Paper: [Arxiv] [Statistics in Medicine]
A power prior is a way of constructing an informative prior distribution based on historical data.
The main idea is to raise the likelihood to a certain scalar, a0, usually between 0 and 1, in order to control the amount of information borrowed from the historical data.
In this paper, Joseph Ibrahim and I explore the so-called normalised power prior, where a0 is allowed to vary according a prior distribution.
We prove a few interesting things about the normalising constant c(a0) and devise an approximate method to sample from the joint posterior of the tempering scalar a0and the parameters of interest (theta).
The package with the routines to run the examples in this repository is npowerPrioR.