# Bayesian estimation using two dimensions Bernstein polynomial 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. ```r 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. ## Returns 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. ## Examples ```r # ---------------------------------------- # 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') # ---------------------------------------- # ``` ## 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()`

BP2D function