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Paper IPM / M / 11455  


Abstract:  
In regression analysis, the Bayesian changepoint 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 Bspline basis. Under continuity restrictions for given changepoint and knot sequence, we build a linear model for which its design matrix is a function of the changepoint and the knot sequence. A set of conjugate priors for the coefficient parameters and the model variance is considered. For the changepoint 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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