Albeit LCDM's fame as the concordance model, there are many interesting mysteries worth exploring, such as the nature of dark energy. Here, we test the viability of several classes of scenarios of the dark sector with linear and non-linear interacting terms. To do so, we use a Bayesian model selection with data from type Ia supernovae, cosmic chronometers, cosmic microwave background and two sets of baryon acoustic oscillations measurements: 2-dimensional angular measurements (BAO2), and 3-dimensional angle-averaged measurements (BAO3). On the other hand, we consider covariance matrices, which are important tools for parameter estimation. We explore ways of compressing them by analysing their eigenvalues and signal-to-noise ratio, by employing a tomographic compression and, lastly, with the Massively Optimized Parameter Estimation and Data compression (MOPED). We find that MOPED is a powerful tool in the comparison of covariance matrices and, towards that end, we build a python code that uses a fast Monte Carlo simulation to obtain comprehensible values for differences between two covariance matrices. This method thus eliminates the need for a full cosmological analysis as we relate its output to the corresponding parameter constraints.