Related papers: Generalized Power Priors for Improved Bayesian Inf…

The Zellner's g-prior and its recent hierarchical extensions are the most popular default prior choices in the Bayesian variable selection context. These prior set-ups can be expressed power-priors with fixed set of imaginary data. In this…

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.…

In high-dimensional problems, choosing a prior distribution such that the corresponding posterior has desirable practical and theoretical properties can be challenging. This begs the question: can the data be used to help choose a good…

Incorporating historical information into the design and analysis of a new clinical trial has been the subject of much recent discussion. For example, in the context of clinical trials of antibiotics for drug resistant infections, where…

Modern predictive systems encode beliefs that can act as useful prior information for statistical inference in data-limited settings. Using them for prior construction introduces a tradeoff: an informative prior built from a predictive…

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.…

In the Bayesian framework power prior distributions are increasingly adopted in clinical trials and similar studies to incorporate external and past information, typically to inform the parameter associated to a treatment effect. Their use…

Generalized Bayes posterior distributions are formed by putting a fractional power on the likelihood before combining with the prior via Bayes's formula. This fractional power, which is often viewed as a remedy for potential model…

Bayesian computational strategies for inference can be inefficient in approximating the posterior distribution in models that exhibit some form of periodicity. This is because the probability mass of the marginal posterior distribution of…

Generalized linear mixed models (GLMMs) are commonly used to analyze correlated discrete or continuous response data. In Bayesian GLMMs, the often-used improper priors may yield undesirable improper posterior distributions. Thus, verifying…

Optimization is widely used in statistics, and often efficiently delivers point estimates on useful spaces involving structural constraints or combinatorial structure. To quantify uncertainty, Gibbs posterior exponentiates the negative loss…

Bayesian inference provides a powerful tool for leveraging observational data to inform model predictions and uncertainties. However, when such data is limited, Bayesian inference may not adequately constrain uncertainty without the use of…

Power-expected-posterior (PEP) methodology, which borrows ideas from the literature on power priors, expected-posterior priors and unit information priors, provides a systematic way to construct objective priors. The basic idea is to use…

It is becoming increasingly popular to elicit informative priors on the basis of historical data. Popular existing priors, including the power prior, commensurate prior, and robust meta-analytic prior provide blanket discounting. Thus, if…

Specifying a Bayesian prior is notoriously difficult for complex models such as neural networks. Reasoning about parameters is made challenging by the high-dimensionality and over-parameterization of the space. Priors that seem benign and…

Bayesian inferences in high energy physics often use uniform prior distributions for parameters about which little or no information is available before data are collected. The resulting posterior distributions are therefore sensitive to…

In this paper we propose an objective Bayesian estimation approach for the parameters of the generalized gamma distribution. Various reference priors are obtained, but showing that they lead to improper posterior distributions. We overcome…

We propose a probabilistic framework to directly insert prior knowledge in reinforcement learning (RL) algorithms by defining the behaviour policy as a Bayesian posterior distribution. Such a posterior combines task specific information…

Bayesian inference for inverse problems hinges critically on the choice of priors. In the absence of specific prior information, population-level distributions can serve as effective priors for parameters of interest. With the advent of…

Bayes factor, defined as the ratio of the marginal likelihood functions of two competing models, is the natural Bayesian procedure for model selection. Marginal likelihoods are usually computationally demanding and complex. This scenario is…