A Comparison of Bayesian Monte Carlo Markov Chain and Maximum Likelihood Estimation Methods for the Statistical Analysis of Geodetic Time Series

One of the objectives of TIGA is to compute precise station coordinates and velocities for GPS stations of interest. Consequently, a comprehensive knowledge of the stochastic features of the GPS time series noise is crucial, as it affects the velocity estimation for each GPS station. For that, we present a Monte Carlo Markov Chain (MCMC) method to simultaneously estimate the velocities and the stochastic parameters of the noise in GPS time series. This method allows to get a sample of the likelihood function and thereby, using Monte Carlo integration, all parameters and their uncertainties are estimated simultaneously. We propose this method as an alternative to optimization methods, such as the Maximum Likelihood Estimator (MLE) method implemented in the widely used CATS software, whenever the likelihood and the parameters of the noise are to be estimated in order to obtain more robust uncertainties for all parameters involved. Furthermore, we assess the MCMC method through comparison with the widely used CATS software using daily height time series from the Jet Propulsion Laboratory.