View source: R/PosteriorModeNPP.R
ModeDeltaLMNPP | R Documentation |
The function returns the posterior mode of the power parameter \delta
in normal linear model.
It calculates the log of the posterior density (up to a normalizing constant), and conduct a grid search
to find the approximate mode.
ModeDeltaLMNPP(y.Cur, y.Hist, x.Cur = NULL, x.Hist = NULL, npoints = 1000,
prior = list(a = 1.5, b = 0, mu0 = 0, Rinv = matrix(1, nrow = 1),
delta.alpha = 1, delta.beta = 1))
y.Cur |
a vector of individual level of the response y in current data. |
y.Hist |
a vector of individual level of the response y in historical data. |
x.Cur |
a vector or matrix or data frame of covariate observed in the current data. If more than 1 covariate available, the number of rows is equal to the number of observations. |
x.Hist |
a vector or matrix or data frame of covariate observed in the historical data. If more than 1 covariate available, the number of rows is equal to the number of observations. |
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 model parameters
|
If b = 1
, prior for (\beta, \sigma)
is (1/\sigma^2)^a * N(mu0, \sigma^2 R^{-1})
, which includes the g-prior.
If b = 0
, prior for (\beta, \sigma)
is (1/\sigma^2)^a
.
The outputs include posteriors of the model parameter(s) and power parameter, acceptance rate when sampling \delta
, and
the deviance information criteria.
Zifei Han hanzifei1@gmail.com
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.
Berger, J.O. and Bernardo, J.M. (1992). On the development of reference priors. Bayesian Statistics 4: Proceedings of the Fourth Valencia International Meeting, Bernardo, J.M, Berger, J.O., Dawid, A.P. and Smith, A.F.M. eds., 35-60, Clarendon Press:Oxford.
Jeffreys, H. (1946). An Invariant Form for the Prior Probability in Estimation Problems. Proceedings of the Royal Statistical Society of London, Series A 186:453-461.
ModeDeltaBerNPP
;
ModeDeltaNormalNPP
;
ModeDeltaMultinomialNPP
;
ModeDeltaNormalNPP
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