LaplacelogC {NPP}

A Function to Calculate logC(\delta) Based on Laplace Approximation

Description

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).

Usage

LaplacelogC(delta, loglikmle, detHessian, ntheta)

Arguments

delta

the power parameter between 0 and 1. The function returns logC(\delta)

loglikmle

a scalar; the loglikelihood of the historical data evaluated at the maximum likelihood estimates based on the historical data

detHessian

determinant of the Hessian matrix evaluated at the loglikelihood function with respect to the maximum likelihood estimates based on the historical data

ntheta

an positive integer indicating number of parameters in the model

Value

logC(\delta) based on the Laplace approximation. Can be used for the posterior sampling in the normalized power prior.

Author(s)

Zifei Han [e-mail]

References

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.

See Also

logCknot