Stats4Grads: Bayes linear kinematics in the design of experiments
26 May 2010 14:15 in CM221
The choice of the design of an experiment, including both selection of
design points and choice of sample size, can be viewed as a decision
problem. We wish to choose the design which maximises the prior
expectation of a utility function which depends on both costs of the
experiment and benefits from the information gained. The latter
may be realised through a second decision to be made after the experiment.
Solving the problem requires the evaluation of this expectation for each
candidate design involving summation or integration over all possible
outcomes for each design. With non-Gaussian models, where posterior
evaluations would typically involve intensive numerical methods such as
Markov Chain Monte Carlo, evaluation of the conditional expectation of the
utility, given an outcome, becomes computationally demanding and so
solving such design problems becomes difficult for all but fairly simple
Bayes linear kinematics (Goldstein and Shaw, 2004) offers an alternative
approach. It gives a method for propagating changes in belief about some
quantities through to others within a Bayes linear structure, for example
when the changes result from observing related non-Gaussian variables. We
adopt a conjugate relationship between observables and parameters and then
update beliefs about other quantities using Bayes linear kinematics.
Applying this approach to the design problem greatly reduces the
computational burden and the problem can be solved without the need for
intensive numerical methods. The method is illustrated using two examples.
See the Stats4Grads page for more details about this series.