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Many legal cases require decisions about causality, responsibility or blame, and these may be based on statistical data. However, causal inferences from such data are beset by subtle conceptual and practical difficulties, and in general it…

Causal discovery algorithms infer causal relations from data based on several assumptions, including notably the absence of measurement error. However, this assumption is most likely violated in practical applications, which may result in…

We analyze various uncertainty measures for spatial diffusion processes. In this manifestly non-quantum setting, we focus on the existence issue of complementary pairs whose joint dispersion measure has strictly positive lower bound.

We tackle the problem of conditioning probabilistic programs on distributions of observable variables. Probabilistic programs are usually conditioned on samples from the joint data distribution, which we refer to as deterministic…

Phenomena such as air pollution levels are of greatest interest when observations are large, but standard prediction methods are not specifically designed for large observations. We propose a method, rooted in extreme value theory, which…

Bidirectional causal relationships arising from mutual interactions between variables are commonly observed within biomedical, econometrical, and social science contexts. When such relationships are further complicated by unobserved…

Density regression characterizes the conditional density of the response variable given the covariates, and provides much more information than the commonly used conditional mean or quantile regression. However, it is often computationally…

In the context of generalized measurement theory, the Gleason-Busch theorem assures the unique form of the associated probability function. Recently, in Flatt et al. Phys. Rev. A 96, 062125 (2017), the case of subsequent measurements has…

We introduce an approach which allows detecting causal relationships between variables for which the time evolution is available. Causality is assessed by a variational scheme based on the Information Imbalance of distance ranks, a…

We describe a formal approach to identify 'root causes' of outliers observed in $n$ variables $X_1,\dots,X_n$ in a scenario where the causal relation between the variables is a known directed acyclic graph (DAG). To this end, we first…

For a continuous random variable $Z$, testing conditional independence $X \perp\!\!\!\perp Y |Z$ is known to be a particularly hard problem. It constitutes a key ingredient of many constraint-based causal discovery algorithms. These…

We describe a formal approach based on graphical causal models to identify the "root causes" of the change in the probability distribution of variables. After factorizing the joint distribution into conditional distributions of each…

The propensity score is a common tool for estimating the causal effect of a binary treatment in observational data. In this setting, matching, subclassification, imputation, or inverse probability weighting on the propensity score can…

This paper considers inference of causal structure in a class of graphical models called "conditional DAGs". These are directed acyclic graph (DAG) models with two kinds of variables, primary and secondary. The secondary variables are used…

We show that including both the system and the apparatus in the quantum description of the measurement process, and using the concept of conditional probabilities, it is possible to deduce the statistical operator of the system after a…

Causal discovery aims to learn causal relationships between variables from targeted data, making it a fundamental task in machine learning. However, causal discovery algorithms often rely on unverifiable causal assumptions, which are…

The aim of this article is to establish basic results in a conditional measure theory. The results are applied to prove that arbitrary kernels and conditional distributions are represented by measures in a conditional set theory. In…

Simultaneous concurrence of extreme values across multiple climate variables can result in large societal and environmental impacts. Therefore, there is growing interest in understanding these concurrent extremes. In many applications, not…

Inference for causal effects can benefit from the availability of an instrumental variable (IV) which, by definition, is associated with the given exposure, but not with the outcome of interest other than through a causal exposure effect.…

Most research questions in agricultural and applied economics are of a causal nature, i.e., how one or more variables (e.g., policies, prices, the weather) affect one or more other variables (e.g., income, crop yields, pollution). Only some…