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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…
In decision-making problems under uncertainty, probabilistic constraints are a valuable tool to express safety of decisions. They result from taking the probability measure of a given set of random inequalities depending on the decision…
Applying standard statistical methods after model selection may yield inefficient estimators and hypothesis tests that fail to achieve nominal type-I error rates. The main issue is the fact that the post-selection distribution of the data…
Process capability indices such as $C_{pk}$ are widely used for manufacturing decisions, yet are typically applied via deterministic thresholding of finite-sample estimates, ignoring uncertainty and leading to unstable outcomes near the…
Bayesian analysis plays a crucial role in estimating distribution of unknown parameters for given data and model. Due to the curse of dimensionality, it becomes difficult for high-dimensional problems, especially when multiple modes exist.…
Susceptibility to misinformation describes the degree of belief in unverifiable claims, a latent aspect of individuals' mental processes that is not observable. Existing susceptibility studies heavily rely on self-reported beliefs, which…
Safety evaluation of self-driving technologies has been extensively studied. One recent approach uses Monte Carlo based evaluation to estimate the occurrence probabilities of safety-critical events as safety measures. These Monte Carlo…
A multiplier bootstrap procedure for construction of likelihood-based confidence sets is considered for finite samples and a possible model misspecification. Theoretical results justify the bootstrap validity for a small or moderate sample…
We introduce inherent measures for effective quality control of brain segmentation based on a Bayesian fully convolutional neural network, using model uncertainty. Monte Carlo samples from the posterior distribution are efficiently…
Extracting maximal information from experimental data requires access to the likelihood function, which however is never directly available for complex experiments like those performed at high energy colliders. Theoretical predictions are…
In Bayesian inference, we seek to compute information about random variables such as moments or quantiles on the basis of {available data} and prior information. When the distribution of random variables is {intractable}, Monte Carlo (MC)…
The incorporation of systematic uncertainties into confidence interval calculations has been addressed recently in a paper by Conrad et al. (Physical Review D 67 (2003) 012002). In their work, systematic uncertainities in detector…
Uncertainty analysis in the outcomes of model predictions is a key element in decision-based material design to establish confidence in the models and evaluate the fidelity of models. Uncertainty Propagation (UP) is a technique to determine…
Methods that bypass analytical evaluations of the likelihood function have become an indispensable tool for statistical inference in many fields of science. These so-called likelihood-free methods rely on accepting and rejecting simulations…
Instance segmentation has witnessed promising advancements through deep neural network-based algorithms. However, these models often exhibit incorrect predictions with unwarranted confidence levels. Consequently, evaluating prediction…
Being able to reliably assess not only the \emph{accuracy} but also the \emph{uncertainty} of models' predictions is an important endeavour in modern machine learning. Even if the model generating the data and labels is known, computing the…
Robust estimation for modern portfolio selection on a large set of assets becomes more important due to large deviation of empirical inference on big data. We propose a distributionally robust methodology for high-dimensional mean-variance…
In various high-energy physics contexts, such as neutrino-oscillation experiments, several assumptions underlying the typical asymptotic confidence interval construction are violated, such that one has to resort to computationally expensive…
We give a finite-sample analysis of predictive inference procedures after model selection in regression with random design. The analysis is focused on a statistically challenging scenario where the number of potentially important…
This paper addresses the challenge of model uncertainty in quantitative finance, where decisions in portfolio allocation, derivative pricing, and risk management rely on estimating stochastic models from limited data. In practice, the…