A universal approach to imprecise probabilities in possibility theory

Hose, Dominik; Hanss, Michael

doi:10.1016/j.ijar.2021.03.010

Cited by 29 publications

(15 citation statements)

References 46 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Here I want to focus on a simple strategy presented recently in Hose and Hanss (2021). Their perspective is to combine pieces of information at the credal set level, which is certainly reasonable.…”

Section: Information Aggregationmentioning

confidence: 99%

Valid and efficient imprecise-probabilistic inference across a spectrum of partial prior information

Martin¹

2022

Preprint

View full text Add to dashboard Cite

Bayesian inference quantifies uncertainty directly and formally using classical probability theory, while frequentist inference does so indirectly and informally through the use of procedures with error rate control. Both have merits in the appropriate context, but the context isn't binary. There's an entire spectrum of contexts depending on what, if any, partial prior information is available to incorporate, with "Bayesian" and "frequentist" sitting on opposite ends of the spectrum corresponding to a complete, fully precise prior distribution and a vacuous, fully imprecise prior distribution, respectively. Common examples between the two extremes include those high-dimensional problems where, e.g., sparsity assumptions are relevant but fall short of determining a complete prior distribution. This paper ties the two frameworks together by treating those cases where only partial prior information is available using the theory of imprecise probability. The end result is a unified framework of (imprecise-probabilistic) statistical inference with a new validity condition that implies both frequentist-style error rate control for derived procedures and Bayesian-style no-sure-loss properties, relative to the given partial prior information. This theory contains both the classical "Bayesian" and "frequentist" frameworks as special cases, since they're both valid in this new sense relative to their respective partial priors. Different constructions of these valid inferential models are considered, and compared based on their efficiency.

show abstract

Section: Information Aggregationmentioning

confidence: 99%

Valid and efficient imprecise-probabilistic inference across a spectrum of partial prior information

Martin¹

2022

Preprint

View full text Add to dashboard Cite

show abstract

“…as described in, e.g., Definition 9 of Hose and Hanss (2021). Since Q is simple, this is relatively easy to arrange.…”

Section: Generalized Im: Basic Ideamentioning

confidence: 99%

Approximately valid probabilistic inference on a class of statistical functionals

Cella,

Martin

2021

Preprint

View full text Add to dashboard Cite

Existing frameworks for probabilistic inference assume the inferential target is the posited statistical model's parameter. In machine learning applications, however, often there is no statistical model, so the quantity of interest is not a model parameter but a statistical functional. In this paper, we develop a generalized inferential model framework for cases when this functional is a risk minimizer or solution to an estimating equation. We construct a data-dependent possibility measure for uncertainty quantification and inference whose computation is based on the bootstrap. We then prove that this new generalized inferential model provides approximately valid inference in the sense that the plausibility values assigned to hypotheses about the unknowns are asymptotically well-calibrated in a frequentist sense. Among other things, this implies that confidence regions for the underlying functional derived from our new generalized inferential model are approximately valid. The method is shown to perform well in classical examples, including quantile regression, and in a personalized medicine application.

show abstract

“…Table 1 lists some hedge words and their possible interpretations. Hedge words can be interpreted as intervals, p-boxes [21], or consonant c-boxes [42].…”

Section: Natural Language Uncertaintymentioning

confidence: 99%

Computing With Uncertainty: Introducing Puffin the Automatic Uncertainty Compiler

Gray¹,

Angelis²,

Ferson³

2019

Proceedings of the 3rd International Conference on Uncertainty Quantification in Computational Sciences and Engineering (UNCECO

View full text Add to dashboard Cite

Although engineers often recognise the advantages of applying uncertainty analysis to their complex simulations, they often lack the time, patience or expertise to undertake that analysis. We describe a software tool, named puffin, that takes existing code and converts in to uncertainty aware code in the same language making use of intrusive uncertainty propagation techniques. It can work either automatically or with user specification of the uncertainties involved in the system.

show abstract

A universal approach to imprecise probabilities in possibility theory

Cited by 29 publications

References 46 publications

Valid and efficient imprecise-probabilistic inference across a spectrum of partial prior information

Valid and efficient imprecise-probabilistic inference across a spectrum of partial prior information

Approximately valid probabilistic inference on a class of statistical functionals

Computing With Uncertainty: Introducing Puffin the Automatic Uncertainty Compiler

Contact Info

Product

Resources

About