BAYESIAN D-OPTIMAL DESIGNS FOR THE EXPONENTIAL-GROWTH MODEL

被引：27

作者：

MUKHOPADHYAY, S

HAINES, LM

机构：

[1] DUKE UNIV,INST STAT & DECIS SCI,DURHAM,NC 27708

[2] UNIV NATAL,NATAL,SOUTH AFRICA

来源：

JOURNAL OF STATISTICAL PLANNING AND INFERENCE | 1995年 / 44卷 / 03期

基金：

美国国家科学基金会;

关键词：

NONLINEAR REGRESSION; EXPONENTIAL GROWTH MODEL; D-OPTIMALITY; LOCALLY OPTIMAL DESIGNS; BAYESIAN DESIGN;

D O I：

10.1016/0378-3758(94)00056-2

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

Bayesian optimal designs for nonlinear regression models are of some interest and importance in the statistical literature. Numerical methods for their construction are well-established, but very few analytical studies have been reported. In this paper, we consider an exponential growth model used extensively in the modelling of simple organisms, and examine the explicit form of the Bayesian D-optimal designs. In particular, we show that D-theta-optimal designs for this model are balanced two-point designs for all values of the parameters. We further derive explicit expressions for Bayesian D-optimal designs which are based on exactly two points of support, and provide necessary and sufficient conditions for such designs to exist. We illustrate our results by means of two examples.

引用

页码：385 / 397

页数：13

共 24 条

[1]

Abdelbasit, Plackett, Experimental design for binary data, Journal of the American Statistical Association, 78, pp. 90-98, (1983)

[2]

Atkinson, Chaloner, Hertzberg, Juritz, Optimum experimental designs for properties of a compartmental model, Biometrics, 49, pp. 325-338, (1993)

[3]

Atkinson, Donev, Optimum Experimental Designs, (1992)

[4]

Bernardo, Expected information as expected utility, The Annals of Statistics, 7, pp. 686-690, (1979)

[5]

Chaloner, A note on optimal Bayesian design for nonlinear problems, J. Statist. Plann. Inference, 37, pp. 229-235, (1993)

[6]

Chaloner, Larntz, Optimal Bayesian design applied to logistic regression experiments, J. Statist. Plann. Inference, 21, pp. 191-208, (1989)

[7]

Chernoff, Locally optimal designs for estimating parameters, The Annals of Mathematical Statistics, 24, pp. 586-602, (1953)

[8]

Dette, Neugebauer, Bayesian D-optimal designs for exponential regression models, Technical Report, (1993)

[9]

Fedorov, Theory of Optimal Experiments, (1972)

[10]

Haines, Optimal design for inverse quadratic polynomials, South African Statist. J., 26, pp. 25-41, (1992)

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