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Imputation methods play a critical role in enhancing the quality of practical time-series data, which often suffer from pervasive missing values. Recently, diffusion-based generative imputation methods have demonstrated remarkable success…

A stream of algorithmic advances has steadily increased the popularity of the Bayesian approach as an inference paradigm, both from the theoretical and applied perspective. Even with apparent successes in numerous application fields, a…

A central challenge in statistical inference is the presence of confounding variables that may distort observed associations between treatment and outcome. Conventional "causal" methods, grounded in assumptions such as ignorability, exclude…

The inferential model (IM) framework offers alternatives to the familiar probabilistic (e.g., Bayesian and fiducial) uncertainty quantification in statistical inference. Allowing this uncertainty quantification to be imprecise makes it…

Discrete state spaces represent a major computational challenge to statistical inference, since the computation of normalisation constants requires summation over large or possibly infinite sets, which can be impractical. This paper…

Many questions of fundamental interest in todays science can be formulated as inference problems: Some partial, or noisy, observations are performed over a set of variables and the goal is to recover, or infer, the values of the variables…

Neuroscience has recently made much progress, expanding the complexity of both neural-activity measurements and brain-computational models. However, we lack robust methods for connecting theory and experiment by evaluating our new big…

Advanced inference techniques allow one to reconstruct the pattern of interaction from high dimensional data sets. We focus here on the statistical properties of inferred models and argue that inference procedures are likely to yield models…

Two different approaches to dealing with probabilistic knowledge are examined -models and inductive inference. Examples of the first are: influence diagrams [1], Bayesian networks [2], log-linear models [3, 4]. Examples of the second are:…

Accurate simulation of complex physical systems enables the development, testing, and certification of control strategies before they are deployed into the real systems. As simulators become more advanced, the analytical tractability of the…

These lectures deal with the problem of inductive inference, that is, the problem of reasoning under conditions of incomplete information. Is there a general method for handling uncertainty? Or, at least, are there rules that could in…

The rapid emergence of massive datasets in various fields poses a serious challenge to traditional statistical methods. Meanwhile, it provides opportunities for researchers to develop novel algorithms. Inspired by the idea of…

Simulation methods are among the most ubiquitous methodological tools in statistical science. In particular, statisticians often is simulation to explore properties of statistical functionals in models for which developed statistical theory…

Statistical hypothesis testing, as formalized by 20th Century statisticians and taught in college statistics courses, has been a cornerstone of 100 years of scientific progress. Nevertheless, the methodology is increasingly questioned in…

Across many domains of science, stochastic models are an essential tool to understand the mechanisms underlying empirically observed data. Models can be of different levels of detail and accuracy, with models of high-fidelity (i.e., high…

Inferential models (IMs) offer prior-free, Bayesian-like posterior degrees of belief designed for statistical inference, which feature a frequentist-like calibration property that ensures reliability of said inferences. The catch is that…

Statistical inference in high dimensional settings has recently attracted enormous attention within the literature. However, most published work focuses on the parametric linear regression problem. This paper considers an important…

Stability selection is a versatile framework for structure estimation and variable selection in high-dimensional setting, primarily grounded in frequentist principles. In this paper, we propose an enhanced methodology that integrates…

We formulate, and present a numerical method for solving, an inverse problem for inferring parameters of a deterministic model from stochastic observational data (quantities of interest). The solution, given as a probability measure, is…

Testing hypotheses is an issue of primary importance in the scientific research, as well as in many other human activities. Much clarification about it can be achieved if the process of learning from data is framed in a stochastic model of…