Related papers: Fiducial Inference and Decision Theory
We study the stability of posterior predictive inferences to the specification of the likelihood model and perturbations of the data generating process. In modern big data analyses, useful broad structural judgements may be elicited from…
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…
Conformal prediction has emerged as a cutting-edge methodology in statistics and machine learning, providing prediction intervals with finite-sample frequentist coverage guarantees. Yet, its interplay with Bayesian statistics, often…
A primary motivation for reasoning under uncertainty is to derive decisions in the face of inconclusive evidence. However, Shafer's theory of belief functions, which explicitly represents the underconstrained nature of many reasoning…
Since the idea of fiducial inference was put forward by Fisher, researchers have been attempting to place it within a rigorous and well motivated framework. It is fair to say that a general definition has remained elusive. In this paper we…
Discovering causal relationships is a hard task, often hindered by the need for intervention, and often requiring large amounts of data to resolve statistical uncertainty. However, humans quickly arrive at useful causal relationships. One…
Recent decades have seen an interest in prediction problems for which Bayesian methodology has been used ubiquitously. Sampling from or approximating the posterior predictive distribution in a Bayesian model allows one to make inferential…
This paper offers a comprehensive introduction to Bayesian inference, combining historical context, theoretical foundations, and core analytical examples. Beginning with Bayes' theorem and the philosophical distinctions between Bayesian and…
Forecasting techniques for assessing the power of future experiments to discriminate between theories or discover new laws of nature are of great interest in many areas of science. In this paper, we introduce a Bayesian forecasting method…
Without assuming any pdf for some measured parameter, we derive a predictive pdf for the outcome of a second measurement, given the outcome of the first measurement and two common assumptions about the noise. These are that (1) it is…
In this article, we review selective inference, a set of techniques for inference when the statistical question asked is a function of the data. This setting often arises in contemporary scientific workflows, where hypotheses and parameters…
Statistics has moved beyond the frequentist-Bayesian controversies of the past. Where does this leave our ability to interpret results? I suggest that a philosophy compatible with statistical practice, labeled here statistical pragmatism,…
Reacting against the limitation of statistics to decision procedures, R. A. Fisher proposed for inductive reasoning the use of the fiducial distribution, a parameter-space distribution of epistemological probability transferred directly…
An inferential model (IM) is a model describing the construction of provably reliable, data-driven uncertainty quantification and inference about relevant unknowns. IMs and Fisher's fiducial argument have similar objectives, but a…
Building on the recent development of the model-free generalized fiducial (MFGF) paradigm (Williams, 2023) for predictive inference with finite-sample frequentist validity guarantees, in this paper, we develop an MFGF-based approach to…
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…
Probability theory, epistemically interpreted, provides an excellent, if not the best available account of inductive reasoning. This is so because there are general and definite rules for the change of subjective probabilities through…
Relative belief inferences are shown to arise as Bayes rules or limiting Bayes rules. These inferences are invariant under reparameterizations and possess a number of optimal properties. In particular, relative belief inferences are based…
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…
There is a growing interest in the so-called Bayesian Predictive Inference approach, which allows to perform Bayesian inference without specifying the likelihood and prior of the model, or the need of any MCMC. Instead, only a sequence of…