loglikBerD0 {NPP}

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

Description

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.

Usage

loglikBerD0(D0, thetalist, ntheta = 1)

Arguments

D0

a vector of each observation(binary) 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. Default is 1 for Bernoulli.

Value

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

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

loglikNormD0; logCknot; logCdelta