Electrochemical impedance spectroscopy (EIS) is a powerful electrochemical characterization technique used in scientific research and industry. Interpreting the EIS data correctly is the essential step to unravel the nature of the underlying physical processes happening inside the electrochemical system (e.g. Li-ion battery) and to obtain the quantitative values of the corresponding parameters (i.e. diffusion coefficients, reaction rate constants, etc.). The most common approach to interpret impedance data is by fitting to an equivalent circuit model (ECM). The problem of this approach is that many (ECMs) can fit the data well. In the past decade, the distribution of relaxation times (DRT) has appeared as a complementary methodology that enables better interpretation to the impedance data. In this method, the time scales of the underlying processes can be directly accessed, enabling the construction of the most relevant ECM. However, obtaining the DRT requires solving an ill-posed inverse problem that is sensitive to the noise level in the data and number of data points available. We tackled this issue by framing the DRT problem in a Bayesian statistical framework. Within this framework, we can introduce our experience regarding the EIS in the form of prior models and define the DRT as probability distribution function (pdf). We employed two prior models. The first one is implemented on the regularization parameter and we become able to detect the discontinuities in the DRT. This allows the recovery of various discontinuous elements including the Gerischer impedance. The second prior model focuses on the weights which we can assign to each individual data point. This allows the detection of outliers in the EIS data. We can also sample the DRT from its pdf given the data and the hypotheses on the regularization parameter and weights. By applying this framework to synthetic experiments and real EIS data of Li-ion battery, we show that we can obtain far more insight about the analysis of the EIS data, typically needed by the EIS practitioner.