Related papers: Combination of Upper and Lower Probabilities
Currently, there is renewed interest in the problem, raised by Shafer in 1985, of updating probabilities when observations are incomplete. This is a fundamental problem in general, and of particular interest for Bayesian networks. Recently,…
Consider a joint quantum state of a system and its environment. A measurement on the environment induces a decomposition of the system state. Using algorithmic information theory, we define the preparation information of a pure or mixed…
We demonstrate that the forecasting combination puzzle is a consequence of the methodology commonly used to produce forecast combinations. By the combination puzzle, we refer to the empirical finding that predictions formed by combining…
We consider a model where an agent is must choose between alternatives that each provide only an imprecise description of the world (e.g. linguistic expressions). The set of alternatives is closed under logical conjunction and disjunction,…
These lectures deal with the problem of inductive inference, that is, the problem of reasoning under conditions of incomplete information. Is there a general method for handling uncertainty? Or, at least, are there rules that could in…
Recently, it has been emphasized that the possibility theory framework allows us to distinguish between i) what is possible because it is not ruled out by the available knowledge, and ii) what is possible for sure. This distinction may be…
The necessary information for specifying a complex system may not be completely accessible to us, i.e., to mathematical treatments. This is not to be confounded with the incompleteness of our knowledge about whatever systems or nature,…
Probabilities of causation are fundamental to individual-level explanation and decision making, yet they are inherently counterfactual and not point-identifiable from data in general. Existing bounds either disregard available covariates,…
As physics searches for invariants in observations, this paper looks for invariants of probabilistic observation without assuming physical structure. Structure emerges from the basic assumption of science that new information shall lead to…
The correct use and interpretation of models depends on several steps, two of which being the calibration by parameter estimation and the analysis of uncertainty. In the biological literature, these steps are seldom discussed together, but…
Given a pair of predictor variables and a response variable, how much information do the predictors have about the response, and how is this information distributed between unique, redundant, and synergistic components? Recent work has…
Conditional mutual information is important in the selection and interpretation of graphical models. Its empirical version is well known as a generalised likelihood ratio test and that it may be represented as a difference in entropy. We…
Abduction is a fundamental and important form of non-monotonic reasoning. Given a knowledge base explaining how the world behaves it aims at finding an explanation for some observed manifestation. In this paper we focus on propositional…
Any strategy and prior probability together are a coherent conditional probability that can be extended, generally not in a unique way, to a full conditional probability. The corresponding class of extensions is studied and a closed form…
A question of some interest is how to characterize the amount of information that a prior puts into a statistical analysis. Rather than a general characterization, we provide an approach to characterizing the amount of information a prior…
How should one combine noisy information from diverse sources to make an inference about an objective ground truth? This frequently recurring, normative question lies at the core of statistics, machine learning, policy-making, and everyday…
This paper investigates a representation language with flexibility inspired by probabilistic logic and compactness inspired by relational Bayesian networks. The goal is to handle propositional and first-order constructs together with…
When dealing with Bayesian inference the choice of the prior often remains a debatable question. Empirical Bayes methods offer a data-driven solution to this problem by estimating the prior itself from an ensemble of data. In the…
Possibilistic logic offers a qualitative framework for representing pieces of information associated with levels of uncertainty of priority. The fusion of multiple sources information is discussed in this setting. Different classes of…
This paper examines how an event from one random variable provides pointwise mutual information about an event from another variable via probability mass exclusions. We start by introducing probability mass diagrams, which provide a visual…