Changepoints (CP)s are abrupt variations in time-series data, where the distribution of the data changes. Detecting CPs has many applications, and it is essential for modeling and predicting time-series data. Changepoint detection (CPD) is used in various fields such as medical condition monitoring, climate change detection, speech recognition, image analysis, human activity analysis, telecommunications, etc. This thesis is interested in using CPD for key performance indicator (KPI) time-series 4G/5G data in telecommunications. Many methods are available for CPD. Nevertheless, in lack of ground truth, computing the uncertainty of the detected CPs is essential, so we are interested in Bayesian CPD. We propose and implement a recursive Bayesian CPD algorithm to detect the number and locations of CPs. Moreover, by drawing from the posterior of the number and locations of CPs, inference about the probability of each point being a CP and the uncertainty associated with each location is made. Using this algorithm, we achieve the three most important objectives of this study; first, detect the number of CPs and their probabilities. Second, find the locations of CPs and make inferences about their probabilities, and third, estimate the uncertainty associated with the inference. We decompose the data into seasonal and trend components. The algorithm shows a promising performance when applied to the trend model, where the number of parameters is low. However, as the parameter space expands, which is the case for the seasonal model, the performance of the algorithm degrades. Therefore, we suggest using other methods such as approximation methods, variable selection, or/and iterative Markov chain Monte Carlo (MCMC) sampling with the recursive BayesianCPD algorithm.