FABADA (Fully Adaptive Bayesian Algorithm for Data Analysis) performs non-parametric noise reduction using Bayesian inference. It iteratively evaluates possible smoothed models of the data to estimate the underlying signal that is statistically compatible with the noisy measurements. Iterations stop based on the evidence E and the χ² statistic of the last smooth model, and the expected value of the signal is computed as a weighted average of the smooth models. Though FABADA was written for astronomical data, such as spectra (1D) or images (2D), it can be used as a general noise reduction algorithm for any one- or two-dimensional data; the only requisite of the input data is an estimation of its associated variance.