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: "A simulation approach to convergence rates for Markov chain Monte Carlo algorithms"
  Abstract: Markov chain Monte Carlo (MCMC) methods, including the Gibbs sampler and the Metropolis-Hastings algorithm, are very commonly used in Bayesian statistics for sampling from complicated, high-dimensional posterior distributions. A continuing source of uncertainty is how long such a sampler must be run in order to converge approximately to its target stationary distribution. Rosenthal (1995b) presents a method to compute rigorous theoretical upper bounds on the number of iterations required to achieve a specified degree of convergence in total variation distance by verifying drift and minorization conditions. We propose the use of auxiliary simulations to estimate the numerical values needed in Rosenthal's theorem. Our simulation method makes it possible to compute quantitative convergence bounds for models for which the requisite analytical computations would be prohibitively difficult or impossible. On the other hand, although our method appears to perform well in our example problems, it can not provide the guarantees offered by analytical proof. Acknowledgements. We thank Brad Carlin for assistance and encouragement.

Connected through hyperedge HE-1 (induced by source paper "Convergence properties of perturbed Markov chains"):
  with members:
    - "Rate of Convergence of the Gibbs Sampler by Gaussian Approximation  SUMMARY"
    - "Analysis of the Gibbs sampler for a model related to James-Stein estimators"
    - "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-2 (induced by source paper "Estimating L 1 Error of Kernel Estimator: Monitoring Convergence of Markov Samplers"):
  with members:
    - "Rates of convergence of the Hastings and Metropolis algorithms"

Connected through hyperedge HE-3 (induced by source paper "A note on convergence rates of Gibbs sampling for nonparametric mixtures"):
  with members:
    - "Convergence properties of perturbed Markov chains"
    - "Auxiliary Variable Methods for Markov Chain Monte Carlo with Applications"
    - "Geometric Ergodicity and Hybrid Markov Chains"
    - "A Note on the Dirichlet Process Prior in Bayesian Nonparametric Inference with Partial Exchangeability 1"

Connected through hyperedge HE-4 (induced by source paper "Adaptive Markov Chain Monte Carlo through Regeneration  Summary"):
  with members:
    - "Adaptation for Self Regenerative MCMC  SUMMARY"
    - "Self Regenerative Markov Chain Monte Carlo  Summary"
    - "Discretization of continuous Markov chains and MCMC convergence assessment"
    - "Adaptive proposal distribution for random walk Metropolis algorithm"

Connected through hyperedge HE-5 (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"
    - "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"
    - "Rates of convergence of the Hastings and Metropolis algorithms"

Connected through hyperedge HE-6 (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"
    - "Rate of Convergence of the Gibbs Sampler by Gaussian Approximation  SUMMARY"
    - "Analysis of the Gibbs sampler for a model related to James-Stein estimators"
    - "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-7 (induced by source paper "APPLICATIONS OF CHEEGER'S CONSTANT TO THE CONVERGENCE RATE OF MARKOV CHAINS ON R n"):
  with members:
    - "Analysis of the Gibbs sampler for a model related to James-Stein estimators"
    - "Geometric Ergodicity and Hybrid Markov Chains"

Connected through hyperedge HE-8 (induced by source paper "Von Mises type statistics for single site updated local interaction random fields"):
  with members:
    - "Outperforming the Gibbs sampler empirical estimator for nearest neighbor random fields"

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