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The recent success of neural network models has shone light on a rather surprising statistical phenomenon: statistical models that perfectly fit noisy data can generalize well to unseen test data. Understanding this phenomenon of…

The problem of a nonrelativistic particle with an internal color degree of freedom, with and without spin, moving in a free random gauge background is discussed. Freeness is a concept developed recently in the mathematical literature…

Any representation of data involves arbitrary investigator choices. Because those choices are external to the data-generating process, each choice leads to an exact symmetry, corresponding to the group of transformations that takes one…

The No Unmeasured Confounding Assumption is widely used to identify causal effects in observational studies. Recent work on proximal inference has provided alternative identification results that succeed even in the presence of unobserved…

In the application of Bayesian methods to metrology, pre-data probabilities play a critical role in the estimation of the model uncertainty. Following the observation that distributions form Riemann's manifolds, methods of differential…

Posterior probabilistic statistical inference without priors is an important but so far elusive goal. Fisher's fiducial inference, Dempster-Shafer theory of belief functions, and Bayesian inference with default priors are attempts to…

Current methods for detecting spurious correlations rely on analyzing dataset statistics or error patterns, leaving many harmful shortcuts invisible when counterexamples are absent. We introduce BEE (Bridging Explainability and Embeddings),…

In many data analyses, each measurement may come with a simple yes/no correction; for example, belonging to one of two populations or being contaminated or not. Ignoring such binary effects may bias the results, while accounting for them…

Semiparametric mixture models are parametric models with latent variables. They are defined kernel, $p_\theta(x | z)$, where z is the unknown latent variable, and $\theta$ is the parameter of interest. We assume that the latent variables…

Conformal prediction is a popular framework of uncertainty quantification that constructs prediction sets with coverage guarantees. To uphold the exchangeability assumption, many conformal prediction methods necessitate an additional…

We consider joint inversion for two or more unknown parameters from observational data in the Bayesian framework. Standard approaches often either treat the parameters as independent or impose structural similarity through regularisation…

Pattern-mixture models provide a transparent approach for handling missing data, where the full-data distribution is factorized in a way that explicitly shows the parts that can be estimated from observed data alone, and the parts that…

Fixed effect estimators of nonlinear panel data models suffer from the incidental parameter problem. This leads to two undesirable consequences in applied research: (1) point estimates are subject to large biases, and (2) confidence…

Inverse Uncertainty Quantification (UQ), or Bayesian calibration, is the process to quantify the uncertainties of random input parameters based on experimental data. The introduction of model discrepancy term is significant because…

Graphical model selection is a seemingly impossible task when many pairs of variables are never jointly observed; this requires inference of conditional dependencies with no observations of corresponding marginal dependencies. This…

Bell's inequalities are defined by sums of correlations involving non-commuting observables in each of the two systems. Violations of Bell's inequalities are only possible because the precision of any joint measurement of these observables…

The lack of non-parametric statistical tests for confounding bias significantly hampers the development of robust, valid and generalizable predictive models in many fields of research. Here I propose the partial and full confounder tests,…

Estimating some mathematical expectations from partially observed data and in particular missing outcomes is a central problem encountered in numerous fields such as transfer learning, counterfactual analysis or causal inference. Matching…

Fitting model parameters to experimental data is a common yet often challenging task, especially if the model contains many parameters. Typically, algorithms get lost in regions of parameter space in which the model is unresponsive to…

The recovery of an exoplanet's atmospheric parameters from its spectrum requires accurate knowledge of the spectral errors and covariances. Unfortunately, the complex image processing used in high-contrast integral-field spectrograph (IFS)…