Related papers: Elements of asymptotic theory with outer probabili…
Classical probability theory supports probability measures, assigning a fixed positive real value to each event, these measures are far from satisfactory in formulating real-life occurrences. The main innovation of this paper is the…
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…
There is a third way of implementing probability models and practicing. This is to answer questions put in terms of observables. This eliminates frequentist hypothesis testing and Bayes factors and it also eliminates parameter estimation.…
The paper studies the asymptotic behaviour of weighted functionals of long-range dependent data over increasing observation windows. Various important statistics, including sample means, high order moments, occupation measures can be given…
Higher criticism is a large-scale testing procedure that can attain the optimal detection boundary for sparse and faint signals. However, there has been a lack of knowledge in most existing works about its asymptotic distribution for more…
Data-driven anomaly detection methods typically build a model for the normal behavior of the target system, and score each data instance with respect to this model. A threshold is invariably needed to identify data instances with high (or…
We propose a general solution to the problem of robust Bayesian inference in complex settings where outliers may be present. In practice, the automation of robust Bayesian analyses is important in the many applications involving large and…
Due to their heterogeneity, insurance risks can be properly described as a mixture of different fixed models, where the weights assigned to each model may be estimated empirically from a sample of available data. If a risk measure is…
Robust Bayesian analysis has been mainly devoted to detecting and measuring robustness w.r.t. the prior distribution. Many contributions in the literature aim to define suitable classes of priors which allow the computation of variations of…
This thesis investigates on measure theoretic aspects of fluctuations of error terms appearing in various asymptotic formulas.
A theory of measurement uncertainty is presented, which, since it is based exclusively on the Bayesian approach and on the subjective concept of conditional probability, is applicable in the most general cases. The recent International…
The use of standard statistical methods, such as maximum likelihood, is often justified based on their asymptotic properties. For suitably regular models, this theory is standard but, when the model is non-regular, e.g., the support depends…
This article explains, and discusses the merits of, three approaches for analyzing the certainty with which statistical results can be extrapolated beyond the data gathered. Sometimes it may be possible to use more than one of these…
Bayesian inference affords scientists with powerful tools for testing hypotheses. One of these tools is the Bayes factor, which indexes the extent to which support for one hypothesis over another is updated after seeing the data. Part of…
Models with intractable normalizing functions arise frequently in statistics. Common examples of such models include exponential random graph models for social networks and Markov point processes for ecology and disease modeling. Inference…
Aleatoric and Epistemic uncertainty have achieved recent attention in the literature as different sources from which uncertainty can emerge in stochastic modeling. Epistemic being intrinsic or model based notions of uncertainty, and…
Bayesian probability theory is used as a framework to develop a formalism for the scientific method based on principles of inductive reasoning. The formalism allows for precise definitions of the key concepts in theories of physics and also…
We develop a new framework of uncertainty variables to model uncertainty. An uncertainty variable is characterized by an uncertainty set, in which its realization is bound to lie, while the conditional uncertainty is characterized by a set…
Outlying observations are frequently encountered across a wide spectrum of scientific domains, posing notable challenges to the generalizability of statistical models and the reproducibility of downstream analysis. They are identified…
This article gives some properties of intervals in $\mathbb{R}$ and discusses some problems involving intervals for which the concept of outer measure on $\mathbb{R}$ provides a more efficient solution than an elementary approach. The outer…