### Bayesian nonparametric estimation of the spectral density of a long memory Gaussian time series

Let $mathbf {X}={X_t, t=1,2,… }$ be a stationary Gaussian random process, with mean $EX_t=mu$ and covariance function $gamma( au)=E(X_t-mu)(X_{t+ au}-mu)$. Let $f(lambda)$ be the corresponding