Scalable Empirical Bayes Inference and Bayesian Sensitivity Analysis.

ABSTRACT: Consider a Bayesian setup in which we observe Y , whose distribution depends on a parameter θ , that is, Y∣θ~πY∣θ . The parameter θ is unknown and treated as random, and a prior distribution chosen from some parametric family πθ(⋅;h),h∈ℋ , is to be placed on it. For the subjective Bayesian there is a single prior in the family which represents his or her beliefs about θ , but determination of this prior is very often extremely difficult. In the empirical Bayes approach, the latent distribution on θ is estimated from the data. This is usually done by choosing the value of the hyperparameter h that maximizes some criterion. Arguably the most common way of doing this is to let m(h) be the marginal likelihood of h , that is, m(h)=∫πY∣θvh(θ)dθ , and choose the value of h that maximizes m(⋅) . U

SUBMITTER: Doss H 

PROVIDER: S-EPMC11654829 | biostudies-literature | 2024 Nov

REPOSITORIES: biostudies-literature