ModeDeltaMultinomialNPP() R function from [NPP]

Calculate Posterior Mode of the Power Parameter in Normalized Power Prior with Grid Search, Multinomial Population

The function returns the posterior mode of the power parameter $\delta$ in multinomial population. It calculates the log of the posterior density (up to a normalizing constant), and conduct a grid search to find the approximate mode.


ModeDeltaMultinomialNPP(Data.Cur, Data.Hist, CompStat = list(n0 = NULL, n1 = NULL),
                        npoints = 1000, prior = list(theta.dir.alpha = c(0.5, 0.5, 0.5),
                        delta.alpha = 1, delta.beta = 1))

Arguments

Data.Cur: a non-negative integer vector of $K$ elements: c(number of success in group 1, number of success in group 2, ..., number of success in group $K$ ) in the current data.
Data.Hist: a non-negative integer vector of $K$ elements: c(number of success in group 1, number of success in group 2, ..., number of success in group $K$ ) in the historical data.
CompStat: a list of two elements that represents the "compatibility(sufficient) statistics" for $\theta$ . Default is NULL so the fitting will be based on the data. If the CompStat is provided then the inputs in Data.Cur and Data.Hist will be ignored. Note: in multinomial case providing CompStat is equivalent to provide the data summary as in Data.Cur and Data.Cur.

n0 is a non-negative integer vector of $K$ elements for compatible statistics in historical data: c(number of success in group 1, number of success in group 2, ..., number of success in group $K$ ).

n1 is a non-negative integer vector of $K$ elements for compatible statistics in current data: c(number of success in group 1, number of success in group 2, ..., number of success in group $K$ ).
npoints: is a non-negative integer scalar indicating number of points on a regular spaced grid between [0, 1], where we calculate the log of the posterior and search for the mode.
prior: a list of the hyperparameters in the prior for both $p$ and $\delta$ .

theta.dir is a vector of $K$ elements of the hyperparameter $\alpha$

in the prior distribution $Dir(\alpha[1],\alpha[2],...,\alpha[K])$ for $\theta$ .

delta.alpha a scalar, the hyperparameter $\alpha$ in the prior distribution $Beta(\alpha, \beta)$ for $\delta$ .

delta.beta a scalar, the hyperparameter $\beta$ in the prior distribution $Beta(\alpha, \beta)$ for $\delta$ .

Returns

A numeric value between 0 and 1.

Details

See example.

Examples


ModeDeltaMultinomialNPP(CompStat = list(n0 = c(25,25,25,25), n1 = c(25,25,25,25)),
                        prior = list(theta.dir.alpha = c(0.5, 0.5, 0.5, 0.5),
                                     delta.alpha = 1, delta.beta = 1))

ModeDeltaMultinomialNPP(CompStat = list(n0 = c(22,25,28,25), n1 = c(25,22,25,28)),
                        prior = list(theta.dir.alpha = c(0.5, 0.5, 0.5, 0.5),
                                     delta.alpha = 1, delta.beta = 1))

ModeDeltaMultinomialNPP(CompStat = list(n0 = c(15,25,30,30), n1 = c(25,25,25,25)),
                        prior = list(theta.dir.alpha = c(0.5, 0.5, 0.5, 0.5),
                                     delta.alpha = 1, delta.beta = 1))

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.

ModeDeltaMultinomialNPP function