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  1. ; (, Annales de l'Institut Henri Poincaré, Probabilités et Statistiques)
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  2. ; (, The Annals of Applied Probability)
    Random-scan Gibbs samplers possess a natural hierarchical structure. The structure connects Gibbs samplers targeting higher-dimensional distributions to those targeting lower-dimensional ones. This leads to a quasi-telescoping property of their spectral gaps. Based on this property, we derive three new bounds on the spectral gaps and convergence rates of Gibbs samplers on general domains. The three bounds relate a chain’s spectral gap to, respectively, the correlation structure of the target distribution, a class of random walk chains, and a collection of influence matrices. Notably, one of our results generalizes the technique of spectral independence, which has received considerable attention for its success on finite domains, to general state spaces. We illustrate our methods through a sampler targeting the uniform distribution on a corner of an n-cube. 
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  3. ; (, Proceedings of Machine Learning Research)
    Accepted Manuscript Full Text Available
  4. ; (, Journal of machine learning research)
    Accepted Manuscript Full Text Available
  5. ; ; ; (, Stochastic Processes and their Applications)
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