When complex Bayesian models exhibit implausible behaviour, one solution is to assemble available information into an informative prior. Challenges arise as prior information is often only available for the observable quantity, or some model-derived marginal quantity, rather than directly pertaining to the (usually latent) parameters in our model. We propose a method for translating available prior information, in the form of an elicited distribution for the observable or model-derived marginal quantity, into an informative joint prior. Our approach proceeds given a parametric class of prior distributions with as yet undetermined hyperparameters, and minimises the difference between the supplied elicited distribution and corresponding prior predictive distribution. We employ a global, multi-stage Bayesian optimisation procedure to locate optimal values for the hyperparameters. Three examples illustrate our approach: a cure-fraction survival model, where censoring implies that the observable quantity is _a priori_ a mixed discrete/continuous quantity; a setting in which prior information pertains to $R^{2}$ -- a model-derived quantity; and a nonlinear regression model.
High-dimensional data often arise from clinical genomics research to infer relevant predictors of a particular trait. A way to improve the predictive performance is to include information on the predictors derived from prior knowledge or previous studies. Such information is also referred to as ``co-data''. To this aim, we develop a novel Bayesian model for including co-data in a high-dimensional regression framework, called Informative Horseshoe regression (infHS). The proposed approach regresses the prior variances of the regression parameters on the co-data variables, improving variable sel…
Informative Distance-Based Priors for Correlation Matrices Centred on a Target Reference
The Alan Turing Institute（艾伦·图灵研究所）；University of Pretoria（比勒陀利亚大学）；King Abdullah University of Science and Technology（阿卜杜拉国王科技大学）；National Institute of Health and Medical Research (Inserm UMR 1219)（法国国家健康与医学研究院 (Inserm UMR 1219)）；Universiti Brunei Darussalam（文莱达鲁萨兰国大学）
Early Prediction of Student Performance Using Bayesian Updating with Informative Priors Across Cohorts
Hector Research Institute of Education Sciences and Psychology, University of Tübingen（蒂宾根大学教育科学与心理学赫克托研究所）；Department of Statistics, TU Dortmund University（多特蒙德工业大学统计系）
When can a posterior predictive check identify the learning rate? Exact degeneracy in Gaussian models and implications for Generalised Bayesian Inerence
We encounter variables with little variation often in educational data mining (EDM) due to the demographics of higher education and the questions we ask. Yet, little work has examined how to analyze such data. Therefore, we conducted a simulation study using logistic regression, penalized regression, and random forest. We systematically varied the fraction of positive outcomes, feature imbalances, and odds ratios. We find the algorithms treat features with the same odds ratios differently based on the features' imbalance and the outcome imbalance. While none of the algorithms fully solved how …
Meta-analytic-predictive priors based on a single study
University Medical Center Göttingen（哥廷根大学医学中心）；DZHK (German Center for Cardiovascular Research)（德国心血管研究中心）；DZKJ (German Center for Child and Adolescent Health)（德国儿童与青少年健康中心）
