Time series have traditionally been analyzed under the assumption of stationarity. Such an assumption is often unreasonable, particularly for time series observed over longer time periods, where the concept of local stationarity is a better fit. This project develops a fully Bayesian approach to local stationary processes in the spectral domain, using recently develop shrinkage prior processes. The posterior distribution is analyzed by Gibbs sampling. The compute resources at NAISS will be used to run experiments on simulated data over a range of different data-generating processes.