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We present an exact Bayesian treatment of a simple, yet sufficiently general probability distribution model. We consider piecewise-constant distributions ( ) with uniform (second-order) prior over location of discontinuity points and assigned chances. The predictive distribution and the model complexity can be determined completely from the data in a computational time that is linear in the number of degrees of freedom and quadratic in the number of possible values of . Furthermore, exactdoi:10.1109/tit.2005.856954 fatcat:3xr44pzdjbfwzn33lfbvrwapna