loglikNormD0 function

A Function to Calculate Log-likelihood of the Historical Data, Given Array-valued Parameters, for Normal Population

The function returns a matrix of class "npp", each element is a log-likelihood of the historical data. It is an intermediate step to calculate the "normalizing constant" $C(\delta)$ in the normalized power prior, for the purpose of providing a flexible implementation. Users can specify their own likelihood function of the same class following this structure.

loglikNormD0(D0, thetalist, ntheta = 2)

Arguments

• D0: a vector of each observation in historical data.

• thetalist: a list of parameter values. The number of elements is equal to ntheta. Each element is a matrix. The sample should come from the posterior of the powered likelihood for historical data, with each column corresponds to a distinct value of the power parameter $\delta$

  (the corresponding power parameter increases from left to right). The number of rows is the number of Monte Carlo samples for each $\delta$ fixed. The number of columns is the number of selected knots (number of distinct $\delta$).

• ntheta: a positive integer indicating number of parameters to be estimated in the model.

Returns

A numeric matrix of log-likelihood, for the historical data given the matrix(or array)-valued parameters.

Author(s)

Zifei Han hanzifei1@gmail.com

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

loglikBerD0; logCknot; logCdelta