Related papers: A note on using Bayes priors for Weibull distribut…
One of the main goals of mathematical modeling in systems medicine related to medical applications is to obtain patient-specific parameterizations and model predictions. In clinical practice, however, the number of available measurements…
Bayesian modeling provides a principled approach to quantifying uncertainty in model parameters and model structure and has seen a surge of applications in recent years. Within the context of a Bayesian workflow, we are concerned with model…
The behavior of many Bayesian models used in machine learning critically depends on the choice of prior distributions, controlled by some hyperparameters that are typically selected by Bayesian optimization or cross-validation. This…
Objectives: The aim of this paper is to contrast the retrospective and prospective use of experts beliefs in choosing between survival models in economic evaluations. Methods: The use of experts retrospective (posterior) beliefs is…
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…
Modeling is a challenging topic and using parametric models is an important stage to reach flexible function for modeling. Weibull distribution has two parameters which are shape $\alpha$ and scale $\beta$. In this study, bimodality…
We consider the problem of Bayesian regression with trustworthy uncertainty quantification. We define that the uncertainty quantification is trustworthy if the ground truth can be captured by intervals dependent on the predictive…
In this work, we develop an objective Bayesian framework for the Dhillon probability distribution. We explicitly derive three objective priors: the Jeffreys prior, the overall reference prior, and the maximal data information prior. We show…
In the popular approach of "Bayesian variable selection" (BVS), one uses prior and posterior distributions to select a subset of candidate variables to enter the model. A completely new direction will be considered here to study BVS with a…
The measurement of the efficiency of an event selection is always an important part of the analysis of experimental data. The statistical techniques which are needed to determine the efficiency and its uncertainty are reviewed. Frequentist…
This paper aims at developing a quasi-Bayesian analysis of the nonparametric instrumental variables model, with a focus on the asymptotic properties of quasi-posterior distributions. In this paper, instead of assuming a distributional…
The Weibull distribution is a very applicable model for the lifetime data. For inference about two Weibull distributions using records, the shape parameters of the distributions are usually considered equal. However, there is not an…
A novel information-theoretic approach is proposed to assess the global practical identifiability of Bayesian statistical models. Based on the concept of conditional mutual information, an estimate of information gained for each model…
In this paper reference and probability-matching priors are derived for the univariate Student $t$-distribution. These priors generally lead to procedures with properties frequentists can relate to while still retaining Bayes validity. The…
It can be important in Bayesian analyses of complex models to construct informative prior distributions which reflect knowledge external to the data at hand. Nevertheless, how much prior information an analyst can elicit from an expert will…
This tutorial gives a quick introduction to Variational Bayes (VB), also called Variational Inference or Variational Approximation, from a practical point of view. The paper covers a range of commonly used VB methods and an attempt is made…
In this paper, we consider the problem of estimating an extreme quantile of a Weibull tail-distribution. The new extreme quantile estimator has a reduced bias compared to the more classical ones proposed in the literature. It is based on an…
Classic Bayesian methods with complex models are frequently infeasible due to an intractable likelihood. Simulation-based inference methods, such as Approximate Bayesian Computing (ABC), calculate posteriors without accessing a likelihood…
The integration of data and knowledge from several sources is known as data fusion. When data is only available in a distributed fashion or when different sensors are used to infer a quantity of interest, data fusion becomes essential. In…
We present a simple method to obtain optimal posterior distributions and improve the quality of Bayesian inference with reduced human and computational effort. Bayes' Theorem is reformulated in the language of statistical mechanics, wherein…