Related papers: On a Class of Objective Priors from Scoring Rules
Variable selection and classification are common objectives in the analysis of high-dimensional data. Most such methods make distributional assumptions that may not be compatible with the diverse families of distributions data can take. A…
The main object of Bayesian statistical inference is the determination of posterior distributions. Sometimes these laws are given for quantities devoid of empirical value. This serious drawback vanishes when one confines oneself to…
Probabilistic classifiers output a probability distribution on target classes rather than just a class prediction. Besides providing a clear separation of prediction and decision making, the main advantage of probabilistic models is their…
Objective probabilistic forecasts of future climate that include parameter uncertainty can be made by using the Bayesian prediction integral with the prior set to Jeffreys' Prior. The calculations involved in determining the prior can then…
Bayesian model selection with improper priors is not well-defined because of the dependence of the marginal likelihood on the arbitrary scaling constants of the within-model prior densities. We show how this problem can be evaded by…
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…
Statistical system models provide the basis for the examination of various sorts of distributions. Classification distributions are a very common and versatile form of statistics in e.g. real economic, social, and IT systems. The…
This paper develops some objective priors for certain parameters of the bivariate normal distribution. The parameters considered are the regression coefficient, the generalized variance, and the ratio of the conditional variance of one…
In high-dimensional problems, choosing a prior distribution such that the corresponding posterior has desirable practical and theoretical properties can be challenging. This begs the question: can the data be used to help choose a good…
For many years it was routine to use equal model prior probabilities in Bayesian model uncertainty analysis. At least twenty years ago it became clear that this was problematic, leading to support of much too large models in the…
The ranking problem is to order a collection of units by some unobserved parameter, based on observations from the associated distribution. This problem arises naturally in a number of contexts, such as business, where we may want to rank…
Bayesian statistics emphasizes the importance of prior distributions, yet finding an appropriate one is practically challenging. When multiple sample results are taken regarding the frequency of the same event, these samples may be…
Feature attribution methods, proposed recently, help users interpret the predictions of complex models. Our approach integrates feature attributions into the objective function to allow machine learning practitioners to incorporate priors…
Unsupervised models can provide supplementary soft constraints to help classify new target data under the assumption that similar objects in the target set are more likely to share the same class label. Such models can also help detect…
We propose a class of structured diffusion models, in which the prior distribution is chosen as a mixture of Gaussians, rather than a standard Gaussian distribution. The specific mixed Gaussian distribution, as prior, can be chosen to…
We study objective Bayesian inference for linear regression models with residual errors distributed according to the class of two-piece scale mixtures of normal distributions. These models allow for capturing departures from the usual…
Reference analysis produces objective Bayesian inference, in the sense that inferential statements depend only on the assumed model and the available data, and the prior distribution used to make an inference is least informative in a…
One of the main approaches used to construct prior distributions for objective Bayes methods is the concept of random imaginary observations. Under this setup, the expected-posterior prior (EPP) offers several advantages, among which it has…
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…
Score-based diffusion models are a recently developed framework for posterior sampling in Bayesian inverse problems with a state-of-the-art performance for severely ill-posed problems by leveraging a powerful prior distribution learned from…