BP2D {BayesBP}

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')
# ---------------------------------------- #