Discussion of “A Gibbs Sampler for a Class of Random Convex Polytopes”

@article{Diaconis2021DiscussionO,
  title={Discussion of “A Gibbs Sampler for a Class of Random Convex Polytopes”},
  author={Persi Diaconis and Guanyang Wang},
  journal={Journal of the American Statistical Association},
  year={2021},
  volume={116},
  pages={1193 - 1195}
}
  • P. Diaconis, Guanyang Wang
  • Published 15 April 2021
  • Mathematics
  • Journal of the American Statistical Association
The paper offers answers to these questions by proposing a Gibbs sampler to perform statistical inference for categorical distributions using the Dempster-Shafer approach. To be precise, let x = (xi) N i=1 be the observations, each comes from one of the K categories. The model assumes that there exists a θ = (θ1, · · · , θK) in the K−simplex ∆ := {(θ1, θ2, · · · , θK) : θi ≥ 0 for every i, ∑K i=1 θi = 1} such that P(xi = k) = θk for every i, k. Moreover, it is assumed that the observations x… 

References

SHOWING 1-10 OF 12 REFERENCES
MCMC for Doubly-intractable Distributions
TLDR
This paper provides a generalization of M0ller et al. (2004) and a new MCMC algorithm, which obtains better acceptance probabilities for the same amount of exact sampling, and removes the need to estimate model parameters before sampling begins.
Explicit stationary distributions for compositions of random functions and products of random matrices
If (Yn)n=1/∞ is a sequence of i.i.d. random variables onE=(0,+∞) and iff is positive onE, this paper studies explicit examples of stationary distributions for the Markov chain (Wn)n=0∞ defined
Donkey walk and Dirichlet distributions
The donkey performs a random walk (Xn)n[greater-or-equal, slanted]0 inside a tetrahedron with vertices A1,...,Ad as follows. For r=1,...,d and t=0,1,..., at time dt+r the donkey moves from the point
Bayesian Goodness of Fit Tests: A Conversation for David Mumford
TLDR
A class of special cases and a class of sensible Bayes tests inspired by Mumford, Wu and Zhu are introduced and Calculating these tests presents the challenge of 'doubly intractable distributions'.
Iterated Random Functions
TLDR
Survey of iterated random functions offers a method for studying the steady state distribution of a Markov chain, and presents useful bounds on rates of convergence in a variety of examples.
A Gibbs Sampler for a Class of Random Convex Polytopes
TLDR
A Gibbs sampler for the Dempster–Shafer approach to statistical inference for categorical distributions is presented and relies on an equivalence between the iterative constraints of the vertex configuration and the nonnegativity of cycles in a fully connected directed graph.
MCMC for doublyintractable distributions
  • In Proceedings of the Twenty-Second Conference on Uncertainty in Artificial Intelligence,
  • 2006
  • Sankhyā: The Indian Journal of Statistics
  • 2002
A Bayesian peek into feller volume I
We develop Bayesian versions of three classic probability problems: the. birthday problem, the coupon collector's problem and the matching problem. In each case, the Bayesian component involves a
Explicit Stationary Distributions
  • 1991
...
1
2
...