Bayesian criteria for discriminating among regression models with one possible change point |
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| Institution: | 1. State Key Laboratory of Environmental Criteria and Risk Assessment, State Environmental Protection Key Laboratory of Ecological Effect and Risk Assessment of Chemicals, Chinese Research Academy of Environmental Sciences, Beijing 100012, China;2. State Environmental Protection Key Laboratory of Drinking Water Source Management and Technology, Shenzhen Key Laboratory of Emerging Contaminants Detection and Control in Water Environment, Guangdong Engineering Research Center of Low Energy Sewage Treatment, Shenzhen Academy of Environmental Sciences, Shenzhen 518001, China;3. School of Medicine, Jinan University, Guangzhou 510632, China;4. Guangdong Provincial Institute of Public Health, Guangdong Provincial Center for Disease Control and Prevention, Guangzhou 511430, China;5. Guangdong Provincial Center for Disease Control and Prevention, Guangzhou 511430, China |
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| Abstract: | The change-point problem for normal regression models is considered here as the problem of choosing the hypothesis H0 of no change or one of the hypotheses Hi that one or more parameters change after the ith observation. The observations are often associated with a known increasing sequence τi (for example, τi is the date of the ith observation). It then seems natural to introduce a quadratic loss function involving (τi − τj)2 for selecting Hi instead of the true hypothesis Hj. A Bayes optimal invariant procedure is derived within such a framework and compared to previous proposals. When H0 is rejected, large errors may arise in the estimation of the change point. To get around this difficulty another procedure is introduced whose main feature is to select one of the Hi's when H0 is rejected only if there is sufficient evidence in favour of this choice. |
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