Related papers: Elements of asymptotic theory with outer probabili…

Hierarchical statistical models are widely employed in information science and data engineering. The models consist of two types of variables: observable variables that represent the given data and latent variables for the unobservable…

A popular strategy for active learning is to specifically target a reduction in epistemic uncertainty, since aleatoric uncertainty is often considered as being intrinsic to the system of interest and therefore not reducible. Yet,…

In arithmetic statistics and analytic number theory, the asymptotic growth rate of counting functions giving the number of objects with order below $X$ is studied as $X\to \infty$. We define general counting functions which count…

This paper focuses on parameter estimation and introduces a new method for lower bounding the Bayesian risk. The method allows for the use of virtually \emph{any} information measure, including R\'enyi's $\alpha$, $\varphi$-Divergences, and…

Bayesian synthetic likelihood is a widely used approach for conducting Bayesian analysis in complex models where evaluation of the likelihood is infeasible but simulation from the assumed model is tractable. We analyze the behaviour of the…

In this paper we show that there is a link between approximate Bayesian methods and prior robustness. We show that what is typically recognized as an approximation to the likelihood, either due to the simulated data as in the Approximate…

A random set is a generalisation of a random variable, i.e. a set-valued random variable. The random set theory allows a unification of other uncertainty descriptions such as interval variable, mass belief function in Dempster-Shafer theory…

Bayes' theorem incorporates distinct types of information through the likelihood and prior. Direct observations of state variables enter the likelihood and modify posterior probabilities through consistent updating. Information in terms of…

In this paper we compare and contrast the behavior of the posterior predictive distribution to the risk of the maximum a posteriori estimator for the random features regression model in the overparameterized regime. We will focus on the…

The goal of this paper is to provide some tools for nonparametric estimation and inference in psychological and economic experiments. We consider an experimental framework in which each of $n$subjects provides $T$ responses to a vector of…

In this article we present very intuitive, easy to follow, yet mathematically rigorous, approach to the so called data fitting process. Rather than minimizing the distance between measured and simulated data points, we prefer to find such…

When searching over a large parameter space for anomalies such as events, peaks, objects, or particles, there is a large probability that spurious signals with seemingly high significance will be found. This is known as the look-elsewhere…

In this paper we propose a procedure to evaluate Bayesian confidence intervals in counting experiments where both signal and background fluctuations are described by the Poisson statistics. The results obtained when the method is applied to…

An important component in deploying machine learning (ML) in safety-critic applications is having a reliable measure of confidence in the ML model's predictions. For a classifier $f$ producing a probability vector $f(x)$ over the candidate…

In this paper, we establish an iterative data-driven approach to derive guaranteed bounds on nonlinearity measures of unknown nonlinear systems. In this context, nonlinearity measures quantify the strength of the nonlinearity of a dynamical…

Note: Published now as a chapter in "Handbook of the History and Philosophy of Mathematical Practice" (Springer Nature, editor B. Sriraman, https://doi.org/10.1007/978-3-030-19071-2_105-1). The application of mathematical probability theory…

Aleatoric uncertainty captures the inherent randomness of the data, such as measurement noise. In Bayesian regression, we often use a Gaussian observation model, where we control the level of aleatoric uncertainty with a noise variance…

A recent paper presents the "false confidence theorem" (FCT) which has potentially broad implications for statistical inference using Bayesian posterior uncertainty. This theorem says that with arbitrarily large (sampling/frequentist)…

This paper introduces and studies a new class of nonparametric prior distributions. Random probability distribution functions are constructed via normalization of random measures driven by increasing additive processes. In particular, we…

Statistical modeling of multivariate and spatial extreme events has attracted broad attention in various areas of science. Max-stable distributions and processes are the natural class of models for this purpose, and many parametric families…