Related papers: Fiducial inference then and now

It is common practice in statistical data analysis to perform data-driven variable selection and derive statistical inference from the resulting model. Such inference enjoys none of the guarantees that classical statistical theory provides…

Emerging research frontiers and computational advances have gradually transformed cognitive science into a multidisciplinary and data-driven field. As a result, there is a proliferation of cognitive theories investigated and interpreted…

Monte Carlo methods to evaluate and maximize the likelihood function enable the construction of confidence intervals and hypothesis tests, facilitating scientific investigation using models for which the likelihood function is intractable.…

We describe inferactive data analysis, so-named to denote an interactive approach to data analysis with an emphasis on inference after data analysis. Our approach is a compromise between Tukey's exploratory (roughly speaking "model free")…

Variable selection for regression models plays a key role in the analysis of biomedical data. However, inference after selection is not covered by classical statistical frequentist theory which assumes a fixed set of covariates in the…

We propose a framework for general Bayesian inference. We argue that a valid update of a prior belief distribution to a posterior can be made for parameters which are connected to observations through a loss function rather than the…

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…

Traditional statistical inference considers relatively small data sets and the corresponding theoretical analysis focuses on the asymptotic behavior of a statistical estimator when the number of samples approaches infinity. However, many…

Ever since the seminal work of R. A. Fisher and F. Yates, factorial designs have been an important experimental tool to simultaneously estimate the effects of multiple treatment factors. In factorial designs, the number of treatment…

The bootstrap, introduced by Efron (1982), has become a very popular method for estimating variances and constructing confidence intervals. A key insight is that one can approximate the properties of estimators by using the empirical…

Bayesian inference can often be sensitive to the choice of hyperparameters of the prior or likelihood, yet defining and quantifying this sensitivity in a principled and computationally feasible way remains challenging in practice.…

Causal inference has recently garnered significant interest among recommender system (RS) researchers due to its ability to dissect cause-and-effect relationships and its broad applicability across multiple fields. It offers a framework to…

This paper is about two things: (i) Charles Sanders Peirce (1837-1914) -- an iconoclastic philosopher and polymath who is among the greatest of American minds. (ii) Abductive inference -- a term coined by C. S. Peirce, which he defined as…

This article addresses calibration challenges in analytical chemistry by employing a random-effects calibration curve model and its generalizations to capture variability in analyte concentrations. The model is motivated by specific issues…

The inferential model (IM) approach, like fiducial and its generalizations, depends on a representation of the data-generating process. Here, a particular variation on the IM construction is considered, one based on generalized…

A very simple example demonstrates that Fisher's application of the conditionality principle to regression ("fixed-$x$ regression"), endorsed by Sprott and many other followers, makes prediction impossible in the context of statistical…

Causal inference is central to many areas of artificial intelligence, including complex reasoning, planning, knowledge-base construction, robotics, explanation, and fairness. An active community of researchers develops and enhances…

This is a review of statistical inference methodology for stochastic differential equations driven by fractional Brownian motion, otherwise called fractional diffusions. The first section reviews the theory needed to rigorously define them.…

Modern science increasingly relies on ever-growing observational datasets and automated inference pipelines, under the implicit belief that accumulating more data makes scientific conclusions more reliable. Here we show that this belief can…

The paper reviews methods that seek to draw causal inference from observational data and demonstrates how they can be applied to empirical problems in engineering research. It presents a framework for causal identification based on the…