相关论文: How to Guide Decisions with Bayes Factors

A common task in physics and astronomy is studying which of the competing hypotheses the data prefer. This is usually done by computing the Bayes factor between the two hypotheses, and either interpreting it in terms of the posterior odds…

Bayesian probability theory is used as a framework to develop a formalism for the scientific method based on principles of inductive reasoning. The formalism allows for precise definitions of the key concepts in theories of physics and also…

In statistical practice, whether a Bayesian or frequentist approach is used in inference depends not only on the availability of prior information but also on the attitude taken toward partial prior information, with frequentists tending to…

This paper describes a decision theoretic formulation of learning the graphical structure of a Bayesian Belief Network from data. This framework subsumes the standard Bayesian approach of choosing the model with the largest posterior…

With the advent of high-performance computing, Bayesian methods are increasingly popular tools for the quantification of uncertainty throughout science and industry. Since these methods impact the making of sometimes critical decisions in…

The measurement of the efficiency of an event selection is always an important part of the analysis of experimental data. The statistical techniques which are needed to determine the efficiency and its uncertainty are reviewed. Frequentist…

The analysis of decision making under uncertainty is closely related to the analysis of probabilistic inference. Indeed, much of the research into efficient methods for probabilistic inference in expert systems has been motivated by the…

In Generalised Bayesian Inference (GBI), the learning rate and hyperparameters of the loss must be estimated. These inference-hyperparameters can't be estimated jointly with the other parameters, from the data, by giving them a prior.…

External pilot trials of complex interventions are used to help determine if and how a confirmatory trial should be undertaken, providing estimates of parameters such as recruitment, retention and adherence rates. The decision to progress…

We introduce a novel rule-based approach for handling regression problems. The new methodology carries elements from two frameworks: (i) it provides information about the uncertainty of the parameters of interest using Bayesian inference,…

Bayes' rule has enabled innumerable powerful algorithms of statistical signal processing and statistical machine learning. However, when model misspecifications exist in prior and/or data distributions, the direct application of Bayes' rule…

We propose a new method for conducting Bayesian prediction that delivers accurate predictions without correctly specifying the unknown true data generating process. A prior is defined over a class of plausible predictive models. After…

The Bayes factor, the data-based updating factor from prior to posterior odds, is a principled measure of relative evidence for two competing hypotheses. It is naturally suited to sequential data analysis in settings such as clinical trials…

Probability models are only useful at explaining the uncertainty of what we do not know, and should never be used to say what we already know. Probability and statistical models are useless at discerning cause. Classical statistical…

While the Bayesian decision-theoretic framework offers an elegant solution to the problem of decision making under uncertainty, one question is how to appropriately select the prior distribution. One idea is to employ a worst-case prior.…

Spurred on by recent successes in causal inference competitions, Bayesian nonparametric (and high-dimensional) methods have recently seen increased attention in the causal inference literature. In this paper, we present a comprehensive…

Priors in which a large number of parameters are specified to be independent are dangerous; they make it hard to learn from data. I present a couple of examples from the literature and work through a bit of large sample theory to show what…

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…

Statisticians often face the choice between using probability models or a paradigm defined by minimising a loss function. Both approaches are useful and, if the loss can be re-cast into a proper probability model, there are many tools to…

Bayesian models quantify uncertainty and facilitate optimal decision-making in downstream applications. For most models, however, practitioners are forced to use approximate inference techniques that lead to sub-optimal decisions due to…