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## Bayesian Experimental Design: A Review (1995)

Venue: | Statistical Science |

Citations: | 304 - 1 self |

### Citations

1829 |
Statistical Decision Theory and Bayesian Analysis
- Berger
- 2010
(Show Context)
Citation Context ...roximation is: `jy; jsN( `; [R + nI( `; j)] \Gamma1 ) (13) where ` now denotes the mode of the joint posterior distribution of ` (also called the gener27 alized maximum likelihood estimate of ` as in =-=Berger, 1985-=-, p.133), and R is the matrix of second derivatives of the logarithm of the prior density function, or the precision matrix of the prior distribution. Several other approximations are possible, for ex... |

1119 |
Optimal Statistical Decisions
- DeGroot
- 1970
(Show Context)
Citation Context ...variate t distributions. Denote by t ffi [m; ; \Sigma] the probability distribution of an m-variate t random variable with ffi degrees of freedom, mean vectorsand scale matrix \Sigma (see for example =-=DeGroot 1970-=-, sec 5.6 or Box and Tiao 1973 page 117). Recall that ` = (nM(j) +R) \Gamma1 (X T y + R` 0 ). Let h(j; y) denote the quantity (2ff+n) \Gamma1 n (y \Gamma X` 0 ) T h I \Gamma X(nM(j) +R) \Gamma1 X T i ... |

719 |
Bayesian Inference in Statistical Analysis
- Box, Tiao
- 1992
(Show Context)
Citation Context ...Denote by t ffi [m; ; \Sigma] the probability distribution of an m-variate t random variable with ffi degrees of freedom, mean vectorsand scale matrix \Sigma (see for example DeGroot 1970, sec 5.6 or =-=Box and Tiao 1973-=- page 117). Recall that ` = (nM(j) +R) \Gamma1 (X T y + R` 0 ). Let h(j; y) denote the quantity (2ff+n) \Gamma1 n (y \Gamma X` 0 ) T h I \Gamma X(nM(j) +R) \Gamma1 X T i (y \Gamma X` 0 ) + 2fi o and l... |

539 | Theory of Optimal Experiments - Fedorov - 1972 |

316 | Bandit problems: sequential allocation of experiments - Berry, Fristedt - 1985 |

314 | Optimum Experimental Designs - Atkinson, Donev - 1992 |

155 | Bayesian Prediction of Deterministic Functions, With Applications to the Design and Analysis of Computer Experiments - Currin, Mitchell, et al. - 1991 |

123 | Predictive Inference: An Introduction - Geisser - 1993 |

108 |
A basis for the selection of a response surface design
- Box, Draper
- 1959
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Citation Context ...usual, a linear approximation to some smooth but unknown surface, then it is at the boundary of this region that the approximation is most inaccurate. 53 These criticisms are not new (see for example =-=Box and Draper, 1959-=-, Sacks and Ylvisaker, 1984, 1985) and apply to both Bayesian and non-Bayesian optimal design for linear models. As discussed in Section 5.2 these criticisms sometimes do not apply to Bayesian optimal... |

107 |
Expected Information as Expected Utility
- Bernardo
- 1979
(Show Context)
Citation Context ...ion. When inference about the parameters is the main goal of the analysis, for example, a utility function based on Shannon information leads to Bayesian D-optimality in the normal linear model (see, =-=Bernardo, 1979-=-). In addition, Shannon information can be used for prediction and in mixed utility functions that describe several simultaneous goals for an experiment. Bayesian equivalents of some other popular opt... |

102 | Locally optimal designs for estimating parameters - Chernoff - 1953 |

101 | Optimal Bayesian designs applied to logistic regression experiments - Chaloner, Larntz - 1989 |

59 |
Sequential Analysis and Optimal Design
- Chernoff
- 1972
(Show Context)
Citation Context ...r, as they do not allow for checking of the model after the experiment is performed. The bound also applies to most local optimality criteria and Bayesian criteria for linear models (see, for example =-=Chernoff, 1972-=-, p. 27 and Chaloner, 1984). In contrast for nonlinear models there is no such bound available on the number of support points. Although the criteria are concave on H, the space of probability measure... |

57 | Optimum allocation in linear regression theory - Elfving - 1952 |

56 | Experimental design and observation for large systems - Bates, Buck, et al. - 1996 |

46 | A Simple Bayesian Modification of DOptimal Designs to Reduce Dependence on an Assumed Model - Dumouchel, Jones - 1994 |

46 | The use of canonical form in the construction of locally optimum designs for nonlinear problems - Ford, Torsney, et al. - 1992 |

45 | Recent advances it! nonlinear experimental design - Ford, Kitsos, et al. - 1989 |

33 | Optimum experimental designs for properties of a compartmental model - Atkinson, Chaloner, et al. - 1993 |

32 | A squentially constructed design for estimating a nonlinear parametric function - FORD, SILVEY - 1980 |

26 | Optimal Bayesian experimental design for linear models - Chaloner - 1984 |

18 | Bayesian D-optimal designs for exponential regression models - Dette, Neugebauer - 1997 |

17 | A note on optimal Bayesian design for nonlinear problems - Chaloner - 1993 |

15 | Bayesian design for estimating the turning point of a quadratic regression - Chaloner - 1989 |

15 | A quadratic design criterion for precise estimation in nonlinear regression models - Hamilton, Watts - 1985 |

14 | Bayesian estimation and optimal designs in partially accelerated life testing - Degroot, Goel - 1979 |

14 |
Optimal Experimental Design for Another’s Analysis
- Etzioni, Kadane
- 1993
(Show Context)
Citation Context ...cess and an informative p(`) will be used to average over in the integral. This echoes the idea given in Tsutakawa (1972) of using different prior distributions for design and for analysis. (See also =-=Etzione and Kadane, 1993-=-). ffl for similar reasons these criteria are appealing in a non-Bayesian framework where it is accepted that prior information must be used in design but should not be used in the analysis. Indeed th... |

14 | A geometric approach to optimal design for one-parameter non-linear models - Haines - 1995 |

13 | Design of experiments for parameter estimation in multiresponse situations - DRAPER, HUNTER - 1966 |

13 | Inference and sequential design - Ford, Titterington, et al. - 1985 |

13 | Optimal designs for rational models - He, Studden, et al. - 1996 |

12 | Studies on the estimation of variance components - Anderson - 1978 |

12 | Quantifying expert opinion in linear regression problems - Garthwaite, Dickey - 1988 |

11 | A note on Bayesian c- and D-optimal designs in nonlinear regression models - Dette - 1996 |

11 | Convex design theory - Fedorov - 1980 |

11 | Optimal Bayesian sequential estimation of the median effective dose - Freeman |

10 | An object-oriented system for Bayesian nonlinear design using XLISP-STAT - Clyde - 1993 |

8 | Bayesian Design for Accelerated Life Testing - Chaloner, Larntz - 1992 |

8 | Review of optimal Bayes designs - DasGupta - 1996 |

8 | The Use of Prior Distributions in the Design of Experiments for Parameter Estimation in Nonl i nea r Si t ua t i ons - Draper, ter |

8 | A clinical experiment in bone marrow transplantation: estimating a percentage point of a quantal response curve - Flournoy - 1993 |

7 |
Planning experiments to detect inadequate regression models
- Atkinson
- 1972
(Show Context)
Citation Context ...se prior information, this criterion is the same as non-Bayesian D-optimality for testing the hypothesis ` 0 = 0, where ` 0 is the subvector of extra parameters in the larger model (see, for example, =-=Atkinson 1972-=-). For the dual purpose of model discrimination and parameter estimation for two nested normal linear models, Spezzaferri showed that the optimality criterion using utility (5) is given by the product... |

7 |
A Decision Theory Approach to Optimal Regression Design
- Brooks
- 1972
(Show Context)
Citation Context ...ian Alphabetical Optimality: Related Work. In the 1970's Lindley's work had a profound influence on many aspects of Bayesian statistics. In the area of experimental design, a set of papers by Brooks (=-=Brooks 1972-=-, 1974, 1976, 1977) were inspired by work of Lindley's on the choice of variables in multiple regression (Lindley 1968). Brooks followed Lindley's approach to motivate the problem of choosing the best... |

7 | Model robust, linear-optimal designs - Cook, Nachtsheim - 1982 |

6 | Optimal designs for the ratios of linear combinations in the general linear model - Buonaccorsi, Iyer - 1986 |

6 | Bayesian optimal designs for approximate normality - Clyde - 1993 |

6 | Incorporating prior parameter uncertainty in the design of sampling schedules for pharmacokinetic parameter estimation experiments - D’Argenio - 1990 |

6 | Bayesian optimal one point designs for one parameter nonlinear models - Dette, Neugebauer - 1996 |

6 | A predictive approach to the Bayesian design problem with application to normal regression models - Eaton, Giovagnoli, et al. - 1996 |

5 | Biased coin designs with a Bayesian bias - Ball, Smith, et al. - 1993 |

5 | On the Loss of Information through Censoring - Brooks - 1982 |

5 | Optimal accelerated life designs for estimation - Chernoff - 1962 |

5 | A note on Bayesian D-optimal designs for a generalization of the exponential growth model - Dette, Sperlich - 1994 |

5 | Optimal designs for polynomial regression when the degree is not known - Dette, Studden - 1995 |

5 | Computer augmentation of experimental designs to maximize |X - Evans - 1979 |

5 | Optimal data augmentation strategies for additive models - Heiberger, Bhaumik, et al. - 1993 |

4 | Experimental design for drug development: a Bayesian approach - Berry - 1991 |

4 | A comparison of confidence regions and designs in estimation of a ratio - Buonaccorsi, Iyer - 1984 |

4 | Compromise designs in heteroscedastic linear models - Dasgupta, Mukhopadhyay, et al. - 1992 |

4 | Elfving’s theorem for D-optimality - Dette - 1993 |

4 |
Construction of optimal designs in random coefficient regression models. Mathematische Operationsforschung und Statistik
- Gladitz, Pilz
- 1982
(Show Context)
Citation Context ...y easy but, as is shown in Section 2.5, algebraically hard. Pilz dealt with Bayes experimental designs for a linear model in a series of papers (Pilz 1979a, b, c, d, 1981a, b, c Nather and Pilz 1980, =-=Gladitz and Pilz 1982-=-a, b, Bandemer, Nather and Pilz 1987). See also the monograph, Pilz (1983) and the revised reprint of the monograph, Pilz (1991). His approach is very general, with no distributional assumptions for t... |

3 | On the choice of an experiment for prediction in linear regression - Brooks - 1974 |

3 | Optimal regression design for control in linear regression - Brooks - 1977 |

3 | Ratios of linear combinations in the general linear model - Buonaccorsi - 1985 |

3 | Design of experiments for parameter estimation involving uncertain systems, with application to pharmacokinetics - D’Argenio, Guilder - 1988 |

3 | Uniform and subuniform posterior robustness: the sample size problem - DasGupta, Mukhopadhyay - 1994 |

3 | Robust Bayes designs in normal linear models - DasGupta, Studden - 1994 |

3 | Concepts of information based on utility - DEGROOT, H - 1986 |

3 | Anote on robust designs for polynomial regression - Dette - 1991 |

3 | D-optimal designs for non-linear models under the Bayesian approach, Regression Experiments - Dubov - 1977 |

3 | Bayesian optimal designs for linear regression models. The Annals of Statist - El-Krunz, Studden - 1991 |

2 | Use of Bayesian analysis to design of clinical trials with one treatment - Achcar - 1984 |

2 | Choice of Response Surface Design and Alphabetic Optimality
- Box
- 1982
(Show Context)
Citation Context ... used. The choice of a utility (or loss) function expresses various reasons for carrying out an experiment. In the linear model, the analogs of widely known non-Bayesian alphabetical design criteria (=-=Box, 1982-=-) such as A-optimality, D-optimality and others can be given decision theoretic justification. When inference about the parameters is the main goal of the analysis, for example, a utility function bas... |

2 | Optimal regression designs for prediction when prior knowledge is available - Brooks - 1976 |

2 | An approach to design for generalized linear models - Chaloner |

2 | Software for logistic regression experiment design - CHALONER, andLARNTZ - 1988 |

2 | Does it make sense to speak of "Good Probabiity Appraisers?" The Scientist Speculates - Finetti - 1962 |

2 | Bayesian design and analysis of accelerated life testing with step stress. Accelerated Life Testing and Experts - DeGroot, Goel - 1988 |

2 | A mean squared error approach to Optimal Design Theory - Duncan, DeGroot - 1976 |

2 |
Bayes designs for multiple linear regression on the unit sphere
- Gladitz, Pilz
- 1982
(Show Context)
Citation Context ...y easy but, as is shown in Section 2.5, algebraically hard. Pilz dealt with Bayes experimental designs for a linear model in a series of papers (Pilz 1979a, b, c, d, 1981a, b, c Nather and Pilz 1980, =-=Gladitz and Pilz 1982-=-a, b, Bandemer, Nather and Pilz 1987). See also the monograph, Pilz (1983) and the revised reprint of the monograph, Pilz (1991). His approach is very general, with no distributional assumptions for t... |

1 | ather and Pilz - Bandemer - 1987 |

1 | An application of influence diagrams. Accel. Life Testing and Experts - Barlow, Mensing, et al. - 1988 |

1 | Computing the optimal design for a calibration experiment - Barlow, Mensing, et al. - 1991 |

1 | On the design of comparative lifetime studies - Brooks - 1987 |

1 | Measuring information and uncertainty. Foundation of Statistical Inference - Buehler - 1971 |

1 | Accelerated life testing and experts' opinions in reliability - Clarotti, Lindley - 1988 |

1 | Optimal design for heart defibrillators. To appear in - Clyde, uller, et al. - 1994 |

1 | Optimal regression designs with previous observations - Covey-Crump, Silvey - 1970 |

1 | Sample sizes in ANOVA: The Bayesian point of view - DasGupta, Vidakovic - 1994 |

1 | A generalization of D\Gamma and D 1 -optimal designs in polynomial regression - Dette - 1990 |

1 | Some applications of continued fractions in the construction of optimal designs for nonlinear regression models - Dette, Sperlich - 1994 |

1 | The use of prior distributions in the design of experiments in non-linear situations - Draper, Hunter - 1967 |

1 | Power and sample size calculations - Dupont, Plummer - 1990 |

1 | The augmentation of experimental data to maximize jX - Dykstra - 1971 |

1 | Active regression experiments - Fedorov - 1981 |

1 | The optimum design of experiments in the presence of uncontrolled variability and prior information - Giovagnoli, Sebastiani - 1989 |

1 | Bayes D-Optimal and E-Optimal Block Designs - Giovagnoli, Verdinelli - 1983 |

1 | Optimal Block Designs under a Hierarchical Linear Model - Giovagnoli, Verdinelli - 1985 |

1 | Comment on Verdinelli - Goldstein - 1992 |

1 | A remark on the optimal regression designs with previous observations of Covey-Crump and Silvey - Guttman - 1971 |