论文信息 - Parameter Neutral Optimum Design for Non‐linear Models

Parameter Neutral Optimum Design for Non‐linear Models

Some Bayesian approaches to D-optimum design of experiments are considered from the viewpoint of invariance under reparameterization of the underlying statistical model. An invariant criterion is proposed which does not require the detailed specification of a prior, and which is shown to be equivalent to G-optimality under a Jeffreys prior. The methods are applied and discussed in the contexts of exponential decay and quantal response models.

John Hinde | David Firth | D. Firth | J. Hinde

[1] K. Chaloner,et al. Bayesian Experimental Design: A Review , 1995 .

[2] S. Lohr. Optimal Bayesian design of experiments for the one-way random effects model , 1995 .

[3] P. Laycock,et al. Optimum Experimental Designs , 1995 .

[4] Kathryn Chaloner,et al. A note on optimal Bayesian design for nonlinear problems , 1993 .

[5] Holger Dette,et al. A note on Bayesian D-optimal designs for a generalization of the exponential growth model , 1994 .

[6] Anthony C. Atkinson,et al. Optimum Experimental Designs , 1992 .

[7] K. Chaloner,et al. Optimal Bayesian design applied to logistic regression experiments , 1989 .

[8] L. White. An extension of the General Equivalence Theorem to nonlinear models , 1973 .

[9] Byron J. T. Morgan. Analysis of Quantal Response Data , 1992 .

[10] Linda M. Haines,et al. A Geometric Approach to Optimal Design for One‐Parameter Non‐Linear Models , 1995 .

[11] D. Lindley. On a Measure of the Information Provided by an Experiment , 1956 .

[12] H. Jeffreys. An invariant form for the prior probability in estimation problems , 1946, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[13] John Hinde,et al. On Bayesian D‐optimum Design Criteria and the Equivalence Theorem in Non‐linear Models , 1997 .

[14] K. Chaloner,et al. Optimum experimental designs for properties of a compartmental model. , 1993, Biometrics.