Related papers: Bayesianize Fuzziness in the Statistical Analysis …

We propose randomized confidence intervals based on the Neyman-Pearson lemma, in order to make them more broadly applicable to distributions that do not satisfy regularity conditions. This is achieved by using the definition of fuzzy…

A central challenge in statistical inference is the presence of confounding variables that may distort observed associations between treatment and outcome. Conventional "causal" methods, grounded in assumptions such as ignorability, exclude…

We introduce an evidential model for time-to-event prediction with censored data. In this model, uncertainty on event time is quantified by Gaussian random fuzzy numbers, a newly introduced family of random fuzzy subsets of the real line…

In this paper, we introduce a fundamental framework to create a bridge between Probability Theory and Fuzzy Logic. Indeed, our theory formulates a random experiment of selecting crisp elements with the criterion of having a certain fuzzy…

Nonparametric Bayesian models are used routinely as flexible and powerful models of complex data. Many times, a statistician may have additional informative beliefs about data distribution of interest, e.g., its mean or subset components,…

The standard approach to Bayesian inference is based on the assumption that the distribution of the data belongs to the chosen model class. However, even a small violation of this assumption can have a large impact on the outcome of a…

We introduce a general theory of epistemic random fuzzy sets for reasoning with fuzzy or crisp evidence. This framework generalizes both the Dempster-Shafer theory of belief functions, and possibility theory. Independent epistemic random…

Rule mining algorithms are one of the fundamental techniques in data mining for disclosing significant patterns in terms of linguistic rules expressed in natural language. In this paper, we revisit the concept of fuzzy implicative rule to…

Selection bias arises when the probability that an observation enters a dataset depends on variables related to the quantities of interest, leading to systematic distortions in estimation and uncertainty quantification. For example, in…

Risk specialists are trying to understand risk better and use complex models for risk assessment, while many risks are not yet well understood. The lack of empirical data and complex causal and outcome relationships make it difficult to…

We investigate the data distribution valuation problem, which aims to quantify the values of data distributions from their samples. This is a recently proposed problem that is related to but different from classical data valuation and can…

There is currently a renewed interest in the Bayesian predictive approach to statistics. This paper offers a review on foundational concepts and focuses on predictive modeling, which by directly reasoning on prediction, bypasses inferential…

On the basis of network analysis, and within the context of modeling imprecision or vague information with fuzzy sets, we propose an innovative way to analyze, aggregate and apply this uncertain knowledge into community detection of…

Decentralized data sources are prevalent in real-world applications, posing a formidable challenge for causal inference. These sources cannot be consolidated into a single entity owing to privacy constraints. The presence of dissimilar data…

Data dispersed across multiple files are commonly integrated through probabilistic linkage methods, where even minimal error rates in record matching can significantly contaminate subsequent statistical analyses. In regression problems, we…

Fuzzy quantification is a subtopic of fuzzy logic which deals with the modelling of the quantified expressions we can find in natural language. Fuzzy quantifiers have been successfully applied in several fields like fuzzy, control, fuzzy…

Count outcomes in longitudinal studies are frequent in clinical and engineering studies. In frequentist and Bayesian statistical analysis, methods such as Mixed linear models allow the variability or correlation within individuals to be…

This research concerns the estimation of latent linear or polychoric correlations from fuzzy frequency tables. Fuzzy counts are of particular interest to many disciplines including social and behavioral sciences, and are especially relevant…

Statistical inference as a formal scientific method to covert experience to knowledge has proven to be elusively difficult. While frequentist and Bayesian methodologies have been accepted in the contemporary era as two dominant schools of…

Bayesian statistics has gained popularity in psychological research due to its intuitive uncertainty quantification and convenient information-updating rules. In many applications, however, prior distributions are introduced merely as…