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

Value

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

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

Getting coefficeint from BP2D result.

Description

This function will return coefficient and length of each set of coefficeint.

Usage

BP2D_coef(result)

Arguments

Value

Coefficients table.

See Also

Other Bayesain estimate: BP2D_table(), BP2D()

Table and Criterion.

Description

If you give more groups of prior,you can use this function to get the table and T criterion.

Usage

BP2D_table(results_list)

Arguments

Value

Table and criterion T.

See Also

Other Bayesain estimate: BP2D_coef(), BP2D()

Two dimensional Bernstein polynomial

Description

Given Bernstein polynomial coeffients to compute Fhat.

Usage

BPFhat(coef, ages, years, basis)

Arguments

Value

This function return outer Bernstein polynomial using coefficients.

See Also

Other outer Bernstein polynomial: PD_BPFhat()

Examples

coef <- runif(9)
ages <- 35:85
years <- 1988:2007
list.basis <- BPbasis(ages,years,10)
BPFhat(coef,ages,years,list.basis)

Bernstein polynomial basis.

Description

This function build two dimensional Bernstein polynomial basis.

Usage

BPbasis(ages, years, n0, N = 1)

Arguments

Value

Bernstein basis.

See Also

Other Bernstein basis: PD_BPbasis()

Examples

ages <- 35:85
years <- 1988:2007
list.basis <- BPbasis(ages,years,10)
list.basis

Credible interval.

Description

Builing two dimensional Bernstein polynomial credible interval.

Usage

Credible_interval(result, n_cluster = 1, alpha = 0.05)

Arguments

Value

Bayesian credible interval with level of significance.

References

L.H. Chien, T.J. Tseng, C.H. Chen, H.F. Jiang, F.Y. Tsai, T.W. Liu, C.A. Hsiung, I.S. Chang Comparison of annual percentage change in breast cancer incidence rate between Taiwan and the United States-A smoothed Lexis diagram approach.

See Also

Other Credible interval: PD_Credible_interval()

Risky population function

Description

Risky population function

Usage

M(x, y)

Arguments

Two dimensional Bernstein polynomial

Description

Given Bernstein polynomial coeffients to compute Fhat.

Usage

PD_BPFhat(coef, ages, years, pdbasis, by = 1)

Arguments

Value

Partial differential Bernstein polynomial given coefficients.

See Also

Other outer Bernstein polynomial: BPFhat()

Examples

coef <- runif(9)
ages <- 35:85
years <- 1988:2007
pdbasis <- PD_BPbasis(ages,years,10,N=1,by=1)
PD_BPFhat(coef,ages,years,pdbasis,by=1)

Partial differential Bernstein polynomial basis.

Description

This function build two dimensional Bernstein polynomial basis.

Usage

PD_BPbasis(ages, years, n0, N = 1, by = 1)

Arguments

Value

Partial differential Bernstein basis.

See Also

Other Bernstein basis: BPbasis()

Examples

ages <- 35:85
years <- 1988:2007
pdbasis <- PD_BPbasis(ages,years,10,by = 1)
pdbasis

Credible interval.

Description

Builing two dimensional Bernstein polynomial credible interval.

Usage

PD_Credible_interval(result, n_cluster = 1, alpha = 0.05, by = 1)

Arguments

Value

Bayesian credible interval with level of significance.

References

L.H. Chien, T.J. Tseng, C.H. Chen, H.F. Jiang, F.Y. Tsai, T.W. Liu, C.A. Hsiung, I.S. Chang Comparison of annual percentage change in breast cancer incidence rate between Taiwan and the United States-A smoothed Lexis diagram approach.

See Also

Other Credible interval: Credible_interval()

Gelman Rubin statistics.

Description

Check Markov chains for convergence.

Usage

Rhat(M, burn.in = 0.5)

Arguments

Value

Gelman Rubin statistics.

References

Gelman A.,Carlin J.B.,Stern H.S.,and Rubin D.B.(2004),Bayesian Data Analysis,Boca Raton,FL:Chapman&Hall/CRC.

Binomial function

Description

Binomial function

Usage

bin(n, i, x)

Arguments

Examples

bin(5,3,.5)

Generated data

Description

Generated data

Usage

gen_data(ages, years, FT, M)

Arguments

Scale to [0,1]

Description

Scale to [0,1]

Usage

scale_to_01(x)

Arguments

Examples

scale_to_01(35:85)
(35:85-35)/(85-35)
scale_to_01(runif(10))

Generate simulated data 1

Description

Given rate function 1 generated data.

Usage

data(simulated_data_1)

Format

list of matrix

Examples

ages <- 35:85
years <- 1988:2007
FT1 <- function(x,y){0.00148*sin(0.5*pi*x*y)+0.00002}
simulated_data_1 <- gen_data(ages,years,FT1,M)

Generate simulated data 2

Description

Given rate function 2 generated data.

Usage

data(simulated_data_2)

Format

list of matrix

Examples

ages <- 35:85
years <- 1988:2007
FT2 <- function(x,y){0.00148*sin(0.5*pi*x*(y+0.2))+0.00002}
simulated_data_2 <- gen_data(ages,years,FT2,M)

Write xlsx file

Description

This function will write result of BP2D to xlsx file.

Usage

write.BP(writedata, filename)

Arguments

Write BPtalbe as xlsx file

Description

If your environment has some result of BP2D,then you can use this function to store BPTable.

Usage

write.BPtable(BPtable, filename)

Arguments