# Gibbs sampler for Bayesian semiparametric inference with the corrected AR likelihood Obtain samples of the posterior of the corrected autoregressive likelihood in conjunction with a Bernstein-Dirichlet prior on the correction. ```r gibbs_npc( data, ar.order, Ntotal, burnin, thin = 1, print_interval = 100, numerical_thresh = 1e-07, adaption.N = burnin, adaption.batchSize = 50, adaption.tar = 0.44, full_lik = F, rho.alpha = rep(1, ar.order), rho.beta = rep(1, ar.order), eta = T, M = 1, g0.alpha = 1, g0.beta = 1, k.theta = 0.01, tau.alpha = 0.001, tau.beta = 0.001, trunc_l = 0.1, trunc_r = 0.9, coars = F, kmax = 100 * coars + 500 * (!coars), L = max(20, length(data)^(1/3)) ) ``` ## Arguments - `data`: numeric vector; NA values are interpreted as missing values and treated as random - `ar.order`: order of the autoregressive model (integer > 0) - `Ntotal`: total number of iterations to run the Markov chain - `burnin`: number of initial iterations to be discarded - `thin`: thinning number (postprocessing) - `print_interval`: Number of iterations, after which a status is printed to console - `numerical_thresh`: Lower (numerical pointwise) bound for the spectral density - `adaption.N`: total number of iterations, in which the proposal variances (of rho) are adapted - `adaption.batchSize`: batch size of proposal adaption for the rho_i's (PACF) - `adaption.tar`: target acceptance rate for the rho_i's (PACF) - `full_lik`: logical; if TRUE, the full likelihood for all observations is used; if FALSE, the partial likelihood for the last n-p observations - `rho.alpha, rho.beta`: prior parameters for the rho_i's: 2*(rho-0.5)~Beta(rho.alpha,rho.beta), default is Uniform(-1,1) - `eta`: logical variable indicating whether the model confidence eta should be included in the inference (eta=T) or fixed to 1 (eta=F) - `M`: DP base measure constant (> 0) - `g0.alpha, g0.beta`: parameters of Beta base measure of DP - `k.theta`: prior parameter for polynomial degree k (propto exp(-k.theta*k*log(k))) - `tau.alpha, tau.beta`: prior parameters for tau (inverse gamma) - `trunc_l, trunc_r`: left and right truncation of Bernstein polynomial basis functions, 0<=trunc_l S. Ghosal and A. van der Vaart (2017) **Fundamentals of Nonparametric Bayesian Inference** O. Barndorff-Nielsen and G. Schou On the parametrization of autoregressive models by partial autocorrelations Journal of Multivariate Analysis (3),408-419

gibbs_npc function