Related papers: Reformulating Confidence as Extended Likelihood
We derive confidence intervals and confidence sequences for causal effects in situations where the back-door or front-door criteria are applicable. Our tightest confidence intervals hold in the standard setting where the training data…
As large language models (LLMs) are increasingly used in high-stakes domains, accurately assessing their confidence is crucial. Humans typically express confidence through epistemic markers (e.g., "fairly confident") instead of numerical…
In this paper we leverage on probability over Riemannian manifolds to rethink the interpretation of priors and posteriors in Bayesian inference. The main mindshift is to move away from the idea that "a prior distribution establishes a…
We generalize the maximum likelihood method to non-Gaussian distribution functions by means of the multivariate Edgeworth expansion. We stress the potential interest of this technique in all those cosmological problems in which the…
We provide a logical framework in which a resource-bounded agent can be seen to perform approximations of probabilistic reasoning. Our main results read as follows. First we identify the conditions under which propositional probability…
In this paper, we propose new sequential estimation methods based on inclusion principle. The main idea is to reformulate the estimation problems as constructing sequential random intervals and use confidence sequences to control the…
A conceptual foundation for approximation of belief functions is proposed and investigated. It is based on the requirements of consistency and closeness. An optimal approximation is studied. Unfortunately, the computation of the optimal…
In this contribution we explore choice revision, a sort of belief change in which the new information is represented by a set of sentences and the agent could accept some of the sentences while rejecting the others. We propose a generalized…
This work presents a new classifier that is specifically designed to be fully interpretable. This technique determines the probability of a class outcome, based directly on probability assignments measured from the training data. The…
The proliferation of probable prime tests in recent years has produced a plethora of definitions with the word ``pseudoprime'' in them. Examples include pseudoprimes, Euler pseudoprimes, strong pseudoprimes, Lucas pseudoprimes, strong Lucas…
Scientists continue to develop increasingly complex mechanistic models to reflect their knowledge more realistically. Statistical inference using these models can be challenging since the corresponding likelihood function is often…
In this paper, we propose a novel association measure for longitudinal studies based on the traditional definition of relative risk. In a Markovian fashion, such a proposal takes into account the information content regarding the previous…
In an empirical Bayes analysis, we use data from repeated sampling to imitate inferences made by an oracle Bayesian with extensive knowledge of the data-generating distribution. Existing results provide a comprehensive characterization of…
Corrected confidence intervals are developed for the mean of the second component of a bivariate normal process when the first component is being monitored sequentially. This is accomplished by constructing a first approximation to a…
In this paper, we give a frequency interpretation of negative probability, as well as of extended probability, demonstrating that to a great extent, these new types of probabilities, behave as conventional probabilities. Extended…
This paper suggests a new interpretation of the Dempster-Shafer theory in terms of probabilistic interpretation of plausibility. A new rule of combination of independent evidence is shown and its preservation of interpretation is…
Conditioning is crucial in applied science when inference involving time series is involved. Belief calculus is an effective way of handling such inference in the presence of epistemic uncertainty -- unfortunately, different approaches to…
Starting from considerations about meaning and subsequent use of asymmetric uncertainty intervals of experimental results, we review the issue of uncertainty propagation. We show that, using a probabilistic approach (the so-called Bayesian…
This is the guest editors' general introduction to a Special Issue of the Journal of Statistical Planning and Inference, dedicated to confidence distributions and related themes. Confidence distributions (CDs) are distributions for…
Many models in natural language processing define probabilistic distributions over linguistic structures. We argue that (1) the quality of a model' s posterior distribution can and should be directly evaluated, as to whether probabilities…