BP2D {BayesBP} R Documentation

## Bayesian estimation using two dimensions Bernstein polynomial

### Description

This function runs Metropolis-Hasting algorithm which is given setting prior and data.This algorithm starts storing coefficients when it runs halfway,so we use second halves of coefficients compute Rhat to check convergence.

### Usage

BP2D(
prior,
ages,
years,
disease,
population,
Iterations = 2e+05,
n_chain = 5,
n_cluster = 1,
nn = 2,
interval = 100,
RJC = 0.35,
seed = TRUE,
set = 1,
double = 4
)


### Arguments

 prior prior=(n0,alpha,L) where alpha is a Poisson parameter,n0 is upper bound of alpha L can be every number which is bigger than one. ages Range of ages. years Range of years. disease Disease matrix. population Population matrix. Iterations Iterations of chain. n_chain Number of Markov chain. n_cluster This parameter means number of cores, five cores is recommended.(default: n_cluster=1). nn The parameter nn is lower bound of alpha. interval Each hundreds save one coefficient. RJC Control parameter for transfer dimension. seed Set seed yes or not. set Choose seed.(defaults:set=1) double If R.hat >1.1 then double the iterations of times.

### Value

This function will return Bayesian estimate of incidence,Stored parameters,posterior mean,posterior max and table.

 Fhat Bayesian estimate of incidence. chain Bayesian estimate of posterior p-value mean. maxchain Bayesian estimate of posterior p-value max. store_coefficients Two dimensional Bernstein coefficients. output When M-H algorithm ends,contruct the table which contains norm,mean of Fhat,maximum of Fhat,R.hat,iterations,P-value and elasped time.

### References

Li-Chu Chien,Yuh-Jenn Wu,Chao A. Hsiung,Lu-Hai Wang,I-Shou Chang(2015).Smoothed Lexis Diagrams With Applications to Lung and Breast Cancer Trends in Taiwan,Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(511), pages 1000-1012, September.

### See Also

Other Bayesain estimate: BP2D_coef(), BP2D_table()

### Examples


# ---------------------------------------- #
library(BayesBP)
ages<-35:85
years<-1988:2007
prior<-c(10,5,2)
data(simulated_data_1)
disease<-simulated_data_1$disease population<-simulated_data_1$population
result<-BP2D(prior,ages,years,disease,population)
# ---------------------------------------- #
# Bernstein basis
basis<-BPbasis(ages,years,10)
pdbasis1<-PD_BPbasis(ages,years,10,by = 1)
pdbasis2<-PD_BPbasis(ages,years,10,by = 2)
# Bernstein polynomial
coef<-result$store_coefficients$chain_1[[1]]
BPFhat(coef,ages,years,basis)
PD_BPFhat(coef,ages,years,pdbasis1,by = 1)
PD_BPFhat(coef,ages,years,pdbasis2,by = 2)
# Credible interval
Credible_interval(result)
PD_Credible_interval(result,by = 1)
PD_Credible_interval(result,by = 2)
# ---------------------------------------- #
# Given four prior set
ages<-35:85
years<-1988:2007
data(simulated_data_2)
disease<-simulated_data_2$disease population<-simulated_data_2$population
p<-expand.grid(n0=c(10,20),alpha=c(5,10),LL=c(2,4))
prior_set<-p[p$n0==p$alpha*2,]
result_list<-paste0('result',1:nrow(prior_set))
for (i in seq_len(nrow(prior_set))) {
prior<-prior_set[i,]
assign(result_list[i],BP2D(prior,ages,years,disease,population))
write.BP(get(result_list[i]),sprintf('%s.xlsx',result_list[i]))
}
tab<-BP2D_table(result_list)
write.BPtable(tab,'result_table.xlsx')
# ---------------------------------------- #



[Package BayesBP version 1.1 Index]