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In regression analysis, the Bayesian change-point problem is considered in terms of changing the mean of the response variable distribution. This can be done via changes in the functional form of the regression function. We consider linear versus nonlinear regression partitioned at the value of the predictor variable that is called the change�point. We assume that the nonlinear regression function is smooth. To represent this smooth function, we used a free knot cubic $B$-spline basis. Under continuity restrictions for given change-point and knot sequence, we build a linear model for which its design matrix is a function of the change-point and the knot sequence. A set of conjugate priors for the coefficient parameters and the model variance is considered. For the change-point and the knot sequence, we use a uniform prior. The reversible jump algorithm produces approximations to the estimates of the parameters as well as to the regression function. Inference on this model is illustrated and compa.red with Denison .pt a1. (2002) via. a set of simulated examples.
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