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Bayesian optimal design for changepoint problems |
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| Authors: | Juli Atherton Benoit Charbonneau David B. Wolfson Lawrence Joseph Xiaojie Zhou Alain C. Vandal |
| Affiliation: | 1. Department of Epidemiology, Biostatistics and Occupational Health, McGill University, Montréal, Québec, Canada H3A 1A2;2. Department of Mathematics, Duke University, Durham, NC 27708, USA;3. Department of Mathematics and Statistics, McGill University, Montréal, Québec, Canada H3A 2K6;4. Division of Clinical Epidemiology, McGill University Health Center, Montréal, Québec, Canada H3A 1A1;5. The Proctor & Gamble Company, Mason, OH 45040, USA;6. Center for Clinical Epidemiology and Community Studies, Sir Mortimer B. Davis Jewish General Hospital, Montréal, Québec H3T IE2 |
| Abstract: | We investigate Bayesian optimal designs for changepoint problems. We find robust optimal designs which allow for arbitrary distributions before and after the change, arbitrary prior densities on the parameters before and after the change, and any log‐concave prior density on the changepoint. We define a new design measure for Bayesian optimal design problems as a means of finding the optimal design. Our results apply to any design criterion function concave in the design measure. We illustrate our results by finding the optimal design in a problem motivated by a previous clinical trial. The Canadian Journal of Statistics 37: 495–513; 2009 © 2009 Statistical Society of Canada |
| Keywords: | Bayesian optimal design changepoint problems design measure estimation testing MSC 2000: Primary 62K05 secondary 62C10 |