相关论文: The formal definition of reference priors

Prior specification for nonparametric Bayesian inference involves the difficult task of quantifying prior knowledge about a parameter of high, often infinite, dimension. Realistically, a statistician is unlikely to have informed opinions…

There are three principle paradigms of statistical inference: (i) Bayesian, (ii) information-based and (iii) frequentist inference. We describe an objective prior (the weighting or $w$-prior) which unifies objective Bayes and…

In Bayesian statistics, the choice of prior distribution is often debatable, especially if prior knowledge is limited or data are scarce. In imprecise probability, sets of priors are used to accurately model and reflect prior knowledge.…

This introduction to Bayesian statistics presents the main concepts as well as the principal reasons advocated in favour of a Bayesian modelling. We cover the various approaches to prior determination as well as the basis asymptotic…

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.…

Although Bayesian inference is an immensely popular paradigm among a large segment of scientists including statisticians, most applications consider objective priors and need critical investigations (Efron, 2013, Science). While it has…

The interpretation of data in terms of multi-parameter models of new physics, using the Bayesian approach, requires the construction of multi-parameter priors. We propose a construction that uses elements of Bayesian reference analysis. Our…

The standard approach to Bayesian inference is based on the assumption that the distribution of the data belongs to the chosen model class. However, even a small violation of this assumption can have a large impact on the outcome of a…

What is the best way to exploit extra data -- be it unlabeled data from the same task, or labeled data from a related task -- to learn a given task? This paper formalizes the question using the theory of reference priors. Reference priors…

In objective Bayesian model selection, no single criterion has emerged as dominant in defining objective prior distributions. Indeed, many criteria have been separately proposed and utilized to propose differing prior choices. We first…

A question of some interest is how to characterize the amount of information that a prior puts into a statistical analysis. Rather than a general characterization, we provide an approach to characterizing the amount of information a prior…

The proposed approach extends the confidence posterior distribution to the semi-parametric empirical Bayes setting. Whereas the Bayesian posterior is defined in terms of a prior distribution conditional on the observed data, the confidence…

The goal of causal inference is to understand the outcome of alternative courses of action. However, all causal inference requires assumptions. Such assumptions can be more influential than in typical tasks for probabilistic modeling, and…

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 hypothesis testing is re-examined from the perspective of an a priori assessment of the test statistic distribution under the alternative. By assessing the distribution of an observable test statistic, rather than prior parameter…

Probabilities in the multiverse can be calculated by assuming that we are typical representatives in a given reference class. But is this class well defined? What should be included in the ensemble in which we are supposed to be typical?…

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…

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…

We study Bayesian approaches to causal inference via propensity score regression. Much of the Bayesian literature on propensity score methods have relied on approaches that cannot be viewed as fully Bayesian in the context of conventional…

Inference is the process of using facts we know to learn about facts we do not know. A theory of inference gives assumptions necessary to get from the former to the latter, along with a definition for and summary of the resulting…