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通过与替代分布混合进行贝叶斯因子的蒙特卡洛近似AI 解读

By mixing the target posterior distribution with a surrogate distribution, of which the normalizing constant is tractable, we propose a method for estimating the marginal likelihood using the Wang–Landau algorithm. We show that a faster convergence of the proposed method can be achieved via the momentum acceleration. Two implementation strategies are detailed: (i) facilitating global jumps between the posterior and surrogate distributions via the multiple-try Metropolis…

基于时间序列分组数据的洛伦兹曲线贝叶斯估计AI 解读

This study is concerned with estimating the inequality measures associated with the underlying hypothetical income distribution from the times series grouped data on the income proportions. We adopt the Dirichlet likelihood approach where the parameters of the Dirichlet likelihood are set to the differences between the Lorenz curve of the hypothetical income distribution for the consecutive income classes and propose a state-space model which combines the transformed…

失业导致结局截断及不可忽略缺失的纵向观察研究中的因果效应评估AI 解读

Important statistical issues pervade the evaluation of training programs’ effects for unemployed people. In particular, the fact that offered wages are observed and well-defined only for subjects who are employed (truncation by death), and the problem that information on the individuals’ employment status and wage can be lost over time (attrition) raise methodological challenges for causal inference. We present an extended framework for simultaneously addressing the…

基于多类连通矩阵凸组合的空间自回归模型贝叶斯平均AI 解读

There is a great deal of literature regarding use of nongeographically based connectivity matrices or combinations of geographic and non-geographic structures in spatial econometric models. We focus on convex combinations of weight matrices that result in a single weight matrix reflecting multiple types of connectivity, where coefficients from the convex combination can be used for inference regarding the relative importance of each type of connectivity in the global…

Barker 提议：结合梯度 MCMC 的稳健性与效率AI 解读

Abstract There is a tension between robustness and efficiency when designing Markov chain Monte Carlo (MCMC) sampling algorithms. Here we focus on robustness with respect to tuning parameters, showing that more sophisticated algorithms tend to be more sensitive to the choice of step-size parameter and less robust to heterogeneity of the distribution of interest. We characterise this phenomenon by studying the behaviour of spectral gaps as an increasingly poor step-size is…

非可逆并行温度法：可扩展的高度并行 MCMC 方案AI 解读

Abstract Parallel tempering (PT) methods are a popular class of Markov chain Monte Carlo schemes used to sample complex high-dimensional probability distributions. They rely on a collection of N interacting auxiliary chains targeting tempered versions of the target distribution to improve the exploration of the state space. We provide here a new perspective on these highly parallel algorithms and their tuning by identifying and formalizing a sharp divide in the behaviour and…

评《具有随机波动率和非共轭先验的大型贝叶斯向量自回归》AI 解读

Fully Bayesian inference in a vector autoregression with stochastic volatility (VAR-SV) typically relies on simulations from a multi-step Markov chain Monte Carlo (MCMC) algorithm. Carriero et al. (2019) propose a new, faster, “triangular” algorithm (TA) to replace the systemwide algorithm (SWA) in the most time-consuming step of the VAR-SV’s standard MCMC algorithm. This paper analytically shows that the TA and SWA generally sample from different distributions, thereby…

贝叶斯模型比较中的自动化先验稳健性分析AI 解读

Summary It is well‐known that the marginal likelihood, the gold standard for Bayesian model comparison, can be sensitive to prior hyperparameter choices. However, most models require computationally intense simulation‐based methods to evaluate the typically high‐dimensional integral of the marginal likelihood expression. Hence, despite the recognition that prior sensitivity analysis is important in this context, it is rarely done in practice. We develop efficient and…

通过风险因子映射高效估计高维动态协方差：金融风险管理应用AI 解读

This paper aims to explore a modified method of high-dimensional dynamic variance–covariance matrix estimation via risk factor mapping, which can yield a dependence estimation of asset returns within a large portfolio with high computational efficiency. The essence of our methodology is to express the time-varying dependence of high-dimensional return variables using the co-movement concept of returns with respect to risk factors. A novelty of the proposed methodology is to…

误分类下流行率与趋势估计的贝叶斯方法AI 解读

Abstract In this paper, we present a Bayesian approach to estimate the mean of a binary variable and changes in the mean over time, when the variable is subject to misclassification error. These parameters are partially identified, and we derive identified sets under various assumptions about the misclassification rates. We apply our method to estimating the prevalence and trend of prescription opioid misuse, using data from the 2002–2014 National Survey on Drug Use and…

稀疏函数型线性判别分析AI 解读

Summary Functional linear discriminant analysis provides a simple yet efficient method for classification, with the possibility of achieving perfect classification. Several methods have been proposed in the literature that mostly address the dimensionality of the problem. On the other hand, there is growing interest in interpretability of the analysis, which favours a simple and sparse solution. In this paper we propose a new approach that incorporates a type of sparsity…

稀疏信号的最优选择后推断：非参数经验贝叶斯方法AI 解读

Summary Many recently developed Bayesian methods focus on sparse signal detection. However, much less work has been done on the natural follow-up question: how does one make valid inferences for the magnitude of those signals after selection? Ordinary Bayesian credible intervals suffer from selection bias, as do ordinary frequentist confidence intervals. Existing Bayesian methods for correcting this bias produce credible intervals with poor frequentist properties. Further,…

以更少资源发现更多基因变异：贝叶斯非参数预测与优化AI 解读

Summary While the cost of sequencing genomes has decreased dramatically in recent years, this expense often remains nontrivial. Under a fixed budget, scientists face a natural trade-off between quantity and quality: spending resources to sequence a greater number of genomes or spending resources to sequence genomes with increased accuracy. Our goal is to find the optimal allocation of resources between quantity and quality. Optimizing resource allocation promises to reveal…

误设广义线性模型中的大规模模型选择AI 解读

Summary Model selection is crucial both to high-dimensional learning and to inference for contemporary big data applications in pinpointing the best set of covariates among a sequence of candidate interpretable models. Most existing work implicitly assumes that the models are correctly specified or have fixed dimensionality, yet both model misspecification and high dimensionality are prevalent in practice. In this paper, we exploit the framework of model selection principles…

无浪费序贯蒙特卡洛AI 解读

Abstract A standard way to move particles in a sequential Monte Carlo (SMC) sampler is to apply several steps of a Markov chain Monte Carlo (MCMC) kernel. Unfortunately, it is not clear how many steps need to be performed for optimal performance. In addition, the output of the intermediate steps are discarded and thus wasted somehow. We propose a new, waste-free SMC algorithm which uses the outputs of all these intermediate MCMC steps as particles. We establish that its…

稀疏贝叶斯预测密度估计的极小极大最优性AI 解读

We study predictive density estimation under Kullback–Leibler loss in ℓ0-sparse Gaussian sequence models. We propose proper Bayes predictive density estimates and establish asymptotic minimaxity in sparse models. Fundamental for this is a new risk decomposition for sparse, or spike-and-slab priors. A surprise is the existence of a phase transition in the future-to-past variance ratio r. For r

旋转不变矩阵的近似消息传递算法AI 解读

Approximate Message Passing (AMP) algorithms have seen widespread use across a variety of applications. However, the precise forms for their Onsager corrections and state evolutions depend on properties of the underlying random matrix ensemble, limiting the extent to which AMP algorithms derived for white noise may be applicable to data matrices that arise in practice. In this work, we study more general AMP algorithms for random matrices W that satisfy orthogonal rotational…

多变点模型中的广义拉普拉斯推断AI 解读

Under the classical long-span asymptotic framework, we develop a class of generalized laplace (GL) inference methods for the change-point dates in a linear time series regression model with multiple structural changes analyzed in, e.g., Bai and Perron (1998, Econometrica 66, 47–78). The GL estimator is defined by an integration rather than optimization-based method and relies on the LS criterion function. It is interpreted as a classical (non-Bayesian) estimator, and the…

带标记仅出现数据建模：马拉维女性性工作者规模估计AI 解读

Certain subpopulations like female sex workers (FSW), men who have sex with men (MSM), and people who inject drugs (PWID) often have higher prevalence of HIV/AIDS and are difficult to map directly due to stigma, discrimination, and criminalization. Fine-scale mapping of those populations contributes to the progress towards reducing the inequalities and ending the AIDS epidemic. In 2016 and 2017, the PLACE surveys were conducted at 3,290 venues in 20 out of the total 28…

采用可逆 SGLD 提议的小批量 Metropolis–Hastings 方法AI 解读

Traditional Markov chain Monte Carlo (MCMC) algorithms are computationally intensive and do not scale well to large data. In particular, the Metropolis–Hastings (MH) algorithm requires passing over the entire dataset to evaluate the likelihood ratio in each iteration. We propose a general framework for performing MH-MCMC using mini-batches of the whole dataset and show that this gives rise to approximately a tempered stationary distribution. We prove that the algorithm…

非理性亢奋：校正概率估计中的偏差AI 解读

We consider the common setting where one observes probability estimates for a large number of events, such as default risks for numerous bonds. Unfortunately, even with unbiased estimates, selecting events corresponding to the most extreme probabilities can result in systematically underestimating the true level of uncertainty. We develop an empirical Bayes approach “excess certainty adjusted probabilities” (ECAP), using a variant of Tweedie’s formula, which updates…

卡方数据的经验贝叶斯方法AI 解读

In a thought-provoking paper, Efron investigated the merit and limitation of an empirical Bayes method to correct selection bias based on Tweedie’s formula first reported in the study by Robbins. The exceptional virtue of Tweedie’s formula for the normal distribution lies in its representation of selection bias as a simple function of the derivative of log marginal likelihood. Since the marginal likelihood and its derivative can be estimated from the data directly without…

贝叶斯因子分析的模态跳跃算法AI 解读

Exploratory factor analysis is a dimension-reduction technique commonly used in psychology, finance, genomics, neuroscience, and economics. Advances in computational power have opened the door for fully Bayesian treatments of factor analysis. One open problem is enforcing rotational identifability of the latent factor loadings, as the loadings are not identified from the likelihood without further restrictions. Nonidentifability of the loadings can cause posterior…

分组回归与稀疏广义加性模型的尖峰—厚尾组 LassoAI 解读

–We introduce the spike-and-slab group lasso (SSGL) for Bayesian estimation and variable selection in linear regression with grouped variables. We further extend the SSGL to sparse generalized additive models (GAMs), thereby introducing the first nonparametric variant of the spike-and-slab lasso methodology. Our model simultaneously performs group selection and estimation, while our fully Bayes treatment of the mixture proportion allows for model complexity control and…