Inference for a generalised stochastic block model with unknown number of blocks and non-conjugate edge models

广义线性模型及其扩展的先验提取

Prior Elicitation for Generalised Linear Models and Extensions

本文提出一种贝叶斯广义线性模型（GLMs）及其扩展的先验提取方法，通过专家概率预测参数化先验分布，提取场景依赖关系构建规范藤copula模型，支持多数据类型并在R包eglm中实现。

Generalised Bayes Updates with $f$-divergences through Probabilistic Classifiers

A stream of algorithmic advances has steadily increased the popularity of the Bayesian approach as an inference paradigm, both from the theoretical and applied perspective. Even with apparent successes in numerous application fields, a rising concern is the robustness of Bayesian inference in the presence of model misspecification, which may lead to undesirable extreme behavior of the posterior distributions for large sample sizes. Generalized belief updating with a loss function represents a central principle to making Bayesian inference more robust and less vulnerable to deviations from the …

基于预测堆叠的时空非高斯数据的贝叶斯推断

Bayesian Inference for Spatial-Temporal Non-Gaussian Data Using Predictive Stacking

本文提出基于预测堆叠的贝叶斯推断方法，用于处理时空非高斯数据，通过共轭先验和广义共轭多变量分布理论实现精确采样，提升推断性能。

Sparse Bayesian Factor Analysis when the Number of Factors is Unknown

Despite the popularity of sparse factor models, little attention has been given to formally address identifiability of these models beyond standard rotation-based identification such as the positive lower triangular constraint. To fill this gap, we provide a counting rule on the number of nonzero factor loadings that is sufficient for achieving uniqueness of the variance decomposition in the factor representation. Furthermore, we introduce the generalised lower triangular representation to resolve rotational invariance and show that within this model class the unknown number of common factors …

Sequential Change Detection in the Presence of Unknown Parameters

It is commonly required to detect change points in sequences of random variables. In the most difficult setting of this problem, change detection must be performed sequentially with new observations being constantly received over time. Further, the parameters of both the pre- and post- change distributions may be unknown. In a recent paper by Hawkins and Zamba (2005), the sequential generalised likelihood ratio test was introduced for detecting changes in this context, under the assumption that the observations follow a Gaussian distribution. However, we show that the asymptotic approximation …

Statistical modelling of COVID-19 data: Putting Generalised Additive Models to work

Over the course of the COVID-19 pandemic, Generalised Additive Models (GAMs) have been successfully employed on numerous occasions to obtain vital data-driven insights. In this paper we further substantiate the success story of GAMs, demonstrating their flexibility by focusing on three relevant pandemic-related issues. First, we examine the interdepency among infections in different age groups, concentrating on school children. In this context, we derive the setting under which parameter estimates are independent of the (unknown) case-detection ratio, which plays an important role in COVID-19 …

Model-robust Bayesian design through Generalised Additive Models for monitoring submerged shoals

Optimal sampling strategies are critical for surveys of deeper coral reef and shoal systems, due to the significant cost of accessing and field sampling these remote and poorly understood ecosystems. Additionally, well-established standard diver-based sampling techniques used in shallow reef systems cannot be deployed because of water depth. Here we develop a Bayesian design strategy to optimise sampling for a shoal deep reef system using three years of pilot data. Bayesian designs are generally found by maximising the expectation of a utility function with respect to the joint distribution of…

后验预测检查何时能识别学习率？高斯模型中的精确退化及其对广义贝叶斯推断的影响

When can a posterior predictive check identify the learning rate? Exact degeneracy in Gaussian models and implications for Generalised Bayesian Inerence

本文通过精确有限样本分析，揭示了在高斯线性模型中，基于后验预测检查的学习率选择器存在退化现象，即p值不依赖于学习率或数据，导致选择器失效，并提出了数据无关的预筛选诊断方法。