Related papers: Conditional Probability formula as a consequence o…
Considering a minimal number of assumptions and in the context of the timeless formalism, conditional probabilities are derived for subsequent measurements in the non-relativistic regime. Only unitary transformations are considered with…
We give a finite-sample analysis of predictive inference procedures after model selection in regression with random design. The analysis is focused on a statistically challenging scenario where the number of potentially important…
There is wide support in logic, philosophy, and psychology for the hypothesis that the probability of the indicative conditional of natural language, $P(\textit{if } A \textit{ then } B)$, is the conditional probability of $B$ given $A$,…
Intercausal reasoning is a common inference pattern involving probabilistic dependence of causes of an observed common effect. The sign of this dependence is captured by a qualitative property called product synergy. The current definition…
Predicting the future is an important component of decision making. In most situations, however, there is not enough information to make accurate predictions. In this paper, we develop a theory of causal reasoning for predictive inference…
The concept of Relative Divergence of one Grading Function from another is extended from totally ordered chains to power sets of finite event spaces. Shannon Entropy concept is extended to normalized grading functions on such power sets.…
We describe a mathematical language for determining all possible patterns of contextuality in the dependence of stochastic outputs of a system on its deterministic inputs. The central notion is that of all possible couplings for…
A simple proof of the convergence of the variational regularization, with the regularization parameter, chosen by the discrepancy principle, is given for linear operators under suitable assumptions. It is shown that the discrepancy…
Possibilistic logic, an extension of first-order logic, deals with uncertainty that can be estimated in terms of possibility and necessity measures. Syntactically, this means that a first-order formula is equipped with a possibility degree…
A general notion of algebraic conditional plausibility measures is defined. Probability measures, ranking functions, possibility measures, and (under the appropriate definitions) sets of probability measures can all be viewed as defining…
There is much interest in providing probabilistic semantics for defaults but most approaches seem to suffer from one of two problems: either they require numbers, a problem defaults were intended to avoid, or they generate peculiar side…
We recently described a formalism for reasoning with if-then rules that re expressed with different levels of firmness [18]. The formalism interprets these rules as extreme conditional probability statements, specifying orders of magnitude…
A theory of measurement uncertainty is presented, which, since it is based exclusively on the Bayesian approach and on the subjective concept of conditional probability, is applicable in the most general cases. The recent International…
This paper presents a categorical account of conditional probability, covering both the classical and the quantum case. Classical conditional probabilities are expressed as a certain "triangle-fill-in" condition, connecting marginal and…
We generalize standard credal set models for imprecise probabilities to include higher order credal sets -- confidences about confidences. In doing so, we specify how an agent's higher order confidences (credal sets) update upon observing…
We study a natural variant of the implicational fragment of propositional logic. Its formulas are pairs of conjunctions of positive literals, related together by an implicational-like connective; the semantics of this sort of implication is…
This paper provides a systematic yet accessible presentation of the Contextuality-by-Default theory. The consideration is confined to finite systems of categorical random variables, which allows us to focus on the basics of the theory…
We present locally complete inference rules for probabilistic deduction from taxonomic and probabilistic knowledge-bases over conjunctive events. Crucially, in contrast to similar inference rules in the literature, our inference rules are…
In 1933 Kolmogorov constructed a general theory that defines the modern concept of conditional probability. In 1955 Renyi fomulated a new axiomatic theory for probability motivated by the need to include unbounded measures. This note…
Conformal predictors are set predictors that are automatically valid in the sense of having coverage probability equal to or exceeding a given confidence level. Inductive conformal predictors are a computationally efficient version of…