Related papers: Inferential models and possibility measures

It is shown that the fiducial distribution in a group model, or more generally a quasigroup model, determines the optimal equivariant frequentist inference procedures. The proof does not rely on existence of invariant measures, and…

Fisher's fiducial argument is widely viewed as a failed version of Neyman's theory of confidence limits. But Fisher's goal -- Bayesian-like probabilistic uncertainty quantification without priors -- was more ambitious than Neyman's, and…

Likelihood-free inference refers to inference when a likelihood function cannot be explicitly evaluated, which is often the case for models based on simulators. Most of the literature is based on sample-based `Approximate Bayesian…

Variational inference is a popular method for estimating model parameters and conditional distributions in hierarchical and mixed models, which arise frequently in many settings in the health, social, and biological sciences. Variational…

Belief functions are a powerful and popular framework for the mathematical characterisation of uncertainty, in particular in situations in which lack of data renders learning a probability distribution for the problem impractical. The first…

Marginal expected shortfall is unquestionably one of the most popular systemic risk measures. Studying its extreme behaviour is particularly relevant for risk protection against severe global financial market downturns. In this context,…

Our paper deals with inferring simulator-based statistical models given some observed data. A simulator-based model is a parametrized mechanism which specifies how data are generated. It is thus also referred to as generative model. We…

A fundamental class of inferential problems are those characterised by there having been a substantial degree of pre-data (or prior) belief that the value of a model parameter was equal or lay close to a specified value, which may, for…

A growing number of empirical models exhibit set-valued predictions. This paper develops a tractable inference method with finite-sample validity for such models. The proposed procedure uses a robust version of the universal inference…

Several different uncertain inference systems (UISs) have been developed for representing uncertainty in rule-based expert systems. Some of these, such as Mycin's Certainty Factors, Prospector, and Bayes' Networks were designed as…

This paper presents a general and efficient framework for probabilistic inference and learning from arbitrary uncertain information. It exploits the calculation properties of finite mixture models, conjugate families and factorization. Both…

As the frontiers of applied statistics progress through increasingly complex experiments we must exploit increasingly sophisticated inferential models to analyze the observations we make. In order to avoid misleading or outright erroneous…

Inference is the process of using facts we know to learn about facts we do not know. A theory of inference gives assumptions necessary to get from the former to the latter, along with a definition for and summary of the resulting…

Implicit probabilistic models are models defined naturally in terms of a sampling procedure and often induces a likelihood function that cannot be expressed explicitly. We develop a simple method for estimating parameters in implicit models…

We consider an empirical likelihood framework for inference for a statistical model based on an informative sampling design. Covariate information is incorporated both through the weights and the estimating equations. The estimator is based…

The general use of subjective probabilities to model belief has been justified using many axiomatic schemes. For example, ?consistent betting behavior' arguments are well-known. To those not already convinced of the unique fitness and…

In this paper, we develop invariance-based procedures for testing and inference in high-dimensional regression models. These procedures, also known as randomization tests, provide several important advantages. First, for the global null…

Time series data with missing values is common across many domains. Healthcare presents special challenges due to prolonged periods of sensor disconnection. In such cases, having a confidence measure for imputed values is critical. Most…

Implicit probabilistic models are a flexible class of models defined by a simulation process for data. They form the basis for theories which encompass our understanding of the physical world. Despite this fundamental nature, the use of…

We give a finite-sample analysis of predictive inference procedures after model selection in regression with random design. The analysis is focused on a statistically challenging scenario where the number of potentially important…