D. V. Lindley. Bayesian statistics--a review. SIAM, Philadelphia, 1972.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....contained in p e (Y #) The primary goal(s) or terminal decision(s) of an experiment may include, but are not limited to, estimating # or other quantities of interest that are functions of #, predicting future observations, selecting among competing models, or testing other hypotheses. Lindley (1972) presented a two part decision theoretic approach to experimental design, which provides a unifying theory for most work in Bayesian experimental design today. Lindley s approach involves specification of a suitable utility function reflecting the purpose and costs of the experiment; the best ....

....e # which maximizes U(e) U(e # ) max e ## max d # # U(d, #, e, Y ) p(# y, e) p(y e)d#dY. 3) This general formulation can be used to find optimal designs for a single exper 6 iment, and can be extended to optimal selection of a sequence of experiments and sequential decision making (Lindley, 1972). 3 Choice of Utility Functions It is important that utility functions be tailored to the goals of a given problem. Optimal designs for discriminating between two di#erent models may be quite di#erent than designs for prediction. In a one way analysis of variance model, the best design for ....

Lindley, D. V., 1972. Bayesian Statistics -- A Review. SIAM (Philadelphia).

....strongly interrelated (and of course, with connections to the above issues) They are identifiability, propriety and parametrization. In particular, the models we address are overparametrized generalized linear mixed models (GLMM s) which we argue are generally not identifiable. The remark of Lindley (1971, p.46) In passing it might be noted that unidentifiability causes no real difficulty in the Bayesian approach recognizes that a Bayesian analysis, in theory, is always possible by assigning proper priors for the model unknowns. However, the formal notion of Bayesian identifiability from Dawid ....

Lindley, D. V. (1971) Bayesian Statistics: A Review (SIAM).

....focus here on parameter identifiability and posterior propriety. In particular, the models we address are generalized linear models, in particular those introducing random effects referred to as generalized linear mixed models (GLMM s) which we argue are generally not identifiable. The remark of Lindley (1971, p.46) In passing it might be noted that unidentifiability causes no real difficulty in the Bayesian approach recognizes that a Bayesian analysis, in theory, is always possible by assigning proper priors for the model unknowns. However, the formal notion of Bayesian identifiability from Dawid ....

Lindley, D. V. (1971) Bayesian Statistics: A Review (SIAM).

....Since the data y depends on the parameter ( ff; fi; fl) only through and the map from ( ff; fi; fl) to is not one to one, ff; fi; fl) is not identified. In principle, lack of identifiability in the likelihood poses no problem to the Bayesian provided the prior distribution is proper (Lindley, 1971 page 46, Lindley Smith, 1972) although in such a situation inference may be very sensitive to prior assumptions. In practice, Markov chain Monte Carlo sampling of the resulting posterior faces slow convergence problems: on contours of constant likelihood the posterior is proportional to the ....

Lindley, D. V. (1971). Bayesian Statistics: a review. Philadelphia: SIAM.

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D. V. Lindley. Bayesian statistics--a review. SIAM, Philadelphia, 1972.

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Lindley, D. V. (1972). Bayesian Statistics --- A Review. SIAM, Philadelphia.

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