Related papers: Foundations for conditional probability
Causal inference can be formalized as Bayesian inference that combines a prior distribution over causal models and likelihoods that account for both observations and interventions. We show that it is possible to implement this approach…
Plausible reasoning concerns situations whose inherent lack of precision is not quantified; that is, there are no degrees or levels of precision, and hence no use of numbers like probabilities. A hopefully comprehensive set of principles…
We examine a new approach to modeling uncertainty based on plausibility measures, where a plausibility measure just associates with an event its plausibility, an element is some partially ordered set. This approach is easily seen to…
The aim of this work is to provide a unified framework for ordinal representations of uncertainty lying at the crosswords between possibility and probability theories. Such confidence relations between events are commonly found in monotonic…
Plausibility measures are structures for reasoning in the face of uncertainty that generalize probabilities, unifying them with weaker structures like possibility measures and comparative probability relations. So far, the theory of…
Positivity, the assumption that every unique combination of confounding variables that occurs in a population has a non-zero probability of an action, can be further delineated as deterministic positivity and stochastic positivity. Here, we…
The aim of this paper is to show that the concept of probability is best understood by dividing this concept into two different types of probability, namely physical probability and analogical probability. Loosely speaking, a physical…
Uncertainty may be taken to characterize inferences, their conclusions, their premises or all three. Under some treatments of uncertainty, the inferences itself is never characterized by uncertainty. We explore both the significance of…
The principle of the common cause claims that if an improbable coincidence has occurred, there must exist a common cause. This is generally taken to mean that positive correlations between non-causally related events should disappear when…
An example shows that weak decoherence is more restrictive than the minimal logical decoherence structure that allows probabilities to be used consistently for quantum histories. The probabilities in the sum rules that define minimal…
Between the two dominant schools of thought in statistics, namely, Bayesian and classical/frequentist, a main difference is that the former is grounded in the mathematically rigorous theory of probability while the latter is not. In this…
With recent advances in natural language processing, rationalization becomes an essential self-explaining diagram to disentangle the black box by selecting a subset of input texts to account for the major variation in prediction. Yet,…
The purpose of this paper is to present a mathematical theory that can be used as a foundation for statistics that include improper priors. This theory includes improper laws in the initial axioms and has in particular Bayes theorem as a…
Conditionals play a key role in different areas of logic and probabilistic reasoning, and they have been studied and formalized from different angles. In this paper we focus on the de Finetti's notion of conditional as a three-valued…
A nonmonotonic logic of thresholded generalizations is presented. Given propositions A and B from a language L and a positive integer k, the thresholded generalization A=>B{k} means that the conditional probability P(B|A) falls short of one…
Conformal prediction (CP) is widely presented as distribution-free predictive inference with finite-sample marginal coverage under exchangeability. We argue that CP is best understood as a rank-calibrated descendant of 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…
Mechanisms for the automation of uncertainty are required for expert systems. Sometimes these mechanisms need to obey the properties of probabilistic reasoning. A purely numeric mechanism, like those proposed so far, cannot provide a…
Quantum theory is a probabilistic theory with fixed causal structure. General relativity is a deterministic theory but where the causal structure is dynamic. It is reasonable to expect that quantum gravity will be a probabilistic theory…
We present a complete reasoning principle for contextual equivalence in an untyped probabilistic language. The language includes continuous (real-valued) random variables, conditionals, and scoring. It also includes recursion, since the…