相关论文: Optimal Priors for the Discounting Parameter of th…

Power priors are used for incorporating historical data in Bayesian analyses by taking the likelihood of the historical data raised to the power $\alpha$ as the prior distribution for the model parameters. The power parameter $\alpha$ is…

The elicitation of power priors, based on the availability of historical data, is realized by raising the likelihood function of the historical data to a fractional power {\delta}, which quantifies the degree of discounting of the…

The power prior and its variations have been proven to be a useful class of informative priors in Bayesian inference due to their flexibility in incorporating the historical information by raising the likelihood of the historical data to a…

The power prior is a class of informative priors designed to incorporate historical data alongside current data in a Bayesian framework. It includes a power parameter that controls the influence of historical data, providing flexibility and…

The power prior is a popular tool for constructing informative prior distributions based on historical data. The method consists of raising the likelihood to a discounting factor in order to control the amount of information borrowed from…

The power prior is a popular class of informative priors for incorporating information from historical data. It involves raising the likelihood for the historical data to a power, which acts as a discounting parameter. When the discounting…

The ongoing replication crisis in science has increased interest in the methodology of replication studies. We propose a novel Bayesian analysis approach using power priors: The likelihood of the original study's data is raised to the power…

Projected priors were originally introduced to accommodate parameter constraints, but have recently regained popularity due to their ability to assign probability mass to low-dimensional parameter sets, such as the spaces of sparse vectors,…

Bayesian model comparison requires the specification of a prior distribution on the parameter space of each candidate model. In this connection two concerns arise: on the one hand the elicitation task rapidly becomes prohibitive as the…

Loss-based priors assign probability mass to parameter values according to the inferential loss incurred when they are excluded from the parameter space, and provide a general solution for discrete parameters. Extending this idea to…

This paper tackles the problem of decomposing binary data using matrix factorization. We consider the family of mean-parametrized Bernoulli models, a class of generative models that are well suited for modeling binary data and enables…

If we have an unbiased estimate of some parameter of interest, then its absolute value is positively biased for the absolute value of the parameter. This bias is large when the signal-to-noise ratio (SNR) is small, and it becomes even…

Bayesian inversion generates a posterior distribution of model parameters from an observation equation and prior information both weighted by hyperparameters. The prior is also introduced for the hyperparameters in fully Bayesian inversions…

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…

We introduce the Blackwell discount factor for Markov Decision Processes (MDPs). Classical objectives for MDPs include discounted, average, and Blackwell optimality. Many existing approaches to computing average-optimal policies solve for…

Posterior tempering reduces the influence of the likelihood in the calculation of the posterior by raising the likelihood to a fractional power $\alpha$. The resulting power posterior - also known as an $\alpha$-posterior or fractional…

A general, variational approach to derive low-order reduced systems is presented. The approach is based on the concept of optimal parameterizing manifold (OPM) that substitutes the more classical notions of invariant or slow manifold when…

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…

This paper considers the topic of finding prior distributions when a major component of the statistical model depends on a nonlinear function. Using results on how to construct uniform distributions in general metric spaces, we propose a…

Objective prior distributions represent an important tool that allows one to have the advantages of using the Bayesian framework even when information about the parameters of a model is not available. The usual objective approaches work off…