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Generalised Bayesian inference updates prior beliefs using a loss function, rather than a likelihood, and can therefore be used to confer robustness against possible mis-specification of the likelihood. Here we consider generalised Bayesian…
Elliptical distribution is a basic assumption underlying many multivariate statistical methods. For example, in sufficient dimension reduction and statistical graphical models, this assumption is routinely imposed to simplify the data…
Generalized linear mixed models are powerful tools for analyzing clustered data, where the unknown parameters are classically (and most commonly) estimated by the maximum likelihood and restricted maximum likelihood procedures. However,…
Probability predictions from binary regressions or machine learning methods ought to be calibrated: If an event is predicted to occur with probability $x$, it should materialize with approximately that frequency, which means that the…
We derive a priori error estimates for Nitsche's method applied to elliptic problems on approximate domains. Such approximations arise, for example, in unfitted finite element methods, data-driven simulations, and evolving domain problems,…
We present the "condensation" method that exploits the heterogeneity of the probability distribution functions (PDF) of event locations to improve the spatial information content of seismic catalogs. The method reduces the size of seismic…
Overconfidence and underconfidence in machine learning classifiers is measured by calibration: the degree to which the probabilities predicted for each class match the accuracy of the classifier on that prediction. How one measures…
What advantage do \emph{sequential} procedures provide over batch algorithms for testing properties of unknown distributions? Focusing on the problem of testing whether two distributions $\mathcal{D}_1$ and $\mathcal{D}_2$ on $\{1,\dots,…
Epidemiologic screening programs often make use of tests with small, but non-zero probabilities of misdiagnosis. In this article, we assume the target population is finite with a fixed number of true cases, and that we apply an imperfect…
Confidence calibration of classification models is a technique to estimate the true posterior probability of the predicted class, which is critical for ensuring reliable decision-making in practical applications. Existing confidence…
Estimating the model evidence - or mariginal likelihood of the data - is a notoriously difficult task for finite and infinite mixture models and we reexamine here different Monte Carlo techniques advocated in the recent literature, as well…
Declustering aims to divide earthquake catalogs into independent events (mainshocks), and dependent (clustered) events, and is an integral component of many seismicity studies, including seismic hazard assessment. We assess the effect of…
Knowledge of the noise distribution in diffusion MRI is the centerpiece to quantify uncertainties arising from the acquisition process. Accurate estimation beyond textbook distributions often requires information about the acquisition…
This article considers exponential families of truncated multivariate normal distributions with one-sided truncation for some or all coordinates. We observe that if all components are one-sided truncated then this family is not full. The…
In this note, we consider the problem of aggregation of estimators in order to denoise a signal. The main contribution is a short proof of the fact that the exponentially weighted aggregate satisfies a sharp oracle inequality. While this…
The cumulative residual extropy (CRJ) is a measure of uncertainty that serves as an alternative to extropy. It replaces the probability density function with the survival function in the expression of extropy. This work introduces a new…
In this paper, we consider the sphericity test for a one-sample problem under high-dimensional two-step monotone incomplete data. Existing asymptotic expansions for the null distributions of the likelihood ratio test (LRT) statistic and…
We investigate the sequence of great earthquakes over the past century. To examine whether the earthquake record includes temporal clustering, we identify aftershocks and remove those from the record. We focus on the recurrence time,…
For the universal hypothesis testing problem, where the goal is to decide between the known null hypothesis distribution and some other unknown distribution, Hoeffding proposed a universal test in the nineteen sixties. Hoeffding's universal…
Calibration of mean estimates for predictions is a crucial property in many applications, particularly in the fields of financial and actuarial decision-making. In this paper, we first review classical approaches for validating…