Bayesian Variable Selection for Skewed Heteroscedastic Response

H-AddiVortes：异方差（贝叶斯）加性 Voronoi 镶嵌模型

H-AddiVortes: Heteroscedastic (Bayesian) Additive Voronoi Tessellations

提出贝叶斯非参数 Heteroscedastic AddiVortes 模型，用自适应 Voronoi 镶嵌的均值求和与方差乘积结构实现异方差回归和不确定性量化。

异方差双贝叶斯弹性网

Heteroscedastic Double Bayesian Elastic Net

本文提出异方差双贝叶斯弹性网（HDBEN），通过分层贝叶斯先验联合建模均值和log方差，在高维异方差场景下实现稀疏估计与变量选择，并证明其后验收缩、选择一致性及渐近正态性。

Detection of latent heteroscedasticity and group-based regression effects in linear models via Bayesian model selection

Standard linear modeling approaches make potentially simplistic assumptions regarding the structure of categorical effects that may obfuscate more complex relationships governing data. For example, recent work focused on the two-way unreplicated layout has shown that hidden groupings among the levels of one categorical predictor frequently interact with the ungrouped factor. We extend the notion of a "latent grouping factor" to linear models in general. The proposed work allows researchers to determine whether an apparent grouping of the levels of a categorical predictor reveals a plausible hi…

Objective Bayesian modelling of insurance risks with the skewed Student-t distribution

Insurance risks data typically exhibit skewed behaviour. In this paper, we propose a Bayesian approach to capture the main features of these datasets. This work extends the methodology introduced in Villa and Walker (2014a) by considering an extra parameter which captures the skewness of the data. In particular, a skewed Student-t distribution is considered. Two datasets are analysed: the Danish fire losses and the US indemnity loss. The analysis is carried with an objective Bayesian approach. For the discrete parameter representing the number of the degrees of freedom, we adopt a novel prior …

A Bayesian Heteroscedastic GLM with Application to fMRI Data with Motion Spikes

We propose a voxel-wise general linear model with autoregressive noise and heteroscedastic noise innovations (GLMH) for analyzing functional magnetic resonance imaging (fMRI) data. The model is analyzed from a Bayesian perspective and has the benefit of automatically down-weighting time points close to motion spikes in a data-driven manner. We develop a highly efficient Markov Chain Monte Carlo (MCMC) algorithm that allows for Bayesian variable selection among the regressors to model both the mean (i.e., the design matrix) and variance. This makes it possible to include a broad range of explan…

带有异方差测量误差的常微分方程模型的贝叶斯推断

Bayesian inference for ordinary differential equations models with heteroscedastic measurement error

本文提出一种半参数框架，用于处理常微分方程模型中存在异方差误差时的贝叶斯参数估计。通过高斯过程估计时间依赖误差，再利用估计的误差进行贝叶斯推断，提升后验推断和预测不确定性可靠性。

潜在高斯模型的可扩展偏态贝叶斯推断

Scalable skewed Bayesian inference for latent Gaussian models

针对潜在高斯模型，提出基于INLA的偏态拉普拉斯变分推断扩展，兼顾偏态与高斯边缘及依赖保持，可扩展处理重尾似然和类别不平衡数据，经模拟和罕见病案例验证。

异方差健康结局数据的贝叶斯核机器回归

Bayesian kernel machine regression for heteroscedastic health outcome data

本文针对环境流行病学中BKMR模型误差项恒定方差假设不成立的问题，开发了异方差HBKMR方法，通过贝叶斯分层方差模型更新健康效应估计，并在两项真实金属暴露案例中显著提升了模型拟合度。

一种应用于尺度问题的异方差贝叶斯广义逻辑回归模型

A Heteroscedastic Bayesian Generalized Logistic Regression Model with Application to Scaling Problems

针对幂律尺度建模中常用方法假设正态分布与固定方差易产生偏差的问题，提出贝叶斯广义逻辑回归框架，结合GLD处理偏态与异方差，用MCMC求解，经COVID-19数据验证效果更优且具普适性。

贝叶斯中介分析中偏态和厚尾误差的建模

Modelling Skewed and Heavy-Tailed Errors in Bayesian Mediation Analysis

针对传统中介模型误差正态假设违背的问题，提出中心化两段式学生t分布建模偏态厚尾误差，结合贝叶斯框架提升检验功效与稳健性，还开发了对应R包。

Flexible Bayesian modelling in dichotomous item response theory using mixtures of skewed item curves

Most Item Response Theory (IRT) models for dichotomous responses are based on probit or logit link functions which assume a symmetric relationship between the probability of a correct response and the latent traits of individuals submitted to a test. This assumption restricts the use of those models to the case in which all items have a symmetric behaviour. On the other hand, asymmetric models proposed in the literature impose that all the items in a test have an asymmetric behaviour. This assumption is inappropriate for great part of the tests which are, in general, composed by both symmetric…

Categorical data analysis using a skewed Weibull regression model

In this paper, we present a Weibull link (skewed) model for categorical response data arising from binomial as well as multinomial model. We show that, for such types of categorical data, the most commonly used models (logit, probit and complementary log-log) can be obtained as limiting cases. We further compare the proposed model with some other asymmetrical models. The Bayesian as well as frequentist estimation procedures for binomial and multinomial data responses are presented in details. The analysis of two data sets to show the efficiency of the proposed model is performed.

通过统一偏态正态先验的贝叶斯非参数重缩放实现未对齐二元时间序列之间的强度借用

Borrowing strength between unaligned binary time-series via Bayesian nonparametric rescaling of Unified Skewed Normal priors

针对未对齐纵向二元数据，提出基于Pitman-Yor先验与SUN二元状态空间模型的贝叶斯半参数方法，以在保留个体异质性的同时跨患者借用信息。

基于INLA的测量误差模型贝叶斯分析

Bayesian analysis of measurement error models using INLA

为了解释解释变量中的测量误差（ME），贝叶斯方法提供了一个灵活的框架，因为关于未观察到的协变量的专家知识可以被纳入先验分布中。然而，由于分析棘手的后验分布，模型推理到目前为止，必须通过耗时和复杂的马尔可夫链蒙特卡罗实现。本文推广了集成嵌套拉普拉斯近似（INLA）方法，使之能在广义线性混合模型中建立高斯ME模型。我们提出了三个应用程序，并显示如何获得常见的ME模型，如经典和Berkson误差模型，包括异方差的参数估计。为了说明实际的可行性，R-代码提供。

Infinite mixtures of multivariate normal-inverse Gaussian distributions for clustering of skewed data

Mixtures of multivariate normal inverse Gaussian (MNIG) distributions can be used to cluster data that exhibit features such as skewness and heavy tails. However, for cluster analysis, using a traditional finite mixture model framework, either the number of components needs to be known $a$-$priori$ or needs to be estimated $a$-$posteriori$ using some model selection criterion after deriving results for a range of possible number of components. However, different model selection criteria can sometimes result in different number of components yielding uncertainty. Here, an infinite mixture model…

使用 R 包 slgf 进行具有潜在分组效应和方差的贝叶斯模型选择

Bayesian Model Selection with Latent Group-Based Effects and Variances with the R Package slgf

本文介绍 R 包 slgf，通过贝叶斯模型选择检测分类预测变量中的潜在分组、回归效应、交互作用及异方差，并在多种 ANOVA/ANCOVA 布局中展示其优势。

面向复杂数据结构特征选择的非参数贝叶斯Knockoff生成器

Nonparametric Bayesian Knockoff Generators for Feature Selection Under Complex Data Structure

本文提出非参数贝叶斯GDPM模型生成高质量knockoff副本，用于复杂数据分布下的FDR控制特征选择，在模拟与TCGA卵巢癌数据中表现出准确FDR控制与更高功效。