We present a new approach to sample from generic binary distributions, based
on an exact Hamiltonian Monte Carlo algorithm applied to a piecewise continuous
augmentation of the binary distribution of interest. An extension of this idea
to distributions over mixtures of binary and possibly-truncated Gaussian or
exponential variables allows us to sample from posteriors of linear and probit
regression models with spike-and-slab priors and truncated parameters. We
illustrate the advantages of these algorithms in several examples in which they
outperform the Metropolis or Gibbs samplers.

本文基于一种分段连续的改进二项分布的哈密顿蒙特卡洛算法， 扩展到了二项和截尾高斯或指数变量混合分布的情况，用以采样线性和 probit 回归模型中的后验概率密度，并在多个案例中展示了这些算法的优点，相比于 Metropolis 或 Gibbs 采样器具有更好的性能。

二元分布的辅助变量精确哈密顿蒙特卡罗采样器

Auxiliary-variable Exact Hamiltonian Monte Carlo Samplers for Binary  Distributions

The Bradley-Terry model is a popular approach to describe probabilities of
the possible outcomes when elements of a set are repeatedly compared with one
another in pairs. It has found many applications including animal behaviour,
chess ranking and multiclass classification. Numerous extensions of the basic
model have also been proposed in the literature including models with ties,
multiple comparisons, group comparisons and random graphs. From a computational
point of view, Hunter (2004) has proposed efficient iterative MM
(minorization-maximization) algorithms to perform maximum likelihood estimation
for these generalized Bradley-Terry models whereas Bayesian inference is
typically performed using MCMC (Markov chain Monte Carlo) algorithms based on
tailored Metropolis-Hastings (M-H) proposals. We show here that these MM\
algorithms can be reinterpreted as special instances of
Expectation-Maximization (EM) algorithms associated to suitable sets of latent
variables and propose some original extensions. These latent variables allow us
to derive simple Gibbs samplers for Bayesian inference. We demonstrate
experimentally the efficiency of these algorithms on a variety of applications.

本文介绍及拓展 Bradley-Terry 模型，研究最大似然估计与 Bayesian 推断方法，并提出一种基于隐变量的 EM 算法与 Gibbs 采样算法，从而有效地应用于多种应用场景中。

广义 Bradley-Terry 模型的高效贝叶斯推断

Efficient Bayesian Inference for Generalized Bradley-Terry Models

In this paper, we describe centering and noncentering methodology as
complementary techniques for use in parametrization of broad classes of
hierarchical models, with a view to the construction of effective MCMC
algorithms for exploring posterior distributions from these models. We give a
clear qualitative understanding as to when centering and noncentering work
well, and introduce theory concerning the convergence time complexity of Gibbs
samplers using centered and noncentered parametrizations. We give general
recipes for the construction of noncentered parametrizations, including an
auxiliary variable technique called the state-space expansion technique. We
also describe partially noncentered methods, and demonstrate their use in
constructing robust Gibbs sampler algorithms whose convergence properties are
not overly sensitive to the data.

本文介绍使用中心化和非中心化方法对广泛类别的分层模型进行参数化的方法，旨在构建有效的 MCMC 算法以探索后验分布。介绍中心化和非中心化何时效果好，并介绍了使用中心化和非中心化参数化的 Gibbs 采样器的收敛时间复杂度理论。同时，还提供了构造非中心化参数化的通用方案，包括称为状态空间扩展技术的辅助变量技术。还介绍了部分非中心化方法，并演示了它们在构建稳健的 Gibbs 采样器算法中的应用，其收敛性不会过于敏感于数据。