Monte Carlo algorithms"

Connected through hyperedge HE-6 (induced by source paper "Rate of Convergence of the Gibbs Sampler by Gaussian Approximation  SUMMARY"):
  with members:
    - "Markov Chain Monte Carlo Convergence Diagnostics: A Comparative Review"
    - "A simulation approach to convergence rates for Markov chain Monte Carlo algorithms"
    - "On Convergence of the EM Algorithm and the Gibbs Sampler  SUMMARY"
    - "Convergence properties of perturbed Markov chains"
    - "Assessing Convergence of Markov Chain Monte Carlo Algorithms"

Connected through hyperedge HE-7 (induced by source paper "Geometric and Subgeometric Convergence of Diffusions with Given Stationary Distributions, and Their Discretizations"):
  with members:
    - "Exponential Convergence of Langevin Diffusions and Their Discrete Approximations"
    - "Self-Targeting Candidates for Metropolis-Hastings Algorithms"

Connected through hyperedge HE-8 (induced by source paper "Analysis of the Gibbs sampler for a model related to James-Stein estimators"):
  with members:
    - "Markov Chain Monte Carlo Convergence Diagnostics: A Comparative Review"
    - "Theoretical rates of convergence for Markov chain Monte Carlo"
    - "A simulation approach to convergence rates for Markov chain Monte Carlo algorithms"
    - "Convergence properties of perturbed Markov chains"
    - "APPLICATIONS OF CHEEGER'S CONSTANT TO THE CONVERGENCE RATE OF MARKOV CHAINS ON R n"

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