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The concept of updating a probability distribution in the light of new evidence lies at the heart of statistics and machine learning. Pearl's and Jeffrey's rule are two natural update mechanisms which lead to different outcomes, yet the…
We characterize probabilities in Bayesian networks in terms of algebraic expressions called quasi-probabilities. These are arrived at by casting Bayesian networks as noisy AND-OR-NOT networks, and viewing the subnetworks that lead to a node…
We study LLM judgments of misinformation expressed with uncertainty. Our experiments study the response of three widely used LLMs (GPT-4o, LlaMA3, DeepSeek-v2) to misinformation propositions that have been verified false and then are…
There are two main approach to probability, one of set-theoretic character where probability is the measure of a set, and another one of linguistic character where probability is the degree of confidence in a proposition. In this work we…
Behavioural economics provides labels for patterns in human economic behaviour. Probability weighting is one such label. It expresses a mismatch between probabilities used in a formal model of a decision (i.e. model parameters) and…
Many domain experts do not have the time or expertise to write formal Bayesian models. This paper takes an informal problem description as input, and combines a large language model and a probabilistic programming language to define a joint…
Many tasks in statistical and causal inference can be construed as problems of \emph{entailment} in a suitable formal language. We ask whether those problems are more difficult, from a computational perspective, for \emph{causal}…
Dependencies on the relative frequency of a state in the domain are common when modelling probabilistic dependencies on relational data. For instance, the likelihood of a school closure during an epidemic might depend on the proportion of…
We examine three probabilistic concepts related to the sentence "two variables have no bearing on each other". We explore the relationships between these three concepts and establish their relevance to the process of constructing similarity…
The systematic biases seen in people's probability judgments are typically taken as evidence that people do not reason about probability using the rules of probability theory, but instead use heuristics which sometimes yield reasonable…
Usually, probabilistic automata and probabilistic grammars have crisp symbols as inputs, which can be viewed as the formal models of computing with values. In this paper, we first introduce probabilistic automata and probabilistic grammars…
Works, briefly surveyed here, are concerned with two basic methods: Maximum Probability and Bayesian Maximum Probability; as well as with their asymptotic instances: Relative Entropy Maximization and Maximum Non-parametric Likelihood.…
By representing the range of fair betting odds according to a pair of confidence set estimators, dual probability measures on parameter space called frequentist posteriors secure the coherence of subjective inference without any prior…
Despite widespread success in language understanding and generation, large language models (LLMs) exhibit unclear and often inconsistent behavior when faced with tasks that require probabilistic reasoning. In this work, we present the first…
Probabilistic forecasts must sum to unity and cannot express ``I don't know.'' Possibility theory relaxes this constraint: a subnormal distribution explicitly measures how much of the plausibility budget remains unassigned, ignorance signal…
Discovery of an accurate causal Bayesian network structure from observational data can be useful in many areas of science. Often the discoveries are made under uncertainty, which can be expressed as probabilities. To guide the use of such…
It is well known that a Bayesian probability forecast for all future observations should be a probability measure in order to satisfy a natural condition of coherence. The main topics of this paper are the evolution of the Bayesian…
In this paper we deal with a new approach to probabilistic reasoning in a logical framework. Nearly almost all logics of probability that have been proposed in the literature are based on classical two-valued logic. After making clear the…
The project aims to provide a semi-supervised approach to identify Multiword Expressions in a multilingual context consisting of English and most of the major Indian languages. Multiword expressions are a group of words which refers to some…
Comprehensible explanations of probabilistic reasoning are a prerequisite for wider acceptance of Bayesian methods in expert systems and decision support systems. A study of human reasoning under uncertainty suggests two different…