Related papers: Evidence with Uncertain Likelihoods
Accepting a proposition means that our confidence in this proposition is strictly greater than the confidence in its negation. This paper investigates the subclass of uncertainty measures, expressing confidence, that capture the idea of…
We construct the belief function that quantifies the agent, beliefs about which event of Q will occurred when he knows that the event is selected by a chance set-up and that the probability function associated to the chance set up is only…
Statistical inference after model selection requires an inference framework that takes the selection into account in order to be valid. Following recent work on selective inference, we derive analytical expressions for inference after…
We consider an empirical likelihood framework for inference for a statistical model based on an informative sampling design. Covariate information is incorporated both through the weights and the estimating equations. The estimator is based…
Prediction, where observed data is used to quantify uncertainty about a future observation, is a fundamental problem in statistics. Prediction sets with coverage probability guarantees are a common solution, but these do not provide…
This paper proposes a belief-based framework for social norms in environments where individuals choose a single action. Relaxing the assumption that the appropriateness standard is common knowledge, the framework allows individuals to be…
A machine that learns a task from observations must encounter and process uncertainty and novelty, especially when it is to maintain performance when observing new information and to select the hypothesis that best fits the current…
We present a propositional logic %which can be used to reason about the uncertainty of events, where the uncertainty is modeled by a set of probability measures assigning an interval of probability to each event. We give a sound and…
We describe a statistical hypothesis test for the presence of a signal based on the likelihood ratio statistic. We derive the test for a case of interest and also show that for that case the test works very well, even far out in the tails…
Information accounting provides a better foundation for hypothesis testing than does uncertainty quantification. A quantitative account of science is derived under this perspective that alleviates the need for epistemic bridge principles,…
When a measurement of a physical quantity is reported, the total uncertainty is usually decomposed into statistical and systematic uncertainties. This decomposition is not only useful to understand the contributions to the total…
Bayesian statistics is based on the subjective definition of probability as {\it ``degree of belief''} and on Bayes' theorem, the basic tool for assigning probabilities to hypotheses combining {\it a priori} judgements and experimental…
The likelihood function plays a pivotal role in statistical inference; it is adaptable to a wide range of models and the resultant estimators are known to have good properties. However, these results hinge on correct specification of the…
What are the criteria that a measure of statistical evidence should satisfy? It is argued that a measure of evidence should be consistent. Consistency is an asymptotic criterion: the probability that if a measure of evidence in data…
The features of a logically sound approach to a theory of statistical reasoning are discussed. A particular approach that satisfies these criteria is reviewed. This is seen to involve selection of a model, model checking, elicitation of a…
Evidential reasoning is cast as the problem of simplifying the evidence-hypothesis relation and constructing combination formulas that possess certain testable properties. Important classes of evidence as identifiers, annihilators, and…
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…
Attempts to replicate probabilistic reasoning in expert systems have typically overlooked a critical ingredient of that process. Probabilistic analysis typically requires extensive judgments regarding interdependencies among hypotheses and…
Evidence for fine-tuning of physical parameters suitable for life can perhaps be explained by almost any combination of providence, coincidence or multiverse. A multiverse usually includes parts unobservable to us, but if the theory for it…
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…