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We present a domain-theoretic framework for probabilistic programming that provides a constructive definition of conditional probability and addresses computability challenges previously identified in the literature. We introduce a novel…

Through case studies, we demonstrate how multiverse analysis can strengthen the robustness and transparency of computational social science findings against alternative methodological decisions. We conduct multiverse analyses of three…

This paper examines the classical matching distribution arising in the "problem of coincidences". We generalise the classical matching distribution with a preliminary round of allocation where items are correctly matched with some fixed…

This paper clarifies a fundamental difference between causal inference and traditional statistical inference by formalizing a mathematical distinction between their respective parameters. We connect two major approaches to causal inference,…

The possibility of unmeasured confounding is one of the main limitations for causal inference from observational studies. There are different methods for (partially) empirically assessing the plausibility of unconfoundedness. However, most…

Several Artificial Intelligence schemes for reasoning under uncertainty explore either explicitly or implicitly asymmetries among probabilities of various states of their uncertain domain models. Even though the correct working of these…

We study a generalization of conditional probability for arbitrary ordered vector spaces. A related problem is that of assigning a numerical value to one vector relative to another. We characterize the groups for which these generalized…

We analyze selected iterated conditionals in the framework of conditional random quantities. We point out that it is instructive to examine Lewis's triviality result, which shows the conditions a conditional must satisfy for its probability…

Mitigating bias in training on biased datasets is an important open problem. Several techniques have been proposed, however the typical evaluation regime is very limited, considering very narrow data conditions. For instance, the effect of…

We present a semantics for adding uncertainty to conditional logics for default reasoning and belief revision. We are able to treat conditional sentences as statements of conditional probability, and express rules for revision such as "If A…

Bayesian inference paradigms are regarded as powerful tools for solution of inverse problems. However, when applied to inverse problems in physical sciences, Bayesian formulations suffer from a number of inconsistencies that are often…

Several procedures have been recently proposed to test the simplifying assumption for conditional copulas. Instead of considering pointwise conditioning events, we study the constancy of the conditional dependence structure when some…

Methods of performing anomaly detection on high-dimensional data sets are needed, since algorithms which are trained on data are only expected to perform well on data that is similar to the training data. There are theoretical results on…

We investigate the sample complexity of mutual information and conditional mutual information testing. For conditional mutual information testing, given access to independent samples of a triple of random variables $(A, B, C)$ with unknown…

Many-party correlations between measurement outcomes in general probabilistic theories are given by conditional probability distributions obeying the non-signalling condition. We show that any such distribution can be obtained from…

While most machine learning models can provide confidence in their predictions, confidence is insufficient to understand a prediction's reliability. For instance, the model may have a low confidence prediction if the input is not…

The modeling of probability distributions, specifically generative modeling and density estimation, has become an immensely popular subject in recent years by virtue of its outstanding performance on sophisticated data such as images and…

Before we combine actions and probabilities two very obvious questions should be asked. Firstly, what does "the probability of an action" mean? Secondly, how does probability interact with nondeterminism? Neither question has a single…

Missingness and measurement frequency are two sides of the same coin. How frequent should we measure clinical variables and conduct laboratory tests? It depends on many factors such as the stability of patient conditions, diagnostic…

People's associations between colors and concepts influence their ability to interpret the meanings of colors in information visualizations. Previous work has suggested such effects are limited to concepts that have strong, specific…