Related papers: Bayesian Statistics: A Review and a Reminder for t…
An imprecise Bayesian nonparametric approach to system reliability with multiple types of components is developed. This allows modelling partial or imperfect prior knowledge on component failure distributions in a flexible way through…
Models for which the likelihood function can be evaluated only up to a parameter-dependent unknown normalising constant, such as Markov random field models, are used widely in computer science, statistical physics, spatial statistics, and…
Markov Chain Monte Carlo based Bayesian data analysis has now become the method of choice for analyzing and interpreting data in almost all disciplines of science. In astronomy, over the last decade, we have also seen a steady increase in…
We present a Bayesian nonparametric system reliability model which scales well and provides a great deal of flexibility in modeling. The Bayesian approach naturally handles the disparate amounts of component and subsystem data that may…
In this paper authors present a general methodology for age dependent reliability analysis of degrading or ageing systems, structures and components.The methodology is based on Bayesian methods and inference, its ability to incorporate…
Especially when facing reliability data with limited information (e.g., a small number of failures), there are strong motivations for using Bayesian inference methods. These include the option to use information from physics-of-failure or…
The systems that statisticians are asked to assess, such as nuclear weapons, infrastructure networks, supercomputer codes and munitions, have become increasingly complex. It is often costly to conduct full system tests. As such, we present…
Data transformations are essential for broad applicability of parametric regression models. However, for Bayesian analysis, joint inference of the transformation and model parameters typically involves restrictive parametric transformations…
Bayesian models are a powerful tool for studying complex data, allowing the analyst to encode rich hierarchical dependencies and leverage prior information. Most importantly, they facilitate a complete characterization of uncertainty…
Increasingly complex applications involve large datasets in combination with non-linear and high dimensional mathematical models. In this context, statistical inference is a challenging issue that calls for pragmatic approaches that take…
Bayesian statistics is a cornerstone of imaging sciences, underpinning many and varied approaches from Markov random fields to score-based denoising diffusion models. In addition to powerful image estimation methods, the Bayesian paradigm…
We propose a Bayesian elastic net that uses empirical likelihood and develop an efficient tuning of Hamiltonian Monte Carlo for posterior sampling. The proposed model relaxes the assumptions on the identity of the error distribution,…
There is a lack of simple and scalable algorithms for uncertainty quantification. Bayesian methods quantify uncertainty through posterior and predictive distributions, but it is difficult to rapidly estimate summaries of these…
For a Bayesian, real-time forecasting with the posterior predictive distribution can be challenging for a variety of time series models. First, estimating the parameters of a time series model can be difficult with sample-based approaches…
Statistical models can involve implicitly defined quantities, such as solutions to nonlinear ordinary differential equations (ODEs), that unavoidably need to be numerically approximated in order to evaluate the model. The approximation…
A key quantity of interest in Bayesian inference are expectations of functions with respect to a posterior distribution. Markov Chain Monte Carlo is a fundamental tool to consistently compute these expectations via averaging samples drawn…
Assessment of replicability is critical to ensure the quality and rigor of scientific research. In this paper, we discuss inference and modeling principles for replicability assessment. Targeting distinct application scenarios, we propose…
Models of stochastic processes are widely used in almost all fields of science. Theory validation, parameter estimation, and prediction all require model calibration and statistical inference using data. However, data are almost always…
In this article, an overview of Bayesian methods for sequential simulation from posterior distributions of nonlinear and non-Gaussian dynamic systems is presented. The focus is mainly laid on sequential Monte Carlo methods, which are based…
This paper presents a Bayesian framework for assessing the adequacy of a model without the necessity of explicitly enumerating a specific alternate model. A test statistic is developed for tracking the performance of the model across…