Related papers: Elicitation of Weibull priors
The quality of probabilistic forecasts is crucial for decision-making under uncertainty. While proper scoring rules incentivize truthful reporting of precise forecasts, they fall short when forecasters face epistemic uncertainty about their…
We propose a novel approach to perform approximate Bayesian inference in complex models such as Bayesian neural networks. The approach is more scalable to large data than Markov Chain Monte Carlo, it embraces more expressive models than…
In variational inference, the benefits of Bayesian models rely on accurately capturing the true posterior distribution. We propose using neural samplers that specify implicit distributions, which are well-suited for approximating complex…
Full Bayesian posteriors are rarely analytically tractable, which is why real-world Bayesian inference heavily relies on approximate techniques. Approximations generally differ from the true posterior and require diagnostic tools to assess…
Bayesian inference requires specification of a single, precise prior distribution, whereas frequentist inference only accommodates a vacuous prior. Since virtually every real-world application falls somewhere in between these two extremes,…
We propose a Bayesian approach using improper priors for hierarchical linear mixed models with flexible random effects and residual error distributions. The error distribution is modelled using scale mixtures of normals, which can capture…
In this paper we introduce objective proper prior distributions for hypothesis testing and model selection based on measures of divergence between the competing models; we call them divergence based (DB) priors. DB priors have simple forms…
We propose the notion of sub-Weibull distributions, which are characterised by tails lighter than (or equally light as) the right tail of a Weibull distribution. This novel class generalises the sub-Gaussian and sub-Exponential families to…
A Bayesian estimator aiming at improving the conditional MLE is proposed by introducing a pair of priors. After explaining the conditional MLE by the posterior mode under a prior, we define a promising estimator by the posterior mean under…
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…
The problem of assigning probability distributions which objectively reflect the prior information available about experiments is one of the major stumbling blocks in the use of Bayesian methods of data analysis. In this paper the method of…
Many models in natural language processing define probabilistic distributions over linguistic structures. We argue that (1) the quality of a model' s posterior distribution can and should be directly evaluated, as to whether probabilities…
We propose an information criterion for multistep ahead predictions. It is also used for extrapolations. For the derivation, we consider multistep ahead predictions under local misspecification. In the prediction, we show that Bayesian…
Bayesian inference promises a framework for principled uncertainty quantification of neural network predictions. Barriers to adoption include the difficulty of fully characterizing posterior distributions on network parameters and the…
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,…
1. Challenging calibration of complex models can be approached by using prior knowledge on the parameters. However, the natural choice of Bayesian inference can be computationally heavy when relying on Markov Chain Monte Carlo (MCMC)…
There are three principle paradigms of statistical inference: (i) Bayesian, (ii) information-based and (iii) frequentist inference. We describe an objective prior (the weighting or $w$-prior) which unifies objective Bayes and…
For a portfolio of life insurance policies observed for a stated period of time, e.g., one year, mortality is typically a rare event. When we examine the outcome of dying or not from such portfolios, we have an imbalanced binary response.…
The Bradley-Terry model is a popular approach to describe probabilities of the possible outcomes when elements of a set are repeatedly compared with one another in pairs. It has found many applications including animal behaviour, chess…
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…