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: "Markov Chain Monte Carlo Convergence Diagnostics: A Comparative Review"
  Abstract: A critical issue for users of Markov Chain Monte Carlo (MCMC) methods in applications is how to determine when it is safe to stop sampling and use the samples to estimate characteristics of the distribution of interest. Research into methods of computing theoretical convergence bounds holds promise for the future but currently has yielded relatively little that is of practical use in applied work. Consequently, most MCMC users address the convergence problem by applying diagnostic tools to the output produced by running their samplers. After giving a brief overview of the area, we provide an expository review of thirteen convergence diagnostics, describing the theoretical basis and practical implementation of each. We then compare their performance in two simple models and conclude that all the methods can fail to detect the sorts of convergence failure they were designed to identify. We thus recommend a combination of strategies aimed at evaluating and accelerating MCMC sampler convergence, including applying diagnostic procedures to a small number of parallel chains, monitoring autocorrelations and cross-correlations, and modifying parameterizations or sampling algorithms appropriately. We emphasize, however, that it is not possible to say with certainty that a finite sample from an MCMC algorithm is representative of an underlying stationary distribution. Mary Kathryn Cowles is Assistant Professor of Biostatistics, Harvard School of Public Health, Boston, MA 02115. Bradley P. Carlin is Associate Professor, Division of Biostatistics, School of Public Health, University of Minnesota, Minneapolis, MN 55455. Much of the work was done while the first author was a graduate student in the Divison of Biostatistics at the University of Minnesota and then Assistant Professor, Biostatistics Section, Department of Preventive and Societal Medicine, University of Nebraska Medical Center, Omaha, NE 68198. The work of both authors was supported in part by National Institute of Allergy and Infectious Diseases FIRST Award 1-R29-AI33466. The authors thank the developers of the diagnostics studied here for sharing their insights, experiences, and software, and Drs. Thomas Louis and Luke Tierney for helpful discussions and suggestions which greatly improved the manuscript.

Connected through hyperedge HE-1 (induced by source paper "Perfect Simulation in Stochastic Geometry"):
  with members:
    - "Perfect Simulation of some Point Processes for the Impatient User"

Connected through hyperedge HE-2 (induced by source paper "Estimating Ratios of Normalizing Constants for Densities with Different Dimensions"):
  with members:
    - "MARKOV CHAIN MONTE CARLO SAMPLING FOR EVALUATING MULTIDIMENSIONAL INTEGRALS WITH APPLICATION TO BAYESIAN COMPUTATION"

Connected through hyperedge HE-3 (induced by source paper "Convergence controls for MCMC algorithms, with applications to hidden Markov chains"):
  with members:
    - "Assessing Convergence of Markov Chain Monte Carlo Algorithms"
    - "MCMC CONVERGENCE DIAGNOSTIC VIA THE CENTRAL LIMIT THEOREM"

Connected through hyperedge HE-4 (induced by source paper "A simulation approach to convergence rates for Markov chain Monte Carlo 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"
    - "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-5 (induced by source paper "Applications and extensions of MCMC in IRT: Multiple item types, missing data, and rated responses"):
  with members:
    - "BAYESIAN STATISTICS 6, pp. 000--000  Exact sampling for Bayesian inference: towards general purpose algorithms"

Connected through hyperedge HE-6 (induced by source paper "Rate of Convergence of the Gibbs Sampler by Gaussian Approximation  SUMMARY"):
  with members:
    - "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"
    - "Rates of convergence of the Hastings and Metropolis algorithms"

Connected through hyperedge HE-7 (induced by source paper "Markov Chain Monte Carlo in Practice: A Roundtable Discussion"):
  with members:
    - "Sampling from Multimodal Distributions Using Tempered Transitions"
    - "On MCMC Sampling in Hierarchical Longitudinal Models  SUMMARY"

Connected through hyperedge HE-8 (induced by source paper "Maximum Working Likelihood Inference with Markov Chain Monte Carlo"):
  with members:
    - "Sampling from Multimodal Distributions Using Tempered Transitions"

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