# BDP-DW method: performing posterior sampling and calculating statistics based on the posterior samples ```r gibbs_bdp_dw( data, m, likelihood_thinning = 1, monitor = TRUE, print_interval = 100, unif_CR = FALSE, rescaled_time, freq, Ntotal = 110000, burnin = 60000, thin = 10, adaptive.batchSize = 50, adaptive.targetAcceptanceRate = 0.44, M = 1, g0.alpha = 1, g0.beta = 1, k1.theta = 0.01, k2.theta = 0.01, tau.alpha = 0.001, tau.beta = 0.001, k1max = 100, k2max = 100, L = 10, bernstein1_l = 0.1, bernstein1_r = 0.9, bernstein2_l = 0.1, bernstein2_r = 0.9 ) ``` ## Arguments - `data`: time series that needs to be analyzed - `m`: window size needed to calculate moving periodogram. - `likelihood_thinning`: the thinning factor of the dynamic Whittle likelihood. - `monitor`: a Boolean value (default TRUE) indicating whether to display the real-time status - `print_interval`: If monitor = TRUE, then this value indicates number of iterations after which a status is printed to console; If monitor = FALSE, it does not have any effect - `unif_CR`: a Boolean value (default FALSE) indicating whether to calculate the uniform credible region - `rescaled_time, freq`: a set of grid lines in $[0,1]$ and $[0,\pi]$, respectively, specifying where to evaluate the estimated tv-PSD - `Ntotal`: total number of iterations to run the Markov chain - `burnin`: number of initial iterations to be discarded - `thin`: thinning number (for post-processing of the posterior sample) - `adaptive.batchSize`: the batch size for the adaptive MCMC algorithm for sampling tau - `adaptive.targetAcceptanceRate`: the target acceptance rate for the adaptive MCMC algorithm for sampling tau - `M`: DP base measure constant (> 0) - `g0.alpha, g0.beta`: parameters of Beta base measure of DP - `k1.theta`: prior parameter for polynomial corresponding to rescaled time (propto exp(-k1.theta*k1*log(k1))) - `k2.theta`: prior parameter for polynomial corresponding to rescaled frequency (propto exp(-k2.theta*k2*log(k2))) - `tau.alpha, tau.beta`: prior parameters for tau (inverse gamma) - `k1max`: upper bound of the degrees of Bernstein polynomial corresponding to rescaled time (for pre-computation of basis functions) - `k2max`: upper bound of the degrees of Bernstein polynomial corresponding to rescaled frequency (for pre-computation of basis functions) - `L`: truncation parameter of DP in stick breaking representation - `bernstein1_l, bernstein1_r`: left and right truncation of Bernstein polynomial basis functions for rescaled time, 0<=bernstein1_l

gibbs_bdp_dw function