Abstract
Consider a sequence of independent observations which change their marginal distribution at most once somewhere in the sequence and one is not certain where the change has occurred. One would be interested in detecting the change and determining the two distributions which would describe the sequence. On the other hand if no change had occurred, one would want to know the common distribution of the observations. This study develops a Bayesian test for detecting a switch from one linear model to another. The test is based on the marginal posterior mass function of the switch point and the posterior probability of a stable model. This test and an informal sequential procedure of Smith are illustrated with data generated from an unstable linear regression model, which changes the linear relationship between the dependent and independent variables
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