BerOMNPP_MCMC2 {NPP} | R Documentation |
MCMC Sampling for Bernoulli Population of multiple ordered historical data using Normalized Power Prior
Description
Multiple ordered historical data are combined individually.
Conduct posterior sampling for Bernoulli population with normalized power prior.
For the power parameter \gamma
, a Metropolis-Hastings algorithm with independence proposal is used.
For the model parameter p
, Gibbs sampling is used.
Usage
BerOMNPP_MCMC2(n0, y0, n, y, prior_gamma, prior_p, gamma_ind_prop, gamma_ini,
nsample, burnin, thin, adjust = FALSE)
Arguments
n0 |
a vector of non-negative integers: numbers of trials in historical data. |
y0 |
a vector of non-negative integers: numbers of successes in historical data. |
n |
a non-negative integer: number of trials in the current data. |
y |
a non-negative integer: number of successes in the current data. |
prior_gamma |
a vector of the hyperparameters in the prior distribution |
prior_p |
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 burn-in. |
thin |
the thinning parameter in MCMC sampling. |
adjust |
Whether or not to adjust the parameters of the proposal distribution. |
Details
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(\theta)L(\theta|D_{0k})^{(\sum_{i=1}^{k}\gamma_i)}}{\int \pi_0(\theta)L(\theta|D_{0k})^{(\sum_{i=1}^{k}\gamma_i)} d\theta}.
Here \pi_0(\gamma)
and \pi_0(\theta)
are the initial prior distributions of \gamma
and \theta
, respectively. L(\theta|D_{0k})
is the likelihood function of historical data D_{0k}
, and \sum_{i=1}^{k}\gamma_i
is the corresponding power parameter.
Value
A list of class "NPP" with three elements:
acceptrate |
the acceptance rate in MCMC sampling for |
p |
posterior of the model parameter |
delta |
posterior of the power parameter |
Author(s)
Qiang Zhang zqzjf0408@163.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
BerMNPP_MCMC1
;
BerMNPP_MCMC2
;
BerOMNPP_MCMC1
Examples
BerOMNPP_MCMC2(n0 = c(275, 287), y0 = c(92, 125), n = 39, y = 17, prior_gamma=c(1,1,1)/3,
prior_p=c(1/2,1/2), gamma_ind_prop=rep(1,3)/2, gamma_ini=NULL,
nsample = 2000, burnin = 500, thin = 2, adjust = FALSE)