We study generalized Bayesian inference under misspecification, i.e. when the
model is 'wrong but useful'. Generalized Bayes equips the likelihood with a
learning rate $\eta$. We show that for generalized linear models (GLMs),
$\eta$-generalized Bayes concentrates around the best approximation of the
truth within the model for specific $\eta \neq 1$, even under severely
misspecified noise, as long as the tails of the true distribution are
exponential. We derive MCMC samplers for generalized Bayesian lasso and
logistic regression and give examples of both simulated and real-world data in
which generalized Bayes substantially outperforms standard Bayes.

该研究探讨了广义贝叶斯推断在错配模型下的应用，包括广义线性模型，通过 MCMC 抽样来实现广义贝叶斯 Lasso 和 Logistic 回归，并在模拟和真实数据中展示了广义贝叶斯在表现上超过标准贝叶斯的优点。

安全贝叶斯广义线性回归

Safe-Bayesian Generalized Linear Regression

Posterior inference with an intractable likelihood is becoming an
increasingly common task in scientific domains which rely on sophisticated
computer simulations. Typically, these forward models do not admit tractable
densities forcing practitioners to make use of approximations. This work
introduces a novel approach to address the intractability of the likelihood and
the marginal model. We achieve this by learning a flexible amortized estimator
which approximates the likelihood-to-evidence ratio. We demonstrate that the
learned ratio estimator can be embedded in MCMC samplers to approximate
likelihood-ratios between consecutive states in the Markov chain, allowing us
to draw samples from the intractable posterior. Techniques are presented to
improve the numerical stability and to measure the quality of an approximation.
The accuracy of our approach is demonstrated on a variety of benchmarks against
well-established techniques. Scientific applications in physics show its
applicability.

该研究提出了一种解决在科学领域中使用高级计算机模拟时出现的后验推断问题的新方法，这种方法使用学习的灵活的摊销估计量来近似似然 - 证据比率，并可以嵌入 MCMC 采样器中以从难以处理的后验中获得样本。

无似然马尔可夫蒙特卡洛与分摊的近似比率估计器

Likelihood-free MCMC with Amortized Approximate Ratio Estimators

Stein's method for measuring convergence to a continuous target distribution
relies on an operator characterizing the target and Stein factor bounds on the
solutions of an associated differential equation. While such operators and
bounds are readily available for a diversity of univariate targets, few
multivariate targets have been analyzed. We introduce a new class of
characterizing operators based on Ito diffusions and develop explicit
multivariate Stein factor bounds for any target with a fast-coupling Ito
diffusion. As example applications, we develop computable and
convergence-determining diffusion Stein discrepancies for log-concave,
heavy-tailed, and multimodal targets and use these quality measures to select
the hyperparameters of biased Markov chain Monte Carlo (MCMC) samplers, compare
random and deterministic quadrature rules, and quantify bias-variance tradeoffs
in approximate MCMC. Our results establish a near-linear relationship between
diffusion Stein discrepancies and Wasserstein distances, improving upon past
work even for strongly log-concave targets. The exposed relationship between
Stein factors and Markov process coupling may be of independent interest.

本文发展了基于 Ito 扩散的新型特征算子，针对任何具有快速耦合 Ito 扩散的目标，开发了明确的多元 Stein 因子边界，并应用于多个实际应用中，从而通过质量度量来选择超参数，比较随机和确定性的积分规则，并量化近似 MCMC 中的偏差 - 方差权衡。