相关论文: Towards Reconciliation between Bayesian and Freque…

We study the stability of posterior predictive inferences to the specification of the likelihood model and perturbations of the data generating process. In modern big data analyses, useful broad structural judgements may be elicited from…

Covariate balancing is a popular technique for controlling confounding in observational studies. It finds weights for the treatment group which are close to uniform, but make the group's covariate means (approximately) equal to those of the…

Bayesian and frequentist methods differ in many aspects, but share some basic optimality properties. In practice, there are situations in which one of the methods is more preferred by some criteria. We consider the case of inference about a…

We present and examine a result related to uncertainty reasoning, namely that a certain plausibility space of Cox's type can be uniquely embedded in a minimal ordered field. This, although a purely mathematical result, can be claimed to…

This paper presents a plausible reasoning system to illustrate some broad issues in knowledge representation: dualities between different reasoning forms, the difficulty of unifying complementary reasoning styles, and the approximate nature…

This paper gives a generative model of the interpretation of formal logic for data-driven logical reasoning. The key idea is to represent the interpretation as likelihood of a formula being true given a model of formal logic. Using the…

In the modern Bayesian view classical probability theory is simply an extension of conventional logic, i.e., a quantitative tool that allows for consistent reasoning in the presence of uncertainty. Classical theory presupposes, however,…

Statistics is sometimes described as the science of reasoning under uncertainty. Statistical models provide one view of this uncertainty, but what is frequently neglected is the 'invisible' portion of uncertainty: that assumed not to exist…

Testing the equality of two proportions is a common procedure in science, especially in medicine and public health. In these domains it is crucial to be able to quantify evidence for the absence of a treatment effect. Bayesian hypothesis…

Bayesian and frequentist inference are two fundamental paradigms in statistical estimation. Bayesian methods treat hypotheses as random variables, incorporating priors and updating beliefs via Bayes' theorem, whereas frequentist methods…

Given a probability density $P({\bf x}|{\boldsymbol \lambda})$, where $\bf x$ represents continuous degrees of freedom and $\lambda$ a set of parameters, it is possible to construct a general identity relating expectations of observable…

Estimation frameworks for statistical inference are preferred to hypothesis testing when quantifying uncertainty and precise estimation are more valuable than binary decisions about statistical significance. Study design for…

We provide finite-sample distribution approximations, that are uniform in the parameter, for inference in linear mixed models. Focus is on variances and covariances of random effects in cases where existing theory fails because their…

Within the Kolmogorov theory of probability, Bayes' rule allows one to perform statistical inference by relating conditional probabilities to unconditional probabilities. As we show here, however, there is a continuous set of alternative…

The intuitive reasoning of physicists in conditions of uncertainty is closer to the Bayesian approach than to the frequentist ideas taught at University and which are considered the reference framework for handling statistical problems. The…

In almost every scientific field, an experiment involves collecting data and then analysing it. The analysis stage will often consist in trying to extract some physical parameter and estimating its uncertainty; this is known as Parameter…

Reasoning is key to many decision making processes. It requires consolidating a set of rule-like premises that are often associated with degrees of uncertainty and observations to draw conclusions. In this work, we address both the case…

We develop our interpretation of the joint belief distribution and of evidential updating that matches the following basic requirements: * there must exist an efficient method for reasoning within this framework * there must exist a clear…

Quantum theory can be viewed as a generalization of classical probability theory, but the analogy as it has been developed so far is not complete. Whereas the manner in which inferences are made in classical probability theory is…

Iterative imputation, in which variables are imputed one at a time each given a model predicting from all the others, is a popular technique that can be convenient and flexible, as it replaces a potentially difficult multivariate modeling…