The function assumes that the prior of the model parameters is very flat that had very minor impact on the shape of the power prior (posterior based on the D0).
LaplacelogC(delta, loglikmle, detHessian, ntheta)the power parameter between 0 and 1. The function returns \(logC(\delta)\)
a scalar; the loglikelihood of the historical data evaluated at the maximum likelihood estimates based on the historical data
determinant of the Hessian matrix evaluated at the loglikelihood function with respect to the maximum likelihood estimates based on the historical data
an positive integer indicating number of parameters in the model
\(logC(\delta)\) based on the Laplace approximation. Can be used for the posterior sampling in the normalized power prior.
Ibrahim, J.G., Chen, M.-H., Gwon, Y. and Chen, F. (2015). The Power Prior: Theory and Applications. Statistics in Medicine 34:3724-3749.
Duan, Y., Ye, K. and Smith, E.P. (2006). Evaluating Water Quality: Using Power Priors to Incorporate Historical Information. Environmetrics 17:95-106.