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Autonomous agents operating in sequential decision-making tasks under uncertainty can benefit from external action suggestions, which provide valuable guidance but inherently vary in reliability. Existing methods for incorporating such…

In this paper we examine the problem of inference in Bayesian Networks with discrete random variables that have very large or even unbounded domains. For example, in a domain where we are trying to identify a person, we may have variables…

Likelihood-free Bayesian inference algorithms are popular methods for calibrating the parameters of complex, stochastic models, required when the likelihood of the observed data is intractable. These algorithms characteristically rely…

A goal in the forensic interpretation of scientific evidence is to make an inference about the source of a trace of unknown origin. The evidence is composed of the following three elements: (a) the trace of unknown origin, (b) a sample from…

This paper investigates the knowledge of language models from the perspective of Bayesian epistemology. We explore how language models adjust their confidence and responses when presented with evidence with varying levels of informativeness…

The generative nature of Large Language Models (LLMs) is reflected in the conditional probabilities they compute to sample each response token given the previous tokens. These probabilities encode the distributional structure that the model…

This paper is concerned with the epistemic question of confirming a hypothesis -- the guilt of a defendant -- by way of testimony heard by a juror over the course of an American-style criminal trial. In it, I attempt to settle a dispute…

This article extends the hypotheses assessment method to the case with two competing simple hypotheses. In doing so we further clarify the benefits that hypotheses assessments can bring to classical statistical analyses. Given that…

Evidence in probabilistic reasoning may be 'hard' or 'soft', that is, it may be of yes/no form, or it may involve a strength of belief, in the unit interval [0, 1]. Reasoning with soft, [0, 1]-valued evidence is important in many situations…

We construct the belief function that quantifies the agent, beliefs about which event of Q will occurred when he knows that the event is selected by a chance set-up and that the probability function associated to the chance set up is only…

Building a safety case is a common approach to make expert judgement explicit about safety of a system. The issue of confidence in such argumentation is still an open research field. Providing quantitative estimation of confidence is an…

Knowing the reliability of a model's response is essential in practical applications. Given the strong generation capabilities of large language models (LLMs), research has focused on generating verbalized confidence. This approach is…

Conscious experience is awash with underlying relationships. Moreover, for various brain regions such as the visual cortex, the system is biased toward some states. Representing this bias using a probability distribution shows that the…

The probability axioms by R. T. Cox can be regarded as the modern foundations of Bayesian inference, the idea of assigning degrees of belief to logical propositions in a manner consistent with Boolean logic. In this work it is shown that…

Bayesian statistics is an integral part of contemporary applied science. bayesics provides a single framework, unified in syntax and output, for performing the most commonly used statistical procedures, ranging from one- and two-sample…

A substantial generalisation is put forward of the theory of subjective fiducial inference as it was outlined in earlier papers. In particular, this theory is extended to deal with cases where the data are discrete or categorical rather…

Eliciting a high-dimensional probability distribution from an expert via noisy judgments is notoriously challenging, yet useful for many applications, such as prior elicitation and reward modeling. We introduce a method for eliciting the…

The problem of assigning probability distributions which objectively reflect the prior information available about experiments is one of the major stumbling blocks in the use of Bayesian methods of data analysis. In this paper the method of…

An increasing number of scientific experiments support the view of perception as Bayesian inference, which is rooted in Helmholtz's view of perception as unconscious inference. Recent study of logic presents a view of logical reasoning as…

Lifted inference algorithms exploit symmetries in probabilistic models to speed up inference. They show impressive performance when calculating unconditional probabilities in relational models, but often resort to non-lifted inference when…