相关论文: Sensitivity analysis for Bayesian hierarchical mod…

Uncertainty quantification is essential when dealing with ill-conditioned inverse problems due to the inherent nonuniqueness of the solution. Bayesian approaches allow us to determine how likely an estimation of the unknown parameters is…

Meta-analysis is a powerful tool to synthesize findings from multiple studies. The normal-normal random-effects model is widely used to account for between-study heterogeneity. However, meta-analysis of sparse data, which may arise when the…

Matching is one of the most widely used study designs for adjusting for measured confounders in observational studies. However, unmeasured confounding may exist and cannot be removed by matching. Therefore, a sensitivity analysis is…

When developing Bayesian hierarchical models, selecting the most appropriate hierarchical structure can be a challenging task, and visualisation remains an underutilised tool in this context. In this paper, we consider visualisations for…

Sensitivity analysis is an important tool used in many domains of computational science to either gain insight into the mathematical model and interaction of its parameters or study the uncertainty propagation through the input-output…

The normal-normal hierarchical model (NNHM) constitutes a simple and widely used framework for meta-analysis. In the common case of only few studies contributing to the meta-analysis, standard approaches to inference tend to perform poorly,…

Causal inference relies on the untestable assumption of no unmeasured confounding. Sensitivity analysis can be used to quantify the impact of unmeasured confounding on causal estimates. Among sensitivity analysis methods proposed in the…

Inverse problems constrained by partial differential equations (PDEs) play a critical role in model development and calibration. In many applications, there are multiple uncertain parameters in a model which must be estimated. Although the…

Differential analysis is a routine procedure in the statistical analysis toolbox across many applied fields, including quantitative proteomics, the main illustration of the present paper. The state-of-the-art limma approach uses a…

Many modern experiments, such as microarray gene expression and genome-wide association studies, present the problem of estimating a large number of parallel effects. Bayesian inference is a popular approach for analyzing such data by…

To account for measurement error (ME) in explanatory variables, Bayesian approaches provide a flexible framework, as expert knowledge about unobserved covariates can be incorporated in the prior distributions. However, given the analytic…

We discuss Bayesian inference for parameters selected using the data. First, we provide a critical analysis of the existing positions in the literature regarding the correct Bayesian approach under selection. Second, we propose two types of…

Count outcomes in longitudinal studies are frequent in clinical and engineering studies. In frequentist and Bayesian statistical analysis, methods such as Mixed linear models allow the variability or correlation within individuals to be…

Bayesian synthetic likelihood (BSL) is a popular method for estimating the parameter posterior distribution for complex statistical models and stochastic processes that possess a computationally intractable likelihood function. Instead of…

Bayesian statistics is an integral part of contemporary applied science. bayesics provides a single framework, unified in syntax and output, for performing the most commonly used statistical procedures, ranging from one- and two-sample…

We revisit the problem of simultaneously testing the means of $n$ independent normal observations under sparsity. We take a Bayesian approach to this problem by introducing a scale-mixture prior known as the normal-beta prime (NBP) prior.…

A central characteristic of Bayesian statistics is the ability to consistently incorporate prior knowledge into various modeling processes. In this paper, we focus on translating domain expert knowledge into corresponding prior…

Observational studies are often conducted to estimate causal effects of treatments or exposures on event-time outcomes. Since treatments are not randomized in observational studies, techniques from causal inference are required to adjust…

The accuracy of probability distributions inferred using machine-learning algorithms heavily depends on data availability and quality. In practical applications it is therefore fundamental to investigate the robustness of a statistical…

Bayesian statistics has gained popularity in psychological research due to its intuitive uncertainty quantification and convenient information-updating rules. In many applications, however, prior distributions are introduced merely as…