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This article shows how coupled Markov chains that meet exactly after a random number of iterations can be used to generate unbiased estimators of the solutions of the Poisson equation. Through this connection, we rederive known unbiased estimators of expectations with respect to the stationary distribution of a Markov chain and provide conditions for the finiteness of their moments. We further construct unbiased estimators of the asymptotic variance of Markov chain ergodic…

基于耦合的高维收缩先验贝叶斯回归 Gibbs 采样收敛评估AI 解读

Abstract We consider Markov chain Monte Carlo (MCMC) algorithms for Bayesian high-dimensional regression with continuous shrinkage priors. A common challenge with these algorithms is the choice of the number of iterations to perform. This is critical when each iteration is expensive, as is the case when dealing with modern data sets, such as genome-wide association studies with thousands of rows and up to hundreds of thousands of columns. We develop coupling techniques…

作者答复：一类随机凸多面体的Gibbs采样器AI 解读

We present a Gibbs sampler for the Dempster-Shafer (DS) approach to statistical inference for Categorical distributions. The DS framework extends the Bayesian approach, allows in particular the use of partial prior information, and yields three-valued uncertainty assessments representing probabilities "for", "against", and "don't know" about formal assertions of interest. The proposed algorithm targets the distribution of a class of random convex polytopes which encapsulate…

一类随机凸多面体的 Gibbs 采样器AI 解读

We present a Gibbs sampler for the Dempster–Shafer (DS) approach to statistical inference for categorical distributions. The DS framework extends the Bayesian approach, allows in particular the use of partial prior information, and yields three-valued uncertainty assessments representing probabilities “for,” “against,” and “don’t know” about formal assertions of interest. The proposed algorithm targets the distribution of a class of random convex polytopes which encapsulate…

利用耦合构造无偏马尔可夫链蒙特卡洛方法AI 解读

Summary Markov chain Monte Carlo (MCMC) methods provide consistent approximations of integrals as the number of iterations goes to ∞. MCMC estimators are generally biased after any fixed number of iterations. We propose to remove this bias by using couplings of Markov chains together with a telescopic sum argument of Glynn and Rhee. The resulting unbiased estimators can be computed independently in parallel. We discuss practical couplings for popular MCMC algorithms. We…

利用条件粒子滤波器耦合进行平滑AI 解读

In state–space models, smoothing refers to the task of estimating a latent stochastic process given noisy measurements related to the process. We propose an unbiased estimator of smoothing expectations. The lack-of-bias property has methodological benefits: independent estimators can be generated in parallel, and CI can be constructed from the central limit theorem to quantify the approximation error. To design unbiased estimators, we combine a generic debiasing technique…

基于Hyvärinen评分的贝叶斯模型比较：计算与一致性AI 解读

The Bayes factor is a widely used criterion in model comparison and its logarithm is a difference of out-of-sample predictive scores under the logarithmic scoring rule. However, when some of the candidate models involve vague priors on their parameters, the log-Bayes factor features an arbitrary additive constant that hinders its interpretation. As an alternative, we consider model comparison using the Hyvärinen score. We propose a method to consistently estimate this score…

基于 Wasserstein 距离的近似贝叶斯计算AI 解读

Summary A growing number of generative statistical models do not permit the numerical evaluation of their likelihood functions. Approximate Bayesian computation has become a popular approach to overcome this issue, in which one simulates synthetic data sets given parameters and compares summaries of these data sets with the corresponding observed values. We propose to avoid the use of summaries and the ensuing loss of information by instead using the Wasserstein distance…

论非负无偏估计量AI 解读

We study the existence of algorithms generating almost surely nonnegative unbiased estimators. We show that given a nonconstant real-valued function $f$ and a sequence of unbiased estimators of $\lambda\in\mathbb{R}$, there is no algorithm yielding almost surely nonnegative unbiased estimators of $f(\lambda)\in\mathbb{R}^{+}$. The study is motivated by pseudo-marginal Monte Carlo algorithms that rely on such nonnegative unbiased estimators. These methods allow “exact…