# Gibbs sampler for multivaiate Bayesian nonparametric inference with Whittle likelihood Obtain samples of the posterior of the multivariate Whittle likelihood in conjunction with an Hpd AGamma process prior on the spectral density matrix. ```r gibbs_vnp( data, Ntotal, burnin, thin = 1, print_interval = 100, numerical_thresh = 1e-07, adaption.N = burnin, adaption.batchSize = 50, adaption.tar = 0.44, eta = ncol(data), omega = ncol(data), Sigma = 10000 * diag(ncol(data)), k.theta = 0.01, kmax = 100 * coars + 500 * (!coars), trunc_l = 0.1, trunc_r = 0.9, coars = F, L = max(20, length(data)^(1/3)) ) ``` ## Arguments - `data`: numeric matrix; NA values are interpreted as missing values and treated as random - `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 eigenvalues of the spectral density - `adaption.N`: total number of iterations, in which the proposal variances (of r and U) are adapted - `adaption.batchSize`: batch size of proposal adaption - `adaption.tar`: target acceptance rate for adapted parameters - `eta`: AGamma process parameter, real number > ncol(data)-1 - `omega`: AGamma process parameter, positive constant - `Sigma`: AGamma process parameter, Hpd matrix - `k.theta`: prior parameter for polynomial degree k (propto exp(-k.theta*k*log(k))) - `kmax`: upper bound for polynomial degree of Bernstein-Dirichlet mixture (can be set to Inf, algorithm is faster with kmax

gibbs_vnp function