This paper presents a Bayesian unfolding method for experimental distributions. The method is based on Bayes' Theorem and is recognized by statisticians as the most powerful tool for statistical inference. The main advantages of this method over other unfolding methods are: it is theoretically well grounded; it can be applied to multidimensional problems; it can use cells of different sizes for the distribution of the true and experimental values; the domain of definition of the experimental values can differ from that of the true values; it can take into account any kind of smearing and migration from the true values to the observed ones; it gives the best results if one makes a realistic guess about the distribution that the true values follow, but, in case of total ignorance, satisfactory results are obtained even starting from a uniform distribution; it can take different sources of background into account; it does not require matrix inversion; it provides the correlation matrix of the results; and it can be implemented in a short, simple and fast program, which deals directly with distributions and not with individual events. The method is based on Bayes' Theorem, which allows one to calculate the probability of a cause given an effect. The method is applied to experimental distributions by considering the true and measured quantities as separate variables. The method is able to handle multidimensional problems and can use cells of different sizes for the distribution of the true and experimental values. The method is also able to take into account any kind of smearing and migration from the true values to the observed ones. The method is able to provide the correlation matrix of the results and can be implemented in a short, simple and fast program, which deals directly with distributions and not with individual events. The method is tested on several examples, including the unfolding of distributions not affected by statistical fluctuations and the unfolding of distributions with limited statistics. The results show that the method is able to recover the true distribution after a few iterations and that the results are stable with respect to variations of the initial probabilities and of the smoothing procedures. The method is also able to provide the covariance matrix of the result, which takes into account the uncertainties due to the limited Monte Carlo statistics used to evaluate the smearing matrix. The method is able to provide the standard deviations of the results, which are close to those calculated from the dispersion of the data around the mean value. The method is also able to provide the correlation matrix of the results, which is used to assess the quality of the unfolding. The method is able to handle background and can be applied to multidimensional problems. The method is able to provide the best results if one makes a realistic guess about the distribution that the true values follow, but, in case of total ignorance, satisfactory results are obtained even starting from a uniform distribution. The method is able to take into account any kind of smearing and migration from the true values to the observed ones. The method is able to provide the correlation matrix of the results and can be implemented in a short, simpleThis paper presents a Bayesian unfolding method for experimental distributions. The method is based on Bayes' Theorem and is recognized by statisticians as the most powerful tool for statistical inference. The main advantages of this method over other unfolding methods are: it is theoretically well grounded; it can be applied to multidimensional problems; it can use cells of different sizes for the distribution of the true and experimental values; the domain of definition of the experimental values can differ from that of the true values; it can take into account any kind of smearing and migration from the true values to the observed ones; it gives the best results if one makes a realistic guess about the distribution that the true values follow, but, in case of total ignorance, satisfactory results are obtained even starting from a uniform distribution; it can take different sources of background into account; it does not require matrix inversion; it provides the correlation matrix of the results; and it can be implemented in a short, simple and fast program, which deals directly with distributions and not with individual events. The method is based on Bayes' Theorem, which allows one to calculate the probability of a cause given an effect. The method is applied to experimental distributions by considering the true and measured quantities as separate variables. The method is able to handle multidimensional problems and can use cells of different sizes for the distribution of the true and experimental values. The method is also able to take into account any kind of smearing and migration from the true values to the observed ones. The method is able to provide the correlation matrix of the results and can be implemented in a short, simple and fast program, which deals directly with distributions and not with individual events. The method is tested on several examples, including the unfolding of distributions not affected by statistical fluctuations and the unfolding of distributions with limited statistics. The results show that the method is able to recover the true distribution after a few iterations and that the results are stable with respect to variations of the initial probabilities and of the smoothing procedures. The method is also able to provide the covariance matrix of the result, which takes into account the uncertainties due to the limited Monte Carlo statistics used to evaluate the smearing matrix. The method is able to provide the standard deviations of the results, which are close to those calculated from the dispersion of the data around the mean value. The method is also able to provide the correlation matrix of the results, which is used to assess the quality of the unfolding. The method is able to handle background and can be applied to multidimensional problems. The method is able to provide the best results if one makes a realistic guess about the distribution that the true values follow, but, in case of total ignorance, satisfactory results are obtained even starting from a uniform distribution. The method is able to take into account any kind of smearing and migration from the true values to the observed ones. The method is able to provide the correlation matrix of the results and can be implemented in a short, simple