Related papers: Confronting classical and Bayesian confidence limi…
Physics increasingly uses Bayesian techniques for systematic data analysis and model-to-data comparison. This paper describes how these methods can be implemented to answer questions of relevance to teaching laboratories. It demonstrates…
In this study, both Bayesian classifiers and mutual information classifiers are examined for binary classifications with or without a reject option. The general decision rules in terms of distinctions on error types and reject types are…
The Bayesian method is noted to produce spuriously high posterior probabilities for phylogenetic trees in analysis of large datasets, but the precise reasons for this over-confidence are unknown. In general, the performance of Bayesian…
We connect the power of Confidence Intervals in different Frequentist methods to their reliability. We show that in the case of a bounded parameter a biased method which near the boundary has large power in testing the parameter against…
Bayesian inference gets its name from *Bayes's theorem*, expressing posterior probabilities for hypotheses about a data generating process as the (normalized) product of prior probabilities and a likelihood function. But Bayesian inference…
This chapter provides a overview of Bayesian inference, mostly emphasising that it is a universal method for summarising uncertainty and making estimates and predictions using probability statements conditional on observed data and an…
We present a universal framework for constructing confidence sets based on sequential likelihood mixing. Building upon classical results from sequential analysis, we provide a unifying perspective on several recent lines of work, and…
Randomized controlled experiments assess new policy impacts on performance metrics to inform launch decisions. Traditional approaches evaluate metrics independently despite correlations, and mixed results (e.g., positive revenue impact,…
The classical conception of falsification presents scientific theories as entities that are decisively refuted when their predictions fail. This picture has long been challenged by both philosophical analysis and scientific practice, yet…
While Bayesian model selection is a useful tool to discriminate between competing cosmological models, it only gives a relative rather than an absolute measure of how good a model is. Bayesian doubt introduces an unknown benchmark model…
Experimentally, certain degrees of freedom may appear classical because their quantum fluctuations are smaller than the experimental error associated with measuring them. An approximation to a fully quantum theory is described in which the…
Objectives: The aim of this paper is to contrast the retrospective and prospective use of experts beliefs in choosing between survival models in economic evaluations. Methods: The use of experts retrospective (posterior) beliefs is…
This paper develops a Bayesian approach for assessing equivalence and non-inferiority hypotheses in two-arm trials using relative belief ratios. A relative belief ratio is a measure of statistical evidence and can indicate evidence either…
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…
We discuss how to determine and combine upper limits based on observed events and estimated backgrounds with a Bayesian method, when insignificant signals are observed in independent measurements. In addition to some general features…
Signal processing makes extensive use of point estimators and accompanying error bounds. These work well up until the likelihood function has two or more high peaks. When it is important for an estimator to remain reliable, it becomes…
This article is geared towards theorists interested in estimating parameters of their theoretical models, and computing their own limits using available experimental data and elementary Mathematica code. The examples given can be useful…
Especially when facing reliability data with limited information (e.g., a small number of failures), there are strong motivations for using Bayesian inference methods. These include the option to use information from physics-of-failure or…
Bayesian synthetic likelihood is a widely used approach for conducting Bayesian analysis in complex models where evaluation of the likelihood is infeasible but simulation from the assumed model is tractable. We analyze the behaviour of the…
Context: Expert judgement is a common method for software effort estimations in practice today. Estimators are often shown extra obsolete requirements together with the real ones to be implemented. Only one previous study has been conducted…