human: Given a hyperedge-centered hypergraph: <hypergraph>, where the center hyperedge groups papers that share a common citing paper.

Details of the hypergraph:
Center hyperedge (induced by source paper "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.

Includes members:
  Member "Markov Chain Monte Carlo Convergence Diagnostics: A Comparative Review":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "Perfect Simulation in Stochastic Geometry")
  Member "Bounding Convergence Time of the Gibbs Sampler in Bayesian Image Restoration":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "Rates of convergence of the Hastings and Metropolis algorithms")
  Member "Theoretical rates of convergence for Markov chain Monte Carlo":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "Rates of convergence of the Hastings and Metropolis algorithms")
  Member "Rate of Convergence of the Gibbs Sampler by Gaussian Approximation  SUMMARY":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "Convergence properties of perturbed Markov chains")
  Member "Analysis of the Gibbs sampler for a model related to James-Stein estimators":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "Convergence properties of perturbed Markov chains")
  Member "Convergence properties of perturbed Markov chains":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "Markov Chain Monte Carlo Methods Based on `Slicing' the Density Function")
  Member "Rates of convergence of the Hastings and Metropolis algorithms":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "WEAK CONVERGENCE AND OPTIMAL SCALING OF RANDOM WALK METROPOLIS ALGORITHMS")
  Member "A note on convergence rates of Gibbs sampling for nonparametric mixtures":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "Convergence properties of perturbed Markov chains")

Question: Please tell me which class the citing paper (i.e., the source paper of the center hyperedge) 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