Likelihood and bayesian approaches to inference for the stationary point of a quadratic response surface |
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Authors: | Valeria Sambucini Ludovico Piccinato |
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Institution: | Dipartimento di Statistica, Probabilité e Statisliche Applicate Université “La Sapienza ”, LT‐00185 Roma, Italy |
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Abstract: | In response surface analysis, a second order polynomial model is often used for inference on the stationary point of the response function. The standard confidence regions for the stationary point are due to Box & Hunter (1954). The authors propose an alternative parametrization, in which the stationary point is the parameter of interest; likelihood techniques and Bayesian analysis are then easier to perform. The authors also suggest an approximate method to get highest posterior density regions for the maximum point (not simply for the stationary point). Furthermore, they study the coverage probabilities of these Bayesian regions through simulations. |
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Keywords: | Bayesian analysis confidence region highest posterior density region integrated likelihood Markov chain Monte Carlo simulation profile likelihood response surface methodology ro‐tatability |
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