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: "Decision Analysis by Augmented Probability Simulation"
  Abstract: We provide a generic Monte Carlo method to find the alternative of maximum expected utility in a decision analysis. We define an artificial distribution on the product space of alternatives and states, and show that the optimal alternative is the mode of the implied marginal distribution on the alternatives. After drawing a sample from the artificial distribution, we may use exploratory data analysis tools to approximately identify the optimal alternative. We illustrate our method for some important types of influence diagrams. (Decision Analysis, Influence Diagrams, Markov chain Monte Carlo, Simulation)

Connected through hyperedge HE-1 (induced by source paper "Assessing Convergence of Markov Chain Monte Carlo Algorithms"):
  with members:
    - "Bounding Convergence Time of the Gibbs Sampler in Bayesian Image Restoration"
    - "Convergence controls for MCMC algorithms, with applications to hidden Markov chains"
    - "Rate of Convergence of the Gibbs Sampler by Gaussian Approximation  SUMMARY"
    - "An Approach to Diagnosing Total Variation Convergence of MCMC Algorithms"
    - "MCMC CONVERGENCE DIAGNOSTIC VIA THE CENTRAL LIMIT THEOREM"

Connected through hyperedge HE-2 (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"
    - "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"
    - "A simulation approach to convergence rates for Markov chain Monte Carlo algorithms"

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