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: "BAYESIAN STATISTICS 6, pp. 000--000  Exact sampling for Bayesian inference: towards general purpose algorithms"
  Abstract: There are now methods for organising a Markov chain Monte Carlo simulation so that it can be guaranteed that the state of the process at a given time is exactly drawn from the target distribution. The question of assessing convergence totally vanishes. Such methods are known as exact or perfect sampling. The approach that has received most attention uses the protocol of coupling from the past devised by Propp and Wilson (Random Structures and Algorithms,1996), in which multiple dependent paths of the chain are run from different initial states at a sequence of initial times going backwards into the past, until they satisfy the condition of coalescence by time 0. When this is achieved the state at time 0 is distributed according to the required target. This process must be implemented very carefully to assure its validity (including appropriate re-use of random number streams), and also requires one of various tricks to enable us to follow infinitely many sample paths with a finite amount of work. With the ultimate objective of Bayesian MCMC with guaranteed convergence, the purpose of this paper is to describe recent efforts to construct exact sampling methods for continuous-state Markov chains. We review existing methods based on gamma-coupling and rejection sampling (Murdoch and Green, Scandinavian Journal of Statistics, 1998), that are quite straightforward to understand, but require a closed form for the transition kernel and entail cumbersome algebraic manipulation. We then introduce two new methods based on random walk Metropolis, that offer the prospect of more automatic use, not least because the difficult, continuous, part of the transition mechanism can be coupled in a generic way, using a proposal distribution of convenience. One of the methods is based on a neat decomposition of any unimodal (multivariate) symmetric density into pieces that may be re-assembled to construct any translated copy of itself: that allows coupling of a continuum of Metropolis proposals to a finite set, at least for a compact state space. We discuss methods for economically coupling the subsequent accept/reject decisions. Our second new method deals with unbounded state spaces, using a trick due to W. S. Kendall of running a coupled dominating process in parallel with the sample paths of interest. The random subset of the state space below the dominating path is compact, allowing efficient coupling and coalescence. We look towards the possibility that application of such methods could become sufficiently convenient that they could become the basis for routine Bayesian computation in the foreseeable future.

Connected through hyperedge HE-1 (induced by source paper "An Approach to Diagnosing Total Variation Convergence of MCMC Algorithms"):
  with members:
    - "Assessing Convergence of Markov Chain Monte Carlo Algorithms"

Connected through hyperedge HE-2 (induced by source paper "Bayesian Forecasting of Multinomial Time Series through Conditionally Gaussian Dynamic Models"):
  with members:
    - "Change Point and Change Curve Modeling in Stochastic Processes and Spatial Statistics"
    - "On Sequential Simulation-Based Methods for Bayesian Filtering"
    - "Analysis of hospital quality monitors using hierarchical time series models"
    - "Priors and Component Structures in Autoregressive Time Series Models"
    - "FILTERING VIA SIMULATION: AUXILIARY PARTICLE FILTERS"
    - "Exploratory Modelling of Multiple Non-Stationary Time Series: Latent Process Structure and Decompositions"
    - "BAYESIAN TIME SERIES: Models and Computations for the Analysis of Time Series in the Physical Sciences"
    - "STUDIES OF QUALITY MONITOR TIME SERIES: THE V.A. HOSPITAL SYSTEM build on foundational contributions in"

Connected through hyperedge HE-3 (induced by source paper "Applications and extensions of MCMC in IRT: Multiple item types, missing data, and rated responses"):
  with members:
    - "Markov Chain Monte Carlo Convergence Diagnostics: A Comparative Review"

Connected through hyperedge HE-4 (induced by source paper "On Bayesian analysis of mixtures with an unknown number of components  Summary"):
  with members:
    - "FLEXIBLE PARAMETRIC MEASUREMENT ERROR MODELS"
    - "Reparameterisation Issues in Mixture Modelling and their bearing on MCMC algorithms"
    - "Bayesian MARS"
    - "Decomposable graphical Gaussian model determination"
    - "Finding Overlapping Distributions with MML"

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