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In this paper we provide a conceptual overview of latent variable models within a probabilistic modeling framework, an overview that emphasizes the compositional nature and the interconnectedness of the seemingly disparate models commonly…
This paper gives yet another definition of game-theoretic probability in the context of continuous-time idealized financial markets. Without making any probabilistic assumptions (but assuming positive and continuous price paths), we obtain…
Probabilities of causation play a crucial role in modern decision-making. Pearl defined three binary probabilities of causation, the probability of necessity and sufficiency (PNS), the probability of sufficiency (PS), and the probability of…
This paper presents a new approach to conditional inference, based on the simulation of samples conditioned by a statistics of the data. Also an explicit expression for the approximation of the conditional likelihood of long runs of the…
A new method is developed to represent probabilistic relations on multiple random events. Where previously knowledge bases containing probabilistic rules were used for this purpose, here a probability distribution over the relations is…
Statistical models of real world data typically involve continuous probability distributions such as normal, Laplace, or exponential distributions. Such distributions are supported by many probabilistic modelling formalisms, including…
While probability theory is normally applied to external environments, there has been some recent interest in probabilistic modeling of the outputs of computations that are too expensive to run. Since mathematical logic is a powerful tool…
Using the Clauser-Horne model of Bell's theorem, the locality condition is examined and it is shown the corresponding formulation is equivalent to a factorization process consisting of three stages. The first stage is introduced based on…
There is currently a renewed interest in the Bayesian predictive approach to statistics. This paper offers a review on foundational concepts and focuses on predictive modeling, which by directly reasoning on prediction, bypasses inferential…
Continued fractions have been introduced in the field of $p$--adic numbers $\mathbb{Q}_p$ by several authors. However, a standard definition is still missing since all the proposed algorithms are not able to replicate all the properties of…
In this paper we introduce the idea of probability in the definition of Sequential Dynamical Systems, thus obtaining a new concept, Probabilistic Sequential System. The introduction of a probabilistic structure on Sequential Dynamical…
In this paper we propose a general approach to define a many-valued preferential interpretation of gradual argumentation semantics. The approach allows for conditional reasoning over arguments and boolean combination of arguments, with…
Computing the probability of a formula given the probabilities or weights associated with other formulas is a natural extension of logical inference to the probabilistic setting. Surprisingly, this problem has received little attention in…
We consider how to define a natural probability distribution over worlds within a simple class of deterministic many-worlds theories. This can help us understand the typical properties of worlds within such states, and hence explain the…
We propose and study properties of maximum likelihood estimators in the class of conditional transformation models. Based on a suitable explicit parameterisation of the unconditional or conditional transformation function, we establish a…
In this paper we define and examine the power of the {\em conditional-sampling} oracle in the context of distribution-property testing. The conditional-sampling oracle for a discrete distribution $\mu$ takes as input a subset $S \subset…
The paper concerns the probabilistic evaluation of plans in the presence of unmeasured variables, each plan consisting of several concurrent or sequential actions. We establish a graphical criterion for recognizing when the effects of a…
We review briefly the concepts underlying complex systems and probability distributions. The later are often taken as the first quantitative characteristics of complex systems, allowing one to detect the possible occurrence of regularities…
Expectation is a central notion in probability theory. The notion of expectation also makes sense for other notions of uncertainty. We introduce a propositional logic for reasoning about expectation, where the semantics depends on the…
This note is concerned with a formal analysis of the problem of non-monotonic reasoning in intelligent systems, especially when the uncertainty is taken into account in a quantitative way. A firm connection between logic and probability is…