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Randomized algorithms depend on accurate sampling from probability distributions, as their correctness and performance hinge on the quality of the generated samples. However, even for common distributions like Binomial, exact sampling is…
A new theoretical approach to non-equilibrium statistical systems has recently been proposed by the author, a co-author and others. It is based on a variational principle which is associated with the discrepancy of a path through…
We establish a link between the phenomenon of Taylor dispersion and the theory of empirical distributions. Using this connection, we derive, upon applying the theory of large deviations, an alternative and much more precise description of…
Uncertainty quantification is essential in decision-making, especially when joint distributions of random variables are involved. While conformal prediction provides distribution-free prediction sets with valid coverage guarantees, it…
Functional data are typically modeled as sample paths of smooth stochastic processes in order to mitigate the fact that they are often observed discretely and noisily, occasionally irregularly and sparsely. The smoothness assumption is…
Difference in proportions is frequently used to measure treatment effect for binary outcomes in randomized clinical trials. The estimation of difference in proportions can be assisted by adjusting for prognostic baseline covariates to…
In this paper we consider a variety of procedures for numerical statistical inference in the family of univariate and multivariate stable distributions. In connection with univariate distributions (i) we provide approximations by finite…
Adaptivity is an important feature of data analysis---typically the choice of questions asked about a dataset depends on previous interactions with the same dataset. However, generalization error is typically bounded in a non-adaptive…
The differential $\lambda$-calculus studies how the quantitative aspects of programs correspond to differentiation and to Taylor expansion inside models of linear logic. Recent work has generalized the axioms of Taylor expansion so they…
Order statistics theory is applied in this paper to probabilistic robust control theory to compute the minimum sample size needed to come up with a reliable estimate of an uncertain quantity under continuity assumption of the related…
In stochastic simulation, input uncertainty refers to the propagation of the statistical noise in calibrating input models to impact output accuracy, in addition to the Monte Carlo simulation noise. The vast majority of the input…
Generalized likelihood ratio statistics have been proposed in Fan, Zhang and Zhang [Ann. Statist. 29 (2001) 153-193] as a generally applicable method for testing nonparametric hypotheses about nonparametric functions. The likelihood ratio…
Statistical learning algorithms provide a generally-applicable framework to sidestep time-consuming experiments, or accurate physics-based modeling, but they introduce a further source of error on top of the intrinsic limitations of the…
We describe inferactive data analysis, so-named to denote an interactive approach to data analysis with an emphasis on inference after data analysis. Our approach is a compromise between Tukey's exploratory (roughly speaking "model free")…
Statistically sound pattern discovery harnesses the rigour of statistical hypothesis testing to overcome many of the issues that have hampered standard data mining approaches to pattern discovery. Most importantly, application of…
Asymptotic statistical theory for estimating functions is reviewed in a generality suitable for stochastic processes. Conditions concerning existence of a consistent estimator, uniqueness, rate of convergence, and the asymptotic…
Inference is the process of using facts we know to learn about facts we do not know. A theory of inference gives assumptions necessary to get from the former to the latter, along with a definition for and summary of the resulting…
Clinical prediction models are estimated using a sample of limited size from the target population, leading to uncertainty in predictions, even when the model is correctly specified. Generally, not all patient profiles are observed…
As data plays an increasingly pivotal role in decision-making, the emergence of data markets underscores the growing importance of data valuation. Within the machine learning landscape, Data Shapley stands out as a widely embraced method…
This paper studies the propagation of finite-sample uncertainty under nonlinear transformations commonly used in statistical decision systems. In particular, we consider process capability indices, which are widely used in manufacturing…