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Biometrika 1966 53(3-4):477-495; doi:10.1093/biomet/53.3-4.477
© 1966 by Biometrika Trust
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Bayesian analysis of random-effect models in the analysis of variance

II. Effect of autocorrelated erros

GEORGE C. TIAO and W. Y. TAN

University of Wisconsin and Harvard Business School
Academia Sinica Taipei, Taiwan

Bayesian methods are utilized to analyse a one-way random effect model yij = µ+ai+eij in which the errors eij are assumed to follow a first-order autoregressive series eij = {rho}ei(j-1)+{varepsilon}ij. For given value of {rho}, the model can be reduced to that considered in our earlier paper (1965). It is shown that inferences about the variances = var(ai), and {sigma}2 = var ({varepsilon}ij) can be very sensitive to changes in the value of {rho} assumed. In particular, in a set of data generated from a population with {rho} = – 0·5, {sigma} = 1·5 and = 1, we find that if the independence assumption {rho} = 0 were made, the classical unbiased estimator of would be negative and the posterior distribution of would have its modal value at the origin. Uncertainty in the inferences about ({sigma}2, ) is then removed by considering the posterior distribution of {rho}. Some sampling theory considerations of the behaviour of certain quantities in the posterior distributions of ({sigma}2, , {rho}) are also discussed.


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