View source: R/PoiOMNPP_MCMC2.R
PoiOMNPP_MCMC2 | R Documentation |
Multiple ordered historical data are combined individually.
Conduct posterior sampling for Poisson population with normalized power prior.
For the power parameter \gamma
, a Metropolis-Hastings algorithm with independence proposal is used.
For the model parameter \lambda
, Gibbs sampling is used.
PoiOMNPP_MCMC2(n0,n,prior_gamma,prior_lambda, gamma_ind_prop,gamma_ini,
nsample, burnin, thin)
n0 |
a natural number vector : number of successes in historical data. |
n |
a natural number : number of successes in the current data. |
prior_gamma |
a vector of the hyperparameters in the prior distribution |
prior_lambda |
a vector of the hyperparameters in the prior distribution |
gamma_ind_prop |
a vector of the hyperparameters in the proposal distribution |
gamma_ini |
the initial value of |
nsample |
specifies the number of posterior samples in the output. |
burnin |
the number of burn-ins. The output will only show MCMC samples after bunrin. |
thin |
the thinning parameter in MCMC sampling. |
The outputs include posteriors of the model parameter(s) and power parameter, acceptance rate in sampling \gamma
.
The normalized power prior distribution is
\pi_0(\gamma)\prod_{k=1}^{K}\frac{\pi_0(\lambda)L(\lambda|D_{0k})^{(\sum_{i=1}^{k}\gamma_i)}}{\int \pi_0(\lambda)L(\lambda|D_{0k})^{(\sum_{i=1}^{k}\gamma_i)} d\lambda}.
Here \pi_0(\gamma)
and \pi_0(\lambda)
are the initial prior distributions of \gamma
and \lambda
, respectively. L(\lambda|D_{0k})
is the likelihood function of historical data D_{0k}
, and \sum_{i=1}^{k}\gamma_i
is the corresponding power parameter.
A list of class "NPP" with three elements:
acceptrate |
the acceptance rate in MCMC sampling for |
lambda |
posterior of the model parameter |
delta |
posterior of the power parameter |
Qiang Zhang zqzjf0408@163.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.
PoiMNPP_MCMC1
;
PoiMNPP_MCMC2
;
PoiOMNPP_MCMC1
PoiOMNPP_MCMC2(n0=c(0,3,5),n=3,prior_gamma=c(1/2,1/2,1/2,1/2),
prior_lambda=c(1,1/10), gamma_ind_prop=rep(1,4),
gamma_ini=NULL, nsample = 2000, burnin = 500, thin = 2)
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